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Federal Reserve Bank of Chicago

Private Takings
Alessandro Marchesiani and Ed Nosal

December 2014
WP 2014-26

Private Takings
Alessandro Marchesiani
University of Bath

Ed Nosal
Federal Reserve Bank of Chicago

December 2, 2014

Abstract
This paper examines the implications associated with a recent Supreme Court
ruling, Kelo v. City of New London. Kelo can be interpreted as supporting eminent domain as a means of transferring property rights from one set
of private agents— landowners— to another private agent— a developer. Under
voluntary exchange, where the developer sequentially acquires property rights
from landowners via bargaining, a holdout problem arises. Eminent domain
gives all of the bargaining power to the developer and, as a result, eliminates
the holdout problem. This is the bene…t of Kelo. However, landowners lose
all their bargaining power and, as a result, their property investments become
more ine¢ cient. This is the cost of Kelo. A policy of eminent domain increases social welfare compared to voluntary sequential exchange only when
the holdout problem is severe, and this occurs only if the developer has very
little bargaining power. We propose an alternative government policy that
eliminates the holdout problem but does not a¤ect the bargaining power of the
various parties. This alternative policy strictly dominates a policy of eminent
domain, which implies that eminent domain is an ine¢ cient way to transfer
property rights between private agents.

1

Introduction

A recent Supreme Court decision, Kelo v. City of New London (2005), rea¢ rmed
that the public-use criterion from the takings clause of the Fifth Amendment of the
US constitution1 can be ful…lled even when a government takes property from one
private agent and gives it to another. Although the Court has long rejected a literal
We wish to thank Aleks Berentsen, Ricardo Cavalcanti, Guillaume Rocheteau and Perry Shapiro.
The views expressed here do not necessarily represent those of the Federal Reserve Bank of Chicago
or the Board of Governors of the Federal Reserve System.
1
“[N]or shall private property be taken for public use, without just compensation.”

1

interpretation of public use,2 the Kelo decision generated a fair amount of controversy
both among the judiciary and the public. Perhaps it is because the public purpose3
of the taking that underlies Kelo is less transparent than previous important Court
rulings.
In the landmark case of Berman v. Parker (1954), the owners of a non-blighted
department store had their property taken as part of a large scale redevelopment
plan to rid parts of Washington D.C. from blight and slums. The redevelopment plan,
provided by the District of Columbia Redevelopment Act, included the condemnation
of non-blighted buildings. The Court unanimously ruled that private property can be
taken for public purpose as long as owners receive just compensation. Furthermore,
it ruled that it is up to lawmakers— not courts— to decide what is in the public’s best
interest.4 In Berman v. Parker, the public purpose of the taking is easy to visualize:
It turns something that is ugly and dangerous into something that is beautiful and
safe.
In another important case, Hawaii Housing Authority v. Midki¤ (1984), the
Hawaiian legislature proposed to regulate an oligopoly in the housing market by
taking away the property rights from a few large landowners, with compensation,
and distributing them to many new owners. As in Berman v. Parker, the Court
deferred to the legislature as to whether the public purpose was being served, and
unanimously ruled in favor of the legislature’s actions. Given that governments have
made a practice of regulating industries that exhibit market power for many years,
it is plausible to envision that the taking served a public purpose.
Qualitatively speaking, the basic facts of Kelo are not so di¤erent from the above
cases. The city of New London formulated an economic development plan that would
bene…t the city and its residents by providing growth opportunities and increased tax
revenues. As in Berman v. Parker and Midki¤, the city’s plan required the taking
of private property that would ultimately be owned by other private parties. The
Court ruled in favor of the city of New London. However, unlike Berman v. Parker
and Midki¤, the Court rendered a split 5-4 decision. And there was a vigorous public
debate regarding the appropriateness of the decision. Much of the debate focused on
whether taking property for private economic development serves a public purpose.
Even though the Court deferred to the legislature regarding the public purpose in
Midki¤, it did not absolve itself from interfering when the public purpose was at
question: “A purely private taking could not withstand the scrutiny of the public
use requirement; it would serve no legitimate purpose of government and would thus
2

In Fallbrook Irrigation Dist. v. Bradley (1896) and Clark v. Nash (1905), the Court ruled in
favor of a taking that only bene…tted a small set of private landowners. A short summary of relevant
cases regarding the de…nition of public use, some of which we refer to, can be found in Rolnick and
Davies (2006).
3
In Mt. Vernon-Woodberry Cotton Duck Co., v. Alabama Interstate Power Co. (1916), the
Court only required that a taking serve a public purpose.
4
“[W]hen the legislature has spoken, the public interest has been declared in terms well-nigh
conclusive ... ,” (Berman at 32).

2

be void ... The court’s cases have repeatedly stated that ‘one person’s property may
not be taken for the bene…t of another private person without a justifying public
purpose, even though compensation be paid, ”(Midki¤ at 245 and 241, respectively).
Evidently, in the minds of a great number of people, the case that private economic
development serves a public purpose was not made in Kelo. In response to the Kelo
decision, 43 states changed their eminent domain laws that placed limitations and/or
restrictions on municipalities’use of eminent domain when the stated public purpose
was economic development.
From an economic perspective, some sort of market failure or friction must exist
if a government taking is to be part of the solution for a redevelopment project. For
example, market solutions to redevelop blighted areas may fail because of a free-rider
externality, see, e.g., Grossman and Hart (1980) and O’Flaherty (1994). In a blighted
area, property owners may be reluctant to sell their properties to developers at “low”
prices— even though these prices are appropriate for the properties in their current
state— because they anticipate the value of their properties will increase as the area
is redeveloped. Because of this, the market will deliver redevelopment projects that
are too small from a social perspective. A government taking, along with just compensation, can internalize this externality, and result in socially preferable outcomes.
The Berman v. Parker decision can be rationalized along these lines.
It would be di¢ cult, however, to justify the Kelo decision by appealing to a freerider argument. For starters, the proposed redevelopment area in New London was
not blighted or run-down. Given this, how would Suzette Kelo’s property value be
a¤ected if the redevelopment project proceeded without the sale of her property?
Being close to a new shopping area would be bene…cial, since it would be convenient
for running errands, dining etc. But the new shopping area and a major research
facility would bring about increased tra¢ c and congestion, which would be costly.
Since it is not at all obvious which e¤ect would dominate, it would not be unreasonable to assume that property values would be una¤ected by the redevelopment.
That is, there are no external bene…ts associated with the taking. One can interpret
the dissenting opinion of Justice Day O’Connor being consistent with such a view,
“Any property may now be taken for the bene…t of another private party ... the
bene…ciaries are likely to be those citizens with disproportionate in‡uence and power
in the political process, including large corporations and development …rms”and the
decision eliminates “any distinction between private and public use of property —
and thereby e¤ectively delete[s] the words ‘for public use’from the Takings Clause of
the Fifth Amendment,”(Kelo at 12-13 and 2, respectively, O’Connor, J., dissenting).
If a free-rider externality argument cannot be used to support the Kelo decision, then
how can the majority decision of the supreme court be justi…ed from an economic
perspective?
One possible justi…cation for the Kelo decision, which we explore in this article,
is that the existence of bargaining frictions prevent the level of redevelopment from
being e¢ cient. Bargaining endows both the developer and seller with pricing powers
3

that can lead to an ine¢ cient level of redevelopment. Ine¢ ciencies associated with
redevelopment can— but need not— be exacerbated because of a holdout problem
that arises when a developer negotiates with many property owners. In particular,
the holdout problem— where each owner attempts to extract additional surplus from
the developer— can arise due to the sequential nature of bargaining between the developer and landowners. Ideas related to bargaining have been explored in Munch
(1976) and Eckart (1985). These authors rely on informational asymmetries to generate an ine¢ ciency in land assembly. Absent these informational asymmetries, there
would be no role for government takings. We specify a simple and intuitive bargaining environment that is free of informational asymmetries. Because bargaining
frictions prevent private agents from implementing e¢ cient allocations, we examine if
government policy can improve matters. One obvious government policy to consider
is eminent domain.
Once the possibility of a government taking that transfers property rights from
one private agent to another is introduced, then, almost by de…nition, property rights
become less secure. As pointed out by Rolnik and Davies (2006) and Garrett and
Rothstein (2007), when property rights are not secure, ine¢ ciencies in land use will
arise. We believe this to be a rather important aspect associated with a government
taking, so we appeal to a model environment— …rst proposed by Blume, Rubinfeld
and Shapiro (1984)— that emphasizes it.
In the model, a policy of ED e¤ectively gives all of the bargaining power to the
developer. As a result, the holdout problem disappears since landowners have no
bargaining power. This is the bene…t of a policy of ED. However, landowners will
invest more resources in their properties when their bargaining power declines. Since
landowners are overinvesting under voluntary exchange, eminent domain exacerbates
the overinvestment problem. This is the cost of a policy of eminent domain. A
policy of eminent domain is socially bene…cial only if the bene…t associated with
the elimination of the holdout problem exceeds the cost associated with increasing
the overinvestment problem, and this occurs only when the developer has very little
bargaining power.
We propose an alternative government policy that, like eminent domain, removes
the holdout problem by eliminating the sequential nature of bargaining. However,
this policy does not a¤ect the bargaining power of the various parties. The policy can
be interpreted as “locking”the developer and all of the landowners whose properties
the developer wants “in a room” and requiring them to collectively determine a set
of prices for the transference of the property rights. Since this collective bargaining
policy eliminates the holdout problem but does not a¤ect the various parties’ bargaining powers, it strictly dominates the eminent domain policy. Hence, a private
taking— i.e., using eminent domain to transfer property rights of one set of private
agents to another— is never socially e¢ cient.
The remainder of the article is as follows. The next section examines a simple
redevelopment and takings environment with one developer and one tract of land
4

owned by a single landowner. Since there is only one landowner and one tract of
land, a holdout problem does not arise. In a very simple way, this section establishes
a connection between the holdout problem and the policy of eminent domain: If
there is no holdout problem, then a private taking— i.e., using eminent domain—
can only lower social welfare. In Section 3, the environment is extended to many
owners. Because of the sequential nature of voluntary exchange, a holdout problem
arises under voluntary exchange because the developer bargains sequentially with
landowners. We examine the e¤ect that two government policies— private takings
and collective bargaining— have on social welfare. Section 4, provides examples and
the …nal section summarizes and concludes.

2

One tract of land

A landowner, or simply the owner, is endowed with capital K` and property rights to
a tract of land. He invests x on his property and K` x in a safe asset. The safe asset
provides a gross rate of return R > 1. The property investment provides a payo¤ of
f (x), where f (0) = 0, 0 < f 0 (0) < 1, and f 00 < 0.5
A developer is endowed with capital Kd . He can redevelop the owner’s property
and can invest in the safe asset. If the property is redeveloped, then the investment x
and its potential payo¤, f (x), are destroyed. Redevelopment entails an expenditure,
y. Redevelopment generates a payo¤ of F (1; y), where
F (1; y) =

F (1; y) if y y
:
0
if y < y

The ‘1’ in F denotes that one tract of land is being redeveloped. If there is redevelopment, then the payo¤ structure implies that the developer spends exactly y on
redevelopment.
The developer must acquire property rights to redevelop. These rights can be
voluntarily transferred via bargaining from the owner to the developer for a price p.
The price p is determined by a simple two-stage proposal game. In the …rst stage, the
developer makes an o¤er to the owner, which he either accepts or rejects. If accepted,
the owner transfers the property rights and gets p. If rejected, then agents move to
the second stage, where, with probability , the developer makes a take-it-or-leave-it
o¤er to the owner and, with probability 1
, the owner makes the o¤er. If the second
stage o¤er is accepted, then the property rights are transferred to the developer at
the agreed upon price; if it is rejected, then the game ends, and redevelopment does
not take place. One can interpret (1
) as the developer’s (owner’s) bargaining
power.
5

We depart from the standard INADA condition that f 0 (0) = 1 because in the numerical
examples that we provide below, f 0 (0) is …nite. We assume, however, that f 0 (0) can be arbitrarily
large.

5

There exists a government that can condemn and expropriate, or take, the property via its power of eminent domain, ED. The law requires the government provide
“just compensation”to the owner in the event that his land is taken. In this article,
just compensation will be de…ned as f (x), i.e., the value of the property in the event
that it is not taken. The government must balance its budget. We assume that if
property is taken, the government sells the property rights to the developer for f (x).
The timing of events is as follows. At date 0, the owner is born; he invests x in
his property and K` x in the safe asset. At date 1, the developer is born; he decides
whether or not to redevelop the owner’s property. If he chooses to redevelop, then he
either bargains with the owner, or the government takes the owner’s property rights
and sells them to the developer. If there is redevelopment, then the developer spends
y on redevelopment and invests (Kd y) in the safe asset; otherwise he invests Kd
in the safe asset. At date 2 all investments pay o¤, payments are exchanged, and the
owner and developer consume.
The objectives of the owner and the developer are to maximize their expected
payo¤s. The timing of the births of the owner and developer prevent them from
interacting before the owner makes his investment decision. This timing assumption
is designed to re‡ect the real world fact that developers enter the scene long after
initial investments are undertaken.

2.1

Social optimum

Social welfare is de…ned as the sum of all agents’ payo¤s. Because redevelopment
destroys investment x, if it is optimal to redevelop, then x = 0. The payo¤ to society
in the event of redevelopment is F (1; y) + (Kd y) R + K` R. If property is not
redeveloped, then the investment x that maximizes social welfare is given by
arg max ff (x) + Kd R + ((K`
x

x) R)g ;

or x = xn , where f 0 (xn ) = R— the ‘n’in xn stands for “no redevelopment.”
It is socially optimal to redevelop property if
F (1; y) + (Kd

y) R + K` R > f (xn ) + Kd R + (K`

xn ) R

or if
F (1; y)

yR > f (xn )

xn R:

(1)

If (1) does not hold, then it is not optimal to redevelop.

2.2

Redevelopment under Voluntary Exchange

Let S represent the total surplus the owner and developer share if there is redevelopment, where
S (x) = F (1; y) f (x) yR:
(2)
6

Note that S 0 (x) < 0, and that (1) can be expressed as S (xn ) > xn R. De…ne the
critical value xc by S (xc ) 0.
If there is redevelopment, then each agent’s share of the surplus is determined by
p. The developer’s payo¤ is F (1; y) yR p, and the owner’s is p f (x).6
Suppose that redevelopment occurs. Then, in the second stage of the two-stage
proposal game, if the developer makes the take-it-or-leave-it o¤er, he will o¤er f (x)
for the owner’s land, which the owner accepts. If the owner makes the o¤er, he will
o¤er yR and his land in exchange for the total value of the redevelopment, F (1; y),
which the developer accepts. Let p1 be the …rst-stage o¤er in the two-stage proposal
game. The developer makes a …rst-stage o¤er so that the owner is indi¤erent between
accepting and rejecting it. Hence, the equilibrium …rst-stage o¤er— which the owner
accepts— is
p1 = f (x) + (1
) (F (1; y) yR) ;
(3)
since, in the second stage, the developer makes the o¤er with probability
and
the owner makes the o¤er with complementary probability 1
. The equilibrium
…rst-stage o¤er, (3), can be rewritten as
p1 = f (x) + (1

(4)

) S (x) :

If there is redevelopment, then, in equilibrium, the developer receives a fraction of
the total surplus S (x), and the owner receives a fraction 1
of the total surplus in
addition to his reservation payo¤ f (x). (A reservation payo¤ is what an agent receives
in the event of “disagreement,” i.e., when redevelopment does not take place. The
developer’s reservation payo¤ is zero.) The developer will redevelop only if S (x) > 0
or, equivalently, if x < xc .
We now consider the owner’s investment decision, x. First, suppose that the owner
correctly believes S (x) > 0 for his choice of x. Then, in equilibrium, there will be
redevelopment, and the investment decision is given by
arg max p1 + (K`
x

x) R = arg max f (x) + (1
x

) S (x) + (K`

x) R:

(5)

The solution, xr , is characterized by
f 0 (xr ) = R,

(6)

where “r”stands for “redevelopment.”Equation (6) implies that xr > 0.7
6

At the time of bargaining, the investment x is sunk, but y is not. This is why the term “yR”
shows up in the developer’s net surplus function and there is no comparable term in the owner’s net
surplus function.
7
Since we assume that f 0 (0) is arbitrarily large and …nite, there exists su¢ ciently small ’s for
which condition (6) does not hold, i.e., < where
is de…ned by f 0 (0) = R. In what follows,
we assume that the developer’s bargaining power is not too small, i.e., > .

7

Now suppose that the owner correctly believes that S (x) < 0 for his choice of x.
Then, in equilibrium, the developer does not redevelop and the investment decision
is given by
arg max f (x) + (K` x) R:
(7)
x

The solution of (7) is characterized by
f 0 (x) = R;

(8)

which implies that x = xn , the e¢ cient level of investment when it is not socially
optimal to redevelop. Comparing (6) and (8), we see that xn > xr . Since S 0 (x) < 0,
we have
S (xr ) > S (xn ) :
The surplus function provides us with a lot of information regarding agents’decisions. If S (xn ) > 0, i.e., xn < xc , then the developer always redevelops. Hence, if
S (xn ) > 0, then the owner’s problem is given by (5) and he invests xr . If S (xr ) < 0,
i.e., xr > xc , then the developer never redevelops, and the owner’s problem is given
by (7), i.e., he invests xn . Finally, if S (xr ) > 0 and S (xn ) < 0, then the owner’s
investment, x, determines whether or not there will be redevelopment. If the owner
invests xr , then there will be redevelopment; if he invests xn , there will not. If
f (xn )

xn R > f (xr )

xr R + (1

) S (xr ) ;

(9)

then the owner invests xn , and the developer will not redevelop; otherwise, the owner
invests xr , and there will be redevelopment.
In many cases the allocation generated by voluntary exchange is socially ine¢ cient.
For example, if it is socially e¢ cient to redevelop and redevelopment occurs under
voluntary exchange, then the allocation of resources is ine¢ cient since the owner
invests xr > 0. Or, if condition (9) does not hold, then there will be redevelopment
even when it is not socially e¢ cient. Proposition 1 provides conditions under which
voluntary exchange results in a socially e¢ cient allocation of resources.
Proposition 1 If S (xn ) < xn R and condition (9) holds, then voluntary exchange
implements a socially e¢ cient allocation characterized by no redevelopment and x =
xn ; otherwise voluntary exchange is always socially ine¢ cient.
Proof. See Appendix 1.
When there is redevelopment, the owner ends up investing too much because
the sale price, p, depends on the level of his investment. This investment distortion
depends on the owner’s share of the surplus, 1
; the larger the share, the smaller
the distortion. The developer’s (property) acquisition decision, however, is always
e¢ cient given the level of investment undertaken by the owner. This is because the
developer acquires the property only if the surplus associated with redevelopment is
positive.
8

Since voluntary exchange can be associated with ine¢ ciencies, perhaps an alternative method of transferring property rights— e.g., ED with just compensation— may
improve matters. We now examine this issue.

2.3

Government Policy

Voluntary exchange generates socially ine¢ cient outcomes. Perhaps a government
policy of ED can improve matters.8 Under ED, the owner receives f (x) if his property
rights are taken. This means that the owner’s share of the surplus associated with
redevelopment is zero. The owner’s investment decision, x, is simply arg maxx f (x) +
(K` x) R, or x = xn .
Many commentators claim that ED can be used to promote redevelopment. We
…nd that the only time ED can improve matters is when it prevents redevelopment
from occurring.
Proposition 2 ED can improve social welfare only by preventing redevelopment when
redevelopment is ine¢ cient; otherwise, ED (weakly) decreases social welfare, compared to voluntary exchange.
Proof. See Appendix 1.
If redevelopment is optimal, then using ED to transfer property rights is always a
bad idea since more investment is destroyed under ED than under voluntary exchange.
The investment distortion is exacerbated under ED because the owner does not care
about the total surplus. Instead, his objective is to adjust his ‘just compensation’
value, f (x), so as to maximize his payo¤.

2.4

Discussion

The analysis so far seems to indicate that the recent Supreme Court decision on Kelo
v. New London is wrong-headed: ED, in conjunction with just compensation, can
never be associated with an increase in redevelopment. If anything, it’s associated
with a decrease in redevelopment activity. The reason is straightforward. ED implies
that owners will invest more; this reduces total surplus and makes redevelopment less
attractive.
Some of our results are reminiscent of those from the property rights and nuisance
literature, especially Pitchford and Snyder (2003). Transferring property rights by
voluntary exchange is equivalent to a …rst-party injunctive rights regime. A …rstparty injunctive rights regime means that after making his investment decision, the
owner gets to choose whether or not to sell his property; hence, he must receive at
least f (x) if he is to sell. And transferring property rights by ED is equivalent to
8

Since there is only one owner, the alternative government policy that we discussed in the Introduction is equivalent to voluntary exchange.

9

a …rst-party damage rights regime. In this regime, the owner is compensated for
exactly what he loses, f (x), if he chooses to sell to the developer. Pitchford and
Snyder (2003) demonstrate that both regimes are characterized by over-investment
and there is less over-investment in a …rst-party injunctive rights regime, which are
precisely our results above. In addition, both parties will make the same ex post
decision,9 and, given x, this decision is ex post optimal. We shall see, however, that
the nice equivalence between our results and those of the property rights and nuisance
literature will break down when the developer can acquire more than one property
and bargains with more than one owner.
There are (at least) two ways to restore social e¢ ciency under government takings.10 One way, as suggested by Hermalin (1995), is to transfer the entire surplus
S to the owner. This scheme is equivalent to giving the owner all of the bargaining
power.11 When the owner has all of the bargaining power, then the owner’s decision
problem is given by (5) with = 0 and the solution is x = 0. A second way to
restore e¢ ciency, as suggested by Blume, Rubinfeld and Shapiro (1984) and Blume
and Rubinfeld (1984), is to give a …xed payment c— perhaps equal to zero— to the
owner. For this scheme, assuming there is redevelopment, the owner’s investment
problem (5) can be rewritten as
max c + (K`
x

x) R:

The solution to this problem is x = 0.
In practice, it is unlikely that either one of these schemes could be implemented.
When a government uses ED it probably wants to provide incentives for redevelopment. Giving developers zero surplus might have the opposite e¤ect. An arbitrary
…xed payment c would probably not pass a “just compensation” criterion (most of
the time).

3

Many tracts of land

We now generalize the environment so that the developer can acquire multiple tracts
of land for redevelopment and his spending on redevelopment is not exogenous. A
holdout problem emerges under voluntary exchange, where the developer sequentially
bargains with many owners for their property rights.
The model in Section 2 is modi…ed in the following way. There are N > 1
contiguous tracts of land located around a circle. In Section 2, it’s obvious which
9

For this article, the ex post decision is to redevelop or not; in Pitchford and Snyder (2003) the
ex post decision is regarding ex post investments.
10
Given that the landowner and developer cannot contract prior to the investment decision, x,
it is not obvious how one can restore e¢ ciency under voluntary exchange, while at the same time
maintaining the notion that exchange is voluntary.
11
It is also equivalent to a second-party injunctive rights regime.

10

tract of land is to be redeveloped since there is only one. When N > 1, we assume
that any redevelopment must include a speci…c— or required— tract of land, and if
redevelopment uses more than one tract of land, then all the redeveloped properties
must be adjacent to one another. In particular, the second property must be clockwise
adjacent to the required tract, the third must be clockwise adjacent to the second,
and so on. The idea here is that once the required tract is determined, the sequence
in which particular tracts can be used for redevelopment is also determined. This
implies that the owners of these tracts have bargaining power vis á vis the developer.
The total value associated with redevelopment is given by F (A; y; P ), where A
represents the tracts of land acquired for redevelopment (which includes the required
tract), y represents total spending on redevelopment, and P represents total factor
productivity. We assume that F (A; y; P ) is strictly increasing in its arguments—
FA ; Fy > 0 and for P2 > P1 , that F (A; y; P2 ) > F (A; y; P1 )— and that Fi (A; y; P2 ) >
Fi (A; y; P1 ), i = A; y. Throughout the analysis P is …xed; so when it causes no
confusion, the total factor productivity argument, P , in F ( ) will be suppressed.
We also assume that the redevelopment value function F (A; y) is strictly concave,
2
FAA FAy
=Fyy G (A; y) < 0, with FA (0; y) = Fy (A; 0) ! 1 for y; A > 0, and that
Assumption 1: GA (A; y)

Gy (A; y) FAy (A; y) =Fyy (A; y) > 0.

Assumption 1 imposes restrictions on the third derivative of F . A standard CobbDouglas function P A y with + < 1, satis…es all of the restrictions that we have
imposed on F . In addition to the restrictions that we have imposed on f (x), we add
Assumption 2: f 000 (x) f 0 (x)

2f 00 (x)2

0.

Assumption 2 also places restrictions on the third derivative of f . Functions such as
b ln (1 + x) or a b= (b=a + x) satisfy the restrictions that we have imposed on f (x),
where the former function satis…es Assumption 2 with an equality and the latter
function with a strict inequality.
The timing of events is as follows: At date 0, N owners are born, each owning
property rights to a tract of land. Each owner has capital K` , invests x in his tract
of land and (K` x) in the safe asset. Owners do not know where the required
(for redevelopment) tract of land is located; at the time they make their investment
decision, each tract is equally likely to be required for redevelopment. At date 1, the
developer is born and the required tract is revealed to all. The developer decides
the number of properties, A, he wishes to acquire and redevelop, where 0 < A
N . The developer then identi…es the set of owners associated with the A tracts
of land, and either bargains with them— sequentially under voluntary exchange or
simultaneously if the government imposes the collective bargaining policy— or has the
government take away their property rights and sell them to him if the government
imposes the ED policy. The details of the bargaining procedures— both sequential and
simultaneous— are provided below. The developer pays either the sum of all bargained
prices or Af (x) (at date 2), depending upon whether he bargains or purchases via
11

ED, respectively, to acquire the property rights for the A tracts of land. The developer
spends y on redevelopment and invests the rest of his capital, Kd y, in the safe asset.
At date 2, all investments pay o¤, payments are exchanged, and the owners and the
developer consume.

3.1

Social Optimum

We …rst characterize the social optimum. Let W (A; x; y) represent social welfare,
which is the sum of the payo¤s of all agents in the economy. The socially e¢ cient
levels of property acquisition, A, investment, x and redevelopment spending, y, are
given by the solution to
max W (A; x; y) = max(N
x;y;A

x;y;A

A)f (x) + F (A; y) + N (K`

x) R + (Kd

y) R: (10)

When the investment decision x is made, it is not known where the required (for
redevelopment) tract of land is located. Therefore, each tract of land— and there
are N of them— receives the same level of investment, x, and the remainder of the
owners’ capital is invested in the safe asset. Since A properties will be acquired
and redeveloped, the total payo¤ to the owners’ investments is (N A)f (x). The
developer spends y on redevelopment so the payo¤ to redevelopment is F (A; y). The
developer places Kd y in the safe asset. The necessary conditions to problem (10)
are,
N A 0
f (x) = R if A `
N
;
(11)
x=0
if A > `
Fy (A; y) = R;

(12)

FA (A; y) = f (x) ;

(13)

and
where ` solves

N

`

f 0 (0) = R:

N
Conditions (11) and (12) simply say that the expected returns to investment x
and spending y equal the opportunity cost of capital, R.12 Condition (13) says that
properties will continue to be acquired until the value of the last property equals
the (social) cost of redevelopment, which is the value of the destroyed investment,
f (x). The conditions that identify an interior maximum to problem (10) are given
by (11)-(13) and,
(14)
(15)

Fyy < 0
2
Fyy FAA FAy
>0
(N

A) f 00 (x) Fyy FAA

12

2
FAy

Fyy f 0 (x)2 < 0:

(16)

The second line in (11) says that the expected return is less than R at x = 0 when A > ` ;
hence, no investment is undertaken.

12

Conditions (14)-(16) are all satis…ed since F (A; y) and f (x) are strictly concave. Let
(A ; x ; y ) represent the solution to (11)-(13).
It will be useful to diagrammatically characterize the social optimum in (x; A)
space. The slope of the locus of points described by (11) for x > 0 is negative and
given by
f 00 (x)
dA
=
N R < 0;
(17)
dx
f 0 (x)2
and the derivative of (17) with respect to x is
d2 A
f 000 (x) f 0 (x) 2f 00 (x)2
NR
=
dx2
f 0 (x)3

0;

(18)

owing to Assumption 2. In our diagrams we will assume that (18) holds with strict
equality, which means that (11) is linear in (A; x) space for x > 0. Equation (11)
is depicted in Figure 1 as ` xmax , where ‘`’ stands for landowner. Note that the
allocation (xmax ; 0) lies on locus ` xmax , where xmax solves f 0 (xmax ) = R, i.e., this is
the condition for investment, (11), when there is no redevelopment, i.e., when A = 0.
The slope of the locus of points described by (13), conditional on e¢ cient redevelopment spending y, (12), is also negative in (x; A) space and is given by
f 0 (x)
f 0 (x)
dA
=
=
< 0;
2
F
dx
G (A; y)
FAA FAy
yy

(19)

since, from (12), dy = FAy =Fyy dA and F (A; y) is strictly concave. The derivative
of (19) with respect to x is
h
i
FAy
00
0 2
G
(A;
y)
G
(A;
y)
f
G
(A;
y)
(f
)
=G
(A;
y)
2
A
y
Fyy
dA
=
>0
2
2
dx
G (A; y)
thanks to Assumption 1. This means that locus (13), conditional on (12), is strictly
convex. Figure 1 depicts equations (12) and (13) as d D , where “d ” stands for
developer.

In Figure 1, the ` xmax and d D loci intersect twice.13 Social welfare is maximized
at allocation a = (x ; A ), where the slope of the ` xmax curve is steeper than that
13

For these loci to intersect at all requires that total factor productivity, P , be not “too big.” If
P is too big, and the loci do not intersect, then the socially optimal outcome is that all N tracts of
land are redeveloped and x = 0. That it is socially optimal to develop all private property, however,
does not appear to describe the world in which we live. Hence, we assume that P is not too big,
which implies that the two loci intersect twice.

13

Figure 1: Social Optimum
of the d D curve. To understand this, note that condition (16) can be rewritten as
f 0 (x)
FAA

2
FAy

Fyy

>

f 00 (x)
(N
f 0 (x)

A) :

This condition says that the local interior maximum occurs where the ` xmax curve
is steeper than that of the d D curve, i.e., compare (17) and (19).
Moving away from allocation a = (x ; A ) along either curve ` xmax or d D
unambiguously lowers social welfare. Assuming that condition (12) holds, the slope
of a social welfare indi¤erence curve is given by
(N
dA
=
dx

A) f 0 (x) N R
:
f (x) FA

For allocations on the ` xmax curve, the slope of the social welfare indi¤erence curve
is zero and for allocations on the d D curve, it is in…nite. A typical social welfare
indi¤erence curve that intersects allocation a
~ (where A~ < A and x~ > x ) is given
~ in Figure 1. Note that for allocations that are south-east
by the ellipse denoted W
of allocation a = (x ; A ) and that lie in between (but not on) the ` xmax and d D
curves— such as allocation a
~— the slopes of the social welfare indi¤erence curves are
all strictly positive and …nite. This implies that if two allocations lie in the cone
given by xmax a D and a line that connects the two allocations has a strictly negative
slope— such as allocations a and a
~ in Figure 1— then the allocation that has higher
14

redevelopment and lower investment will generate a higher level of social welfare, i.e.,
the social welfare associated with allocation a exceeds that of a
~.14

3.2

Redevelopment under Voluntary Exchange

If the developer wants to acquire property rights from A owners he can do so by
sequentially bargaining with them. In particular, the developer and A owners play
the following A-stage sequential bargaining game. First, each of the A owners are
placed in a bargaining queue. Let i 2 f1; : : : ; Ag represent the place in the queue
held by a particular owner, owner i. An owner’s place in the queue is determined by
the sequence in which particular tracts can be used for redevelopment as described
above, i.e., the …rst person in the queue owns the required tract, the second person
in the queue has his property clockwise adjacent to the required tract, and so on.
Since the owner knows the location of his own property as well as the location of
the required tract, he knows his position in the bargaining queue. The developer
sequentially bargains with each of the A owners: The developer bargains …rst with
owner i = 1, second with owner i = 2, and so on. The A-stage bargaining game
between the developer and A owners can be viewed as a sequence of the two-stage
proposal game described at the beginning of Section 2. That is, in stage i of the
A-stage game, the developer and owner i play the two-stage proposal game. The
developer can proceed from stage i to stage i + 1 in the A-stage bargaining game
only if he has reached an agreement with the …rst i owners. If the developer and
owner i do not reach an agreement, i.e., the owner rejects the developer’s initial o¤er
and the second stage o¤er is also rejected, then the A-stage bargaining game ends,
all the agreements with the previous i 1 owners are extinguished or invalidated,
and no redevelopment takes place. This means that once the developer chooses the
number of tracts of land to redevelop, A, and owners to bargain with, the developer
either acquires the property rights for all A tracts and redevelops them, or there is
no redevelopment.15
At date 0, each of the N owners invests x on his tract of land and at date 1,
the developer decides on the number of properties to acquire, A, and bargains with
14

Note that in Figure 1 the developer’s locus, d D , extends beyond N . Feasibility requires that
^ in Figure 1. This implies
A N . Therefore, the feasible developer’s locus is given by locus D dN
that the feasible developer’s locus intersects the owner’s locus at (0; N ), in addition to the two
intersections already described. Our numerical exercises indicate that it is possible to have social
welfare at allocation (0; N ) exceed that of allocation a . This happens when total factor productivity,
P , is “su¢ ciently large.” We shall assume that P is not too big so that social welfare attains its
maximum value at allocation a . The numerical examples that we generate are all consistent with
social welfare being maximized at allocation a .
15
One can imagine a di¤erent bargaining game, where if agreement is not reached for a particular
owner, then the size of the redevelopment is reduced by one tract. So, if the developer initially
chooses to redevelop A tracts of land and fails to reach an agreement with a < A owners, then A a
tracts of land will be redeveloped. We take the all-or-nothing approach because we want the results
to be directly comparable to those in section 3.3.2.

15

A owners. Let pi represent the equilibrium price that the developer pays to the ith
owner in the bargaining queue. The equilibrium price, pi , which is determined by the
A-stage sequential bargaining game, is given by
pi = f (x) + (1

i 1

)

[F (A; y)

yR

Af (x)]; i = 1; : : : ; A:

(20)

See Appendix 2 for the derivation of pi . The equilibrium price, pi , provides owner i
with his reservation value, f (x), plus a share of the redevelopment surplus, F (A; y)
yR Af (x). De…ne S (A; x; y) F (A; y) yR Af (x). Note that the share of each
owner’s surplus depends on his place in the bargaining queue. In particular, pi > pi+1
for all i = 1; : : : ; A 1, so there is an “early-mover” advantage for the owners. The
average price per tract of land that the developer pays is
A
X
pi
i=1

A

p = f (x) +

A

1
A

S (A; x; y) :

(21)

When an owner makes his investment decision, x, he does not know if his land
will be acquired by the developer and, if it is, what place in the bargaining queue he
will occupy. Given these informational restrictions, the typical owner’s investment
decision is given by
arg max
x

N

A
N

f (x) +

A
p + (K`
N

x) R:

(22)

The function in (22) has the following interpretation: With probability (N A) =N ,
the owner’s property rights will not be acquired by the developer, in which case
his payo¤ is f (x), and, with complementary probability, his property rights will be
acquired for an expected (or average) price of p, given by (21). The solution to the
owner’s problem (22) is given implicitly by
8
< N (1 A )A
f 0 (x) = R; if A `V
N
(23)
:
x=0
if A > `V
where the “V ”in `V stands for “voluntary exchange,”and `V solves
!
`V
N
1
`V
f 0 (0) = R:
N
The slope of the locus of points described by (23) for x > 0 is
dA
f 00 (x)
=
1
dx
f 0 (x)2

A

(1 + A ln ( ))

16

1

N R < 0;

(24)

Figure 2: Voluntary Exchange
A
since 1
(1 + A ln ( )) > 0.16 The solution to the owner’s decision problem (23)
is illustrated in Figure 2 by the line `V xmax . For comparison, the socially e¢ cient
owner’s decision line, ` xmax , is also illustrated in Figure 2. Notice that since 0 <
1 + A ln ( ) < 1, the slope of the owner’s decision curve under voluntary exchange,
(24), is greater in absolute value than that of the owner’s socially e¢ cient decision
curve, (17).
The developer’s acquisition and spending choices, A and y, respectively, are given
by the solution to
max F (A; y) pA + (Kd y) R;
(25)
A;y

where the price per tract of land, p, is given by (21). Substituting (21) into the
developer’s problem and rearranging, we get
max
A;y

A

S (A; x; y) + Kd R:

(26)

The solution to the developer’s problem (26) is given by
Fy (A; y) = R;

(27)

and
16

In Appendix 3, we demonstrate that 1 + A ln( ) > 0. We also show that the curve described
^ where A^ solves 1 + A ln( ) = 0, and strictly
by (23) is strictly concave for all x > 0 and A < 2A,
^
convex for all x > 0 and A > 2A.

17

FA (A; y) = f (x)

ln ( ) S (A; x; y) :

(28)

Although the developer’s spending decision, y, is e¢ cient for the level of acquisition,
A, that he undertakes, (27), it follows from (28) that his property acquisition decision
is not. As we shall see, the ine¢ cient property acquisition decision is due to the
holdout problem that arises from the sequential nature of bargaining between the
developer and owners. Because of the holdout problem, the developer’s property
acquisition decision is distorted in the direction of purchasing too few properties
since FA (A; y) > f (x).
The slope of the locus of points described by (28) is given by17
dA
1 + A ln ( )
< 0;
= f 0 (x)
dx
G (A; y) ln ( )2 S (A; y; x)

(29)

since 1 + A ln ( ) > 0 for all x > 0 and G(A; y) < 0.18 The solution to the developer’s
decision problem, (27) and (28), is illustrated in Figure 2 by the curve dV DV . Diagrammatically speaking, since FA > f (x), curve dV DV lies below the e¢ cient curve
d D ; and, the smaller is ;the bigger is the downward shift of dV DV from d D . Figure 2 illustrates that when the developer bargains sequentially with owners, there is
unambiguously too much investment and too little redevelopment compared to what
is socially e¢ cient. Notice that in Figure 2, the dV DV curve lies everywhere below
^ In Appendix 3, we show that dV DV , which is given by the solution to (28), is
A:
^ where A^ solves 1 + A^ ln( ) = 0.
bounded above by A,
We can summarize the above discussion in the following proposition,
Proposition 3 Voluntary exchange results in an allocation characterized by too much
investment and too little redevelopment compared to what is socially optimal.
Proof. Compare allocation aV with allocation aED in Figure 2.

3.3

Government Policy

Voluntary exchange generates socially ine¢ cient outcomes. Perhaps government policies can improve matters. We consider two government polices. One policy is eminent
domain, ED. The other policy, which we call collective bargaining, CB, has the government forcing the developer and the all A property owners to bargain simultaneously
with one another.
17

Of course, we are assuming that Fy (A; y) = R. Henceforth, to avoid repetition, we always
assume that Fy (A; y) = R.
18
Since the developer’s problem (26) is highly non-linear, the locus of points described by (28) is
not necessarily a convex function in (x; A) space. In Appendix 3, we document that the solutions
to the developer’s and owners’problems are well behaved.

18

Figure 3: Eminent Domain
3.3.1

Eminent Domain

Under ED, the owner receives “just compensation” if his property is taken. This
implies that each owner gets f (x) whether or not his property rights are taken, i.e.,
pi = f (x) for all i = 1; : : : ; A. Alternatively, ED can be interpreted as giving all of
the bargaining power to the developer, i.e., if = 1, then (20) implies that pi = f (x)
for all i = 1; : : : ; A.
When p = f (x) in (22), the owner’s investment decision problem is
A
f (x) + (K` x) R:
(30)
x
N
N
The solution is given implicitly by f 0 (x) = R or x = xmax . The locus of points
that describe the owner’s optimal investment decision under ED is described by the
perpendicular line `ED xmax in Figure 3.
arg max

N

A

f (x) +

The developer pays f (x) for each property he acquires. His decision problem is
given by the solution to (25), which under ED can be simpli…ed to
(31)

max S (A; x; y) + Kd R:
A;y

Hence, the developer maximizes the surplus S associated with redevelopment. Since
the social welfare function (10) can be rewritten as
W (A; x; y) = S (A; x; y) + N f (x) + N (K`
19

x) R + Kd R;

(32)

the developer’s objective under ED, (31), for a given x, coincides with maximizing
social welfare. As a result, the developer’s spending, y, and acquisition, A, decisions
are e¢ cient, and are given by (12) and (13), respectively. The developer’s decision
regarding the level of redevelopment is given by the socially optimal locus d D in
Figure 3. The allocation associated with an ED regime, aED , is illustrated by the
intersection of the d D and `ED xmax loci in Figure 3, and the level of social welfare
associated with this allocation is given by the curve WED .
A policy of ED eliminates the holdout problem because it gives all of the bargaining power to the developer. And, since the developer has all of the bargaining
power— he receives all of the surplus— he has an incentive to maximize total surplus
or social welfare. Although an ED policy eliminates the holdout problem, it creates
another: It exacerbates the owners’overinvestment in their properties. As Figure 3 illustrates, owners undertake the maximum investment in their properties, xmax , which
exceeds the level of investment undertaken by voluntary exchange, xV , described by
allocation aV = (xV ; AV ).19
Is a policy of ED socially desirable? In Figure 3, social welfare associated with ED
is given by WED . Suppose that under voluntary exchange, the developer’s decision
locus (which is not illustrated) intersects the owner’s decision locus, `V xmax , at aV
in Figure 3. In this situation, social welfare associated with allocation aV exceeds
that associated with ED, WED . Hence, from a social perspective, ED would be an
inappropriate policy. Although ED eliminates the holdout problem— which is bene…cial from a social welfare perspective— the increase in overinvestment that results
ultimately reduces social welfare compared to voluntary exchange. Suppose, instead,
that the holdout problem is more severe than that depicted in Figure 3. (The holdout
problem can be made more severe by lowering the developer’s bargaining power .)
Then, it is possible that the developer’s decision locus intersects the owner’s decision
locus, `V xmax , below the intersection of WED with the owner’s decision locus, say at
allocation a0V . In this situation, a policy of ED increases social welfare. The following
de…nition is helpful.
De…nition 4 The holdout problem is said to be severe if the developer’s decision
locus under voluntary exchange intersects the `V xmax locus below the intersection of
WED and `V xmax curves in Figure 3.
We can summarize the above discussion by the following proposition,
Proposition 5 A necessary condition for welfare associated with ED to exceed that
of voluntary exchange is that the developer’s holdout problem is “severe.” As well,
investment under ED always exceeds investment under voluntary exchange.
19

Allocation aV is determined by the intersection of the owner’s locus `V xmax and the developer’s
locus dV DV (which is not illustrated in Figure 3). Depending on the developer’s bargaining strength
2 (0; 1), voluntary exchange allocation, aV , will lie somewhere on locus `V xmax between points a1
and (xmax ; 0) in Figure 3.

20

Proof. Given De…nition 4, compare allocation aED with allocation a0V in Figure 3.
Investment under ED, aED , always exceeds investment under voluntary exchange,
aV . Investment under ED takes on its maximum possible value, xmax ; for all < 1,
investment under voluntary exchange is strictly less than this maximum value, see
Figure 3.
We are, however, unable to make any general claims regarding the level of development. To see why, notice that decreasing shifts the developer’s decision locus
down from d D ; holding the owner’s locus constant, a reduction in increases investment x, see Figure 3. However, decreasing , decreases the slope of the owner’s
decision locus `V xmax , which e¤ectively causes it to pivot at xmax toward the origin;
holding the developer’s decision locus constant, a reduction in decreases investment
x, see Figure 3. The decisions of owners and the developer work in opposite directions
regarding changes in the level of redevelopment brought about by changes in . As
a result, the level of redevelopment under ED may be greater than or less than that
under voluntary exchange. Note, however, we were unable to generate any examples
where the level of redevelopment under voluntary exchange exceeded that under ED,
(more on this in Section 4).
3.3.2

Collective Bargaining

We now consider an alternative government policy that requires the developer and all
of the A owners to bargain simultaneously over the transference of property rights.
Intuitively, the government gets the developer and A owners into a room and tells
them to collectively determine the price(s) for the transference of the owners’property
rights to the developer. In the model, the government’s collective bargaining, CB,
policy speci…es a simultaneous bargaining game that agents play.
The collective bargaining game is similar to the two-stage proposal game— which
involves 2 players— but is augmented to accommodate A + 1 players. After the
developer chooses the A tracts of land that he wants to acquire for development, the
two-stage collective bargaining game has the developer making A simultaneous o¤ers
to each of the owners, where each owner simultaneously either accepts or rejects the
o¤er. If all owners accept, then property rights are transferred between the owners
and the developer at the terms of trade speci…ed in the bargain. Suppose, instead,
that one or more of the owners reject the developer’s o¤er. Then, with probability ,
the developer gets to make A take-it-or-leave-it o¤ers to the owners. In this case, the
developer will, in equilibrium, o¤er f (x) to each of the A owners; since owners are
indi¤erent between accepting and rejecting, they all accept. With probability 1
,
one of the owners is randomly chosen and gets to make A take-it-or-leave-it o¤ers to
the A 1 other owners and the developer. The probability that a particular owner
gets to make the o¤er is 1=A. In this case, the owner will, in equilibrium, o¤er f (x) to
each of the A 1 other owners and Ry to the developer, where y solves Fy (A; y) = R;
since the owners and developer are indi¤erent between accepting and rejecting, they

21

all accept. Hence, the equilibrium price that the developer o¤ers to each of the A
owners in the …rst stage, p, is given by
p =

f (x) + (1

= f (x) +

1
A

1
[F (A; y)
A

)

yR

(A

1) f (x)] +

A

1
A

f (x)

(33)

S (A; x; y) :

Since all A owners are indi¤erent between accepting and rejecting the …rst-stage o¤er
p, (33), they will all accept. Notice that the collective bargaining price, (33), is lower
than the average price associated with voluntary exchange, (21). This implies that
collective bargaining mitigates the holdout problem since, on average, owners receive
a smaller share of the surplus that is generated through redevelopment compared
with voluntary exchange. (In fact, the government policy of collective bargaining
eliminates the holdout problem.)
Under the policy of collective bargaining, an owner’s investment decision, x, is
given by the solution to
arg max

N

A
N

x

f (x) +

A
p + (K`
N

x) R;

(34)

where p is given by (33). The solution to (34) is (implicitly) given by,
N (1
N

)A

f 0 (x) = R if A `CB
x=0
if A > `CB

(35)

where “CB”in `CB stands for “collective bargaining,”and `CB solves
N

(1

) `CB
N

f 0 (0) = R:

The developer’s acquisition and spending choices, A and y, respectively, are given
by the solution to (25). In light of (33), the developer’s problem can be rewritten as
max S (A; x; y) + Kd R:
A;y

(36)

Hence, the developer’s objective is to maximize surplus, S (A; x; y), which implies
that the developer’s objective is consistent with maximizing social welfare, taking
x as given. Therefore, the developer behaves e¢ ciently, and his spending, y, and
acquisition, A, decisions are given by (12) and (13), respectively. Notice that since
the developer receives the same share of the total surplus, , independent of the
number of properties that are acquired and redeveloped, he does not face a hold-out
problem.

22

Figure 4: Collective Bargaining
The developer’s decision is described by locus d D in Figure 4, which is identical
to the locus d D in Figure 1. The locus of points that describe the owner’s investment
decision, (35), is depicted in Figure 4 by `CB xmax for x > 0 and the locus that describes
the socially e¢ cient decision, (11), is depicted by ` xmax . (Comparing (35) with (11),
note that locus `CB xmax is steeper than locus ` xmax , as depicted.) The equilibrium
collective bargaining outcome, aCB = (xCB ; ACB ), is given by the lower intersection
of the `CB xmax and d D curves, and the socially e¢ cient outcome is a . As with
the policy of ED, the CB policy has too much investment and too little development
compared to what is socially e¢ cient.
Figure 4 reveals a rather important policy result,
Proposition 6 Social welfare is strictly lower under a policy of ED compared to a
policy of CB. As well, investment is higher and redevelopment is lower under ED
compared to CB.
Proof. Both the ED and CB allocations lie on the e¢ cient developer’s decision locus
d D , see Figure 4. Since welfare decreases when moving away from the e¢ cient
allocation, a , along the locus d D , the welfare associated with allocation aCB is
greater than that associated with allocation aED . To see that investment is higher
and redevelopment is lower under ED compared to CB, compare allocations aCB and
aED in Figure 4.
The economic intuition that underlies this proposition is straightforward: Both
policies eliminate the holdout problem, which is bene…cial from a social perspec23

tive. However, a policy of ED leads to more overinvestment than a policy of CB.
Proposition 6 implies that the government should only entertain a policy of collective
bargaining; the government should never pursue a policy of ED.
3.3.3

Optimal Policy

Given Proposition 6, the government should never choose a policy of ED because it
is dominated by the CB policy. Is a policy of CB socially desirable? In Figure 5,
social welfare associated with CB is given by WCB which, in turn, is determined by
the intersection of the owner’s decision locus, `CB xmax , and the developer’s decision
locus, d D . Suppose that under voluntary exchange, the developer’s decision locus
(which is not illustrated in Figure 5) intersects the owner’s decision locus, `V xmax ,
at aV in Figure 5.20 In this situation, social welfare associated with allocation aV
exceeds that associated with CB, WCB . Hence, a policy of CB will lower social
welfare. Although CB eliminates the holdout problem— as was also the case with the
ED policy— the resulting increase in overinvestment that results from the CB policy
leads to a decrease in social welfare compared to voluntary exchange. Suppose, now
that the holdout problem under voluntary exchange is worse than depicted in Figure
5. Then, it is possible that the developer’s decision locus intersects the owner’s
decision locus, `V xmax , below the intersection of WCB with the owner’s decision locus
at allocation a0V . In this situation, a policy of CB increases social welfare. The
following de…nition is needed for what follows.
De…nition 7 The holdout problem is said to be signi…cant if the developer’s decision locus under voluntary exchange intersects the `V xmax locus below the intersection
of WCB and `V xmax curves and above the intersection of the WED and `V xmax curves
in Figure 5.
We can summarize this discussion by the following proposition,
Proposition 8 A necessary condition for welfare associated with CB to exceed that
of voluntary exchange is that the developer’s holdout problem is “signi…cant.”
Proof. Given De…nition 7, compare allocation aCB with allocation a0V in Figure 5.
The condition is not su¢ cient because the welfare associated with CB exceeds that
of voluntary exchange if the holdout problem is “severe.”
The allocation and social welfare associated with the ED policy is illustrated in
Figure 5 by aED and WED , respectively. Consider the voluntary exchange allocation
a0V . Notice that for this allocation the holdout problem is signi…cant but not severe.
In the subsequent section, we provide examples of the various outcomes described in
Figures 2, 4 and 5.
20

The owner’s decision locus, `CB xmax , lies above the voluntary exchange for all A > 1. We
assume the model parameters are such that the developer wants to redevelop multiple tracts. If,
instead, the developer only wants to redevelop one tract, then the results of Section 2 apply.

24

Figure 5: Desirability of a CB Policy

4

Examples

Intuitively, compared to voluntary exchange, transferring property rights by either
the CB or ED policy eliminates the holdout problem but worsens the investment
distortion. Whether social welfare increases or decreases under either of these policies
depends on which of these e¤ects dominate, which, in turn, depends on important
model parameters values such as , a measure of the developer’s bargaining power.
We construct a number of examples to illustrate these ideas. Although Proposition
6 tells us that the government should never pursue a policy of ED, we characterize
the payo¤s associated with this policy in our examples: The Kelo ruling pertains to
the ED policy and, because of this, we are interested in the circumstances where a
policy of ED is better than voluntary exchange.
The examples are constructed using the following functional forms and parameters. Let f (x) = 11 log (1 + x), F (A; y; P ) = 23 A:44 y :36 , N = 30, and R = 1:05.
In Table 1 we report the levels of redevelopment, A, investment, x,21 the developer’s
payo¤, d , the owner’s payo¤, ` , and social welfare, W , under voluntary exchange,
V , eminent domain, ED, and collective bargaining, CB, for di¤erent values of . The
socially optimal, SO, levels of investment and redevelopment are also reported in
Table 1, as is the socially optimal level of welfare. We identify values for where the
holdout problem is not signi…cant, = 0:99, where it is signi…cant, = 0:966, and
21

Economy-wide investment is simply 30x.

25

where it is severe, = 0:894.22
The examples, summarized in Table 1, are consistent with theory. For example,
for all values of investment under voluntary exchange is greater than the socially
optimal level and redevelopment under voluntary exchange is less than the socially
optimal level as theory— Proposition 3— predicts and as illustrated in Figure 2. Investment under voluntary exchange is less than that under ED— Proposition 5— as
illustrated in Figure 3). Notice that redevelopment under ED exceeds that under voluntary exchange for the examples in Table 1. We tried many other parameter values,
e.g., having arbitrarily close to 1, and it was always the case that redevelopment
under ED exceeded that under voluntary exchange. Finally, redevelopment (investment) under CB exceeds (is less than) that under ED— Proposition 6— as illustrated
in Figure 4.
The examples also demonstrate that the notions that the holdout problem is “not
signi…cant,” “signi…cant”or “severe” has empirical content.23 In all of the examples
in Table 1— and, in fact, in all of the examples that we generated— the level of
redevelopment under CB always exceeds the level of redevelopment under voluntary
exchange; theory does not make a prediction regarding this relationship. When =
0:99, the holdout problem is not signi…cant in the sense that welfare associated with
voluntary exchange exceeds welfare under CB; this situation is depicted in Figure
5 when the voluntary exchange allocation is aV . When
= 0:966, the holdout
problem is signi…cant because welfare associated with voluntary exchange exceeds
the welfare associated with ED; this situation is illustrated in Figure 5 when the
voluntary exchange allocation is a0V . Finally, when the developer’s bargaining power
is reduced to = 0:894, the holdout problem is severe since ED is welfare improving
compared to voluntary exchange; this is illustrated in Figure 3 when the voluntary
exchange allocation is given by a0V .
22

It should be emphasized that the purpose of this example is to illustrate the qualitative features
of various equilibrium outcomes. In particular, it demonstrates that there exist bargaining power
values such that the holdout problem is not signi…cant, i.e., social welfare is higher under voluntary
exchange than under the CB policy, signi…cant, i.e., social welfare is higher under the CB policy than
voluntary exchange, and social welfare for voluntary exchange exceeds that under ED, and severe,
i.e., social welfare is higher under ED than voluntary exchange. For di¤erent model parameters and
functional forms, the bargaining power values that describe these hold-out problems could be quite
di¤erent. To make the welfare comparisons easy, we subtract 500 + r (K` + Kd ) from the welfare
numbers generated by the examples, and then multiply this di¤erence by 1000.
23
We say that the holdout problem is not signi…cant if it is neither signi…cant nor severe.

26

0:990

x
A
W

SO
8:67755
2:28702
1650

d
`

0:966

x
A
W

8:67755
2:28702
1650

d
`

0:894

x
A
W
d
`

8:67755
2:28702
1650

V
9:4624
1:9923
794
23:6118
15:9061
9:4357
1:8608
776
22:5727
15:9401
9:3935
1:51567
257
19:8826
16:0125
Table 1

CB
9:4690
2:0509
787
23:8415
15:8982
9:4518
2:0555
823
23:2995
15:9175
9:3996
2:0697
929
21:6644
15:9755

ED
9:4762
2:0490
772
24:0669
15:8902
9:4762
2:0490
772
24:0669
15:8902
9:4762
2:0490
772
24:0669
15:8902

Notice that social welfare may either increase or decrease when moving from a
voluntary exchange regime to either an ED or CB regime. In particular, both CB
and ED begin to look attractive, from a welfare perspective, when the developer’s
bargaining power, , becomes lower. As
falls, not surprisingly, the developer’s
payo¤ decreases and the owners’ payo¤s increase. The examples also inform us as
to how owners and the developer fare when moving from voluntary exchange to ED
or CB. It is straightforward to demonstrate that, independent of how social welfare
changes, owners are always made worse o¤ when moving from voluntary exchange to
ED. To see this, note that under voluntary exchange when < 1, it is optimal for
the representative owner to invest xV < xmax , where xV solves (23) and xmax solves
f 0 (xmax ) = R (which is the investment level associated with ED). The representative
agent could invest xmax but chooses not to because his expected payo¤ is higher
with an investment of xV . If the representative owner did invest xmax , then under
voluntary exchange he would receive a payo¤ of f (xmax ) with positive probability,
and a payo¤ of p > f (xmax ) with complementary probability, see (22). Note that
under an ED regime, the representative owner receives a payo¤ of f (xmax ) with
probability one. Hence, his ED payo¤ is strictly lower than what he would receive
if he invested xmax under voluntary exchange, which implies that the representative
owner is strictly worse o¤ under an ED regime compared to voluntary exchange. If
social welfare increases when moving from voluntary exchange to ED, then, clearly,
the developer is made strictly better o¤. This situation is illustrated in Table 1
when = 0:894. However, the examples indicate that the developer is made better
o¤ moving from voluntary exchange to ED even when welfare falls, as is the case

27

for either = 0:990 or = 0:966.24 Furthermore, the examples indicate that the
payo¤s to owners decrease when moving from voluntary exchange to a CB policy
and decrease further when moving from a CB policy to an ED policy; the payo¤s to
the developer increase in these circumstances. Hence, developers “like” government
policy, compared to voluntary exchange, because these policies eliminate the holdout
problem, which is bene…cial for developers.
In light of our results and examples, it is perhaps not that surprising that ED is
widespread and popular with local governments and developers. If local governments
want large scale redevelopment for their communities, then ED is a tool that can be
used to increase the level of redevelopment, compared to voluntary exchange. The
developers are more than happy to go along with such a scheme because, independent
of whether large scale redevelopment is a good or bad idea for society as a whole,
their payo¤s will be higher under ED. Regarding a policy of CB, the developer prefers
it to voluntary exchange, but prefers a policy of ED to that of CB.

4.1

Discussion

In defending the state’s right to take property from one private agent and give
it to another private agent, proponents of the Kelo decision— who are often local
governments— point to the increased bene…ts associated with higher levels of redevelopment, such as more employment and higher taxes collected. Although it may
be the case that the use of ED will increase the level of redevelopment— and other
activities associated with it— it is not obvious that this translates into higher social
welfare. For example, allocation aED in Figure 5 has a higher level of redevelopment
compared to either voluntary exchange allocations aV or a0V , but a lower level of social welfare. (See also Table 1 for = 0:99 and 0:966.) If local governments equate
higher levels of employment and tax revenue— that usually accompany higher levels
of redevelopment— with a higher level of social welfare, then allowing communities to
use ED to promote redevelopment can lead to bad outcomes. For example, if local
governments use their power of ED when the holdout problem is not severe, then
there will be a negative impact on social welfare compared to voluntary exchange.
If government policy can improve matters, it is not obvious that using ED is the
most e¢ cient way to do it. We have shown that an alternative policy of collective
bargaining dominates ED. One may argue that this dominance result depends on
the precise speci…cation of the simultaneous bargaining game. Perhaps, but the big
insight is that collective bargaining, in general, does not dilute the bargaining power
of the owners, as does ED. This implies that the owners’ incentive to overinvest is
mitigated compared to ED. And this insight is important because the bene…t of both
the ED and CB policies is the elimination of the holdout problem. But the cost to
24

In an earlier version of the paper, using di¤erent functional forms, we were able to show numerically that the developer’s payo¤ could decrease when moving from voluntary exchange to ED if he
has “almost all” the bargaining power; otherwise, his payo¤ would increase.

28

both policies is the tendency to increase the level of overinvestment, and the incentive
to overinvest is lessened under CB compared to ED.

5

Concluding Comments

A government policy that allows developers to purchase as many properties that
they want for “just” compensation will promote redevelopment compared to a situation where developers obtain property rights by bargaining with owners that have
an incentive to create a holdout problem.25 However, such a policy also results in
landowners further increasing their already ine¢ cient levels of investment on their
properties. From a social perspective, eminent domain is a good policy only if the
former— redevelopment— e¤ect dominates the latter— overinvestment— e¤ect. The
general Kelo ruling, which allows communities to transfer property rights from one
private agent to another with just compensation, can be justi…ed from a social perspective only if it is always the case that the holdout problem is “severe”(in the sense
described in De…nition 4). It is unlikely, however, that in all instances developers face
severe holdout problems. The general Kelo ruling makes for bad public policy on two
counts. First, in many applications of the Kelo ruling, social welfare will fall because
the holdout problem is not severe. Second, there exist other policies, such as the collective bargaining policy outlined above, that strictly dominate eminent domain. The
latter implies that eminent domain should never be used to transfer property rights
of one private agent to another private agent. Similarly, an unconditional policy of
collective bargaining is not optimal since such a policy will lower social welfare if the
holdout problem is not “signi…cant”(in the sense described in De…nition 7). An optimal policy requires that the government …rst accesses the magnitude of the holdout
problem that the developer faces and then to impose a policy of collective bargaining
only if the holdout problem is signi…cant; otherwise, the government should allow
voluntary exchange to determine the level of redevelopment in its community.

25

Although theory gives an ambigous relationship between redevelopment under ED and voluntary
exchange, all of the examples we generated featured this outcome.

29

6

References
1. Berman v. Parker, 1954, 348 U.S. 26.
2. Blume, L., Rubinfeld, D., 1984. Compensation for takings: An economic analysis. California Law Review 72, 569-628.
3. Blume, L., Rubinfeld, D., Shapiro, P., 1984. The taking of land: When should
compensation be paid? Quarterly Journal of Economics 99, 71-91.
4. Clark v. Nash, 1905, 198 U.S. 361.
5. Eckart, W., 1985. On the land assembly problem. Journal of Urban Economics
18, 364–378.
6. Fallbrook Irrigation Dist v. Bradley, 1896, 164 U.S. 112.
7. Garrett, T, Rothstein, P., 2007. The taking of prosperity? Kelo vs. New London and the economics of eminent domain. The Regional Economist, Federal
Reserve Bank of Saint Louis, January, 4-9.
8. Grossman, S.J., Hart, O.D., 1980. Takeover bids, the free-rider problem, and
the theory of the corporation. The Bell Journal of Economics 11, 42-64.
9. Hawaii Housing Authority v. Midki¤, 1984, 467 U.S. 229.

10. Hermalin, B,. 1995. An economic analysis of takings. The Journal of Law,
Economics & Organization 11, 64-86.
11. Kelo v. City of New London, 2005, 545 U.S. 469.
12. Munch, P., 1976. An economic analysis of eminent domain. Journal of Political
Economy 84, 473-497.
13. Mt. Vernon-Woodberry Cotton Duck Co. v. Alabama Interstate Power, 1916,
240 U.S. 30.
14. O’Flaherty, B., 1994. Land assembly and urban renewal. Regional Science &
Urban Economics 24, 287-300.
15. Pitchford, R., Snyder, C., 2003. Coming to the nuisance: An economic analysis
from an incomplete contracts perspective. The Journal of Law, Economics &
Organization 19, 491-516.
16. Rolnick, A., Davies, P., 2006. The cost of Kelo. The Region, Federal Reserve
Bank of Minneapolis, 20 no. 2 12-17, 42-45.

30

7

Appendix 1: Proofs

Proposition 1 If S (xn ) < xn R and condition (9) holds, then voluntary exchange
results in a socially e¢ cient allocation characterized by no redevelopment and x = xn ;
otherwise voluntary exchange is always socially ine¢ cient.
Proof to Proposition 1.
Assume …rst that S (xn ) < xn R. This condition
implies that it is not socially e¢ cient to redevelop, see condition (1). If, in addition,
condition (9) holds, then the owner invests xn . Since S (xn ) < 0, redevelopment
does not occur under voluntary exchange. In this case both the investment and
redevelopment decisions are socially optimal. In all other cases, the allocation will
be socially ine¢ cient.
If condition (9) does not hold (and S (xn ) < xn R), then the owner invests xr .
But this implies that S (xr ) > 0 and there will be redevelopment, which is socially
ine¢ cient.
Assume now that S (xn ) > xn R, which means that it is socially e¢ cient to redevelop. If S (xn ) > 0, then redevelopment occurs, which is socially e¢ cient. However,
the level of investment, xn , is too high from a social perspective. If S (xn ) < 0 and
condition (9) holds, then redevelopment does not occur, which is socially ine¢ cient.
If S (xn ) < 0 and condition (9) does not hold, then redevelopment occurs but the
level of investment, xr , is socially too high.
Proposition 2 ED can improve social welfare only by preventing redevelopment
when redevelopment is ine¢ cient; otherwise, ED (weakly) decreases social welfare,
compared to voluntary exchange.
Proof. Suppose that S (xn ) < xn R, S (xr ) > 0 and condition (9) is not valid. Then,
under voluntary exchange, redevelopment will occur, even though it is socially ine¢ cient. Under ED, the developer pays f (x) to obtain the property. In this situation,
the owner, directly or indirectly, receives f (x) from his property investment. Hence,
he will invest xn since f (xn ) + (K` xn ) R > f (x) + (K` x) R for all x xn . Since
S (xn ) < 0, the developer is not redevelop the property and the outcome is socially
e¢ cient.
Suppose now that S (xn ) < xn R and condition (9) is valid. Under voluntary
exchange the owner invests xn and no redevelopment occurs, which is socially e¢ cient. Under ED the owner will continue to invest xn (independent of the developer’s
redevelopment decision). The developer will not redevelop since S (xn ) < 0; the
introduction of ED has no e¤ect on welfare in this case.
Finally, suppose that S (xn ) > 0; then it is always socially e¢ cient to redevelop.
Under voluntary exchange or ED, redevelopment will always occurs since S (xr ) >
S (xn ) > 0. However, under voluntary transfer, the investor invests xr but under
ED he invests xn > xr . Compared to voluntary transfer, social welfare falls under
ED because the owner invests more and the investment is destroyed, (it is socially
e¢ cient to invest zero).

31

8

Appendix 2: Derivation of pi

Suppose the developer wants to redevelop A tracts of land. He selects A owners and
plays an A-stage bargaining game with them. At stage i of the A-stage game, the
developer plays the two-stage proposal game with owner i. Suppose that owner j
can observe the accepted o¤ers of the previous j 1 owners. If redevelopment is
to occur, the developer must reach an agreement with each of the A owners; if not,
redevelopment does not occur. If redevelopment does not occur, then, at date 2 all
N owners receive the payo¤ f (x) + (K` x) R and the developer gets Kd R.
Consider the last owner, owner A, that the developer bargains with. Suppose that
owner A rejects the developer’s …rst-stage o¤er. Then with probability 1
, owner
A makes the second stage take-it-or-leave-it o¤er. The o¤er will make the developer
indi¤erent between accepting and
Hence, the o¤er is yR, which implies that
PArejecting.
1
owner A gets F (A; y) yR
i=1 pi , since the developer has promised to pay the
PA 1
…rst A 1 owners i=1 pi . With probability , the developer makes the second stage
o¤er, and o¤ers f (x), which owner A accepts. Therefore, the equilibrium …rst-stage
o¤er that the developer makes to owner A is
!
A 1
X
pA = f (x) + (1
) F (A; y) yR
pi :
i=1

Consider now owner j and suppose that the owner rejects the developer’s …rststage o¤er. If the developer makes the second-stage o¤er, he o¤ers f (x),
Pj which
owner j accepts. If owner j makes the second-stage o¤er, he o¤ers yR + i=11 pi +
(A j) f (x), i.e., the o¤er compensates the developer
his redevelopment costs,
Pj for
1
yR, his promised payments to the …rst j 1 owners, i=1 pi , and su¢ cient resources
to pay the remaining A j owners their reservation values, (A j) f (x). Therefore,
the equilibrium …rst stage o¤er that the developer makes to owner j is
!
j 1
X
pj = f (x) + (1
) F (A; y) yR
pi (A j) f (x) :
(37)
i=1

Using (37), the …rst-stage o¤er that the developer makes to the …rst owner in the
bargaining queue, p1 , is
p1 = f (x) + (1

) (F (A; y)

yR

(A

1) f (x)) :

(38)

which can be rearranged to
p1 = f (x) + (1

) S (A; x; y) ;

(39)

where S (A; x; y) = F (A; y) yR Af (x).
Again, using (37), the …rst-stage o¤er that developer makes to owner 2, p2 , is
32

p2 = f (x) + (1

) (F (A; y)

yR

p1

(A

2) f (x)) :

(40)

If (39) is substituted into (40), then p2 can be rearranged to
p2 = f (x) + (1

) S (A; x; y) :

(41)

Continuing in this manner, a simple induction argument implies that if the developer wants to redevelop A tracts of land, then the …rst-stage o¤er that he makes to
owner j, pj , j = 1; :::; A, is
pj = f (x) + (1

9

)

j 1

(42)

SA :

Appendix 3

Slope of developer’s decision curve is negative. It must necessarily be the
case that 1 + A ln ( ) > 0 for all x > 0, which implies that (29) is negative. To see
this, suppose that there exists an x0 > 0 such that 1 + A0 ln ( ) < 0, where (x0 ; A0 )
satis…es (28), (and where y0 is determined by (27).) Now, choose an A~ < 1= ln ( ).
~ If x is reduced from x~, by (29),
From (28), there exists an x = x~ that satis…es A = A.
~
A will increase from A. Since the developer’s decision functions (27) and (28) are
continuous and “well behaved”in (x; A; y) and since there exists an x0 > 0 such that
1 + A0 ln ( ) < 0, A will continue to increase as x decreases until A = A^ = 1= ln ( ).
De…ne the x associated with A^ as x^. Since (29) is negative for all x > x^, it must
be the case that x0 < x^. Now, consider increasing x from x0 . Since A0 > A^ and
the developer’s decision functions (27) and (28) are continuous in (x; A; y), A must
increase from A0 . In other words, equation (29) implies that A is an increasing
function of x for all x 2 (x0 ; x^), and that A (^
x ") > A^ for " > 0, where " is
arbitrarily small. Hence, there is a discontinuity in (27) and (28) at x^, i.e., A and
the corresponding y must “jump” when x is reduced slightly from x^. But all of
the developer’s decision functions (27) and (28) are continuous and well behaved in
(x; A; y); a contradiction. Hence, 1 + A ln ( ) > 0. Note also that the absolute value
of the slope of the developer’s decision locus (29) is strictly less than that of the
developer’s e¢ cient decision locus (19).
Owner’s decision curve is strictly convex over the economically relevant
range. The derivative of (24) with respect to x is
f 000 (x) f 0 (x) 2f 00 (x)2
d2 A
=
1
dx2
f 0 (x)3

A

(1 + A ln ( ))

1

NR

f 00 (x) ln ( ) A (2 + A ln ( )) dA
+
N R: (43)
2
A
f 0 (x)2 1
(1 + A ln ( )) dx

33

Figure 6: Voluntary Exchange Equilibrium
The …rst term on the right side of (43) is negative by Assumption 1; the second term
is strictly negative for A 2 (0; 2= ln ( )) and strictly positive for A > 2= ln ( ).
Therefore, the owner’s locus (23) is strictly concave for all A 2 (0; 2= ln ( )). Recall
that the developer’s decision curve is bounded from above by 1= ln( ); therefore,
the owner’s decision curve is strictly convex over the economically relevant range.
Developer’s curve is not convex. The derivative of (29) with respect to x is
d2 A
=
dx2

f 0 (x) (1 + A ln ( ))

GA

ln ( )2 [(FA

FAy dA 2
=D
Fyy dx
dA
f (x))]
Af 0 (x) =D2
dx
Gy

+ f 00 (x) (1 + A ln ( )) =D + f 0 (x) ln ( )

dA
=D;
dx

where D = G (A; y) ln ( )2 S (A; y; x). This condition cannot be signed: the last
term is negative, while all the other terms are positive.
In principle, then, the owner’s decision locus, (23), and the developer’s decision
locus, (28), may intersect more than twice.26 We believe, however, that such an
outcome is highly unlikely. If anything, we …nd that, unless the developer has virtually
all of the bargaining power, these loci will intersect only once. This …nding is a
result of the combination that: (i) the developer’s ‘holdout’locus (28) lies below the
26

Although this may happen in principle, we were unable to construct such examples.

34

e¢ cient locus (13); (ii) the slope of the developer’s holdout locus (29) is strictly less
in absolute value than that of the e¢ cient locus (19); and (iii) the maximum value of
A that the developer chooses in the holdout environment is …nite and less than A^ =
1= ln ( ). Intuitively, compared to the developer’s e¢ cient locus (13), his holdout
locus (28) is, in (x; A) space, “pushed down,” “‡attened out” and “constrained in
its height.” A simple example and diagram might be helpful here. Suppose that
= 0:95 and N = 50. The developer’s decision locus, which we denote as dV DV
in Figure 6, intersects the A axis at a value that is strictly less than A^ = 19:5, i.e.,
A^ = 1= ln ( ).27 When = 0:95 (and assuming that f 0 (0) is “large”) the owner’s
decision locus, which we denote as `V xmax in Figure 6, intersects the A axis at a
value that exceeds N = 50. The owner’s decision locus is strictly concave for all
^ Note that the owner’s decision locus intersects the A-axis at a level that
A < 2A.
is signi…cantly higher than where the developer’s locus intersects. This is in direct
contrast to the CB or ED environments, where the developer’s locus tends to in…nity
as x tends to zero. The developer’s and owner’s decision loci intersect at allocation
a1 = (x1 ; A1 ) in Figure 6. Since the absolute value of the slope of the developer’s
decision locus dV DV is less than that of the e¢ cient decision locus, for comparison
purposes, we shift down the developer’s e¢ cient locus, (13), in Figure 6 until it
intersects allocation a1 , and denote this locus as ds Ds , (‘s’ for shift). In Figure 6,
locus ds Ds intersects the owner’s locus `V xmax twice; at allocations a1 and a2 . If the
developer’s locus dV DV is to intersect the owner’s locus at least twice, the second
and subsequent intersections would have to lie north-west of allocation a2 = (x2 ; A2 )
(since locus dV DV is less steep than locus ds Ds ). But this is not possible in Figure 6
^ One could, however, imagine that locus d D is actually much steeper
since A2 > A.
s s
than what is depicted in Figure 6 so that it intersects the owner’s locus `V xmax at,
^ It is then possible for the developer’s curve to
say, allocation a3 , where A3 < A.
intersect the owner’s locus `V xmax at an allocation where the number of tracts that
^ For this to happen, the slope of the developer’s locus
are redeveloped is less than A.
would have to be only slightly less in absolute value than that of the e¢ cient locus as
x is reduced from x1 ; but then the slope would have to dramatically ‡atten out after
it intersects the owner’s locus `V xmax for a second time in order to ensure that A < A^
for all possible choices of x. Such a characterization, however, is not feasible. If the
values of the slopes of the holdout and e¢ cient loci are very close to one another—
and, hence, as well as the loci themselves— then this implies that is arbitrarily close
to 1 and A^ is arbitrarily high. In this situation, the CB policy and voluntary exchange
environments will deliver similar equilibrium outcomes since the holdout problem is
“not that important,” i.e., when is arbitrarily close to 1, ln ( ) is arbitrarily close
to 0 and the developer’s decision problem is characterized by FA (A; y)
f (x). In
such a case, the `V xmax and dV DV loci in the voluntary exchange environment will
intersect twice, and the lower intersection will deliver a higher level of social welfare.28
27
28

Exactly where it intersects will depend on the model parameters.
All of our numerical exercises indicate that if
is arbitrarily high, the developer’s and the

35

So unless

is arbitrarily close to 1, the `V xmax and dV DV loci will only intersect once.

owner’s loci will intersect only twice and that the lower intersection generates the higher level of
social welfare.

36

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WP-11-07

Estimation of Panel Data Regression Models with Two-Sided Censoring or Truncation
Sule Alan, Bo E. Honoré, Luojia Hu, and Søren Leth–Petersen

WP-11-08

Fertility Transitions Along the Extensive and Intensive Margins
Daniel Aaronson, Fabian Lange, and Bhashkar Mazumder

WP-11-09

Black-White Differences in Intergenerational Economic Mobility in the US
Bhashkar Mazumder

WP-11-10

Can Standard Preferences Explain the Prices of Out-of-the-Money S&P 500 Put Options?
Luca Benzoni, Pierre Collin-Dufresne, and Robert S. Goldstein

WP-11-11

Business Networks, Production Chains, and Productivity:
A Theory of Input-Output Architecture
Ezra Oberfield

WP-11-12

Equilibrium Bank Runs Revisited
Ed Nosal

WP-11-13

Are Covered Bonds a Substitute for Mortgage-Backed Securities?
Santiago Carbó-Valverde, Richard J. Rosen, and Francisco Rodríguez-Fernández

WP-11-14

The Cost of Banking Panics in an Age before “Too Big to Fail”
Benjamin Chabot

WP-11-15

1

Working Paper Series (continued)
Import Protection, Business Cycles, and Exchange Rates:
Evidence from the Great Recession
Chad P. Bown and Meredith A. Crowley

WP-11-16

Examining Macroeconomic Models through the Lens of Asset Pricing
Jaroslav Borovička and Lars Peter Hansen

WP-12-01

The Chicago Fed DSGE Model
Scott A. Brave, Jeffrey R. Campbell, Jonas D.M. Fisher, and Alejandro Justiniano

WP-12-02

Macroeconomic Effects of Federal Reserve Forward Guidance
Jeffrey R. Campbell, Charles L. Evans, Jonas D.M. Fisher, and Alejandro Justiniano

WP-12-03

Modeling Credit Contagion via the Updating of Fragile Beliefs
Luca Benzoni, Pierre Collin-Dufresne, Robert S. Goldstein, and Jean Helwege

WP-12-04

Signaling Effects of Monetary Policy
Leonardo Melosi

WP-12-05

Empirical Research on Sovereign Debt and Default
Michael Tomz and Mark L. J. Wright

WP-12-06

Credit Risk and Disaster Risk
François Gourio

WP-12-07

From the Horse’s Mouth: How do Investor Expectations of Risk and Return
Vary with Economic Conditions?
Gene Amromin and Steven A. Sharpe

WP-12-08

Using Vehicle Taxes To Reduce Carbon Dioxide Emissions Rates of
New Passenger Vehicles: Evidence from France, Germany, and Sweden
Thomas Klier and Joshua Linn

WP-12-09

Spending Responses to State Sales Tax Holidays
Sumit Agarwal and Leslie McGranahan

WP-12-10

Micro Data and Macro Technology
Ezra Oberfield and Devesh Raval

WP-12-11

The Effect of Disability Insurance Receipt on Labor Supply: A Dynamic Analysis
Eric French and Jae Song

WP-12-12

Medicaid Insurance in Old Age
Mariacristina De Nardi, Eric French, and John Bailey Jones

WP-12-13

Fetal Origins and Parental Responses
Douglas Almond and Bhashkar Mazumder

WP-12-14

2

Working Paper Series (continued)
Repos, Fire Sales, and Bankruptcy Policy
Gaetano Antinolfi, Francesca Carapella, Charles Kahn, Antoine Martin,
David Mills, and Ed Nosal

WP-12-15

Speculative Runs on Interest Rate Pegs
The Frictionless Case
Marco Bassetto and Christopher Phelan

WP-12-16

Institutions, the Cost of Capital, and Long-Run Economic Growth:
Evidence from the 19th Century Capital Market
Ron Alquist and Ben Chabot

WP-12-17

Emerging Economies, Trade Policy, and Macroeconomic Shocks
Chad P. Bown and Meredith A. Crowley

WP-12-18

The Urban Density Premium across Establishments
R. Jason Faberman and Matthew Freedman

WP-13-01

Why Do Borrowers Make Mortgage Refinancing Mistakes?
Sumit Agarwal, Richard J. Rosen, and Vincent Yao

WP-13-02

Bank Panics, Government Guarantees, and the Long-Run Size of the Financial Sector:
Evidence from Free-Banking America
Benjamin Chabot and Charles C. Moul

WP-13-03

Fiscal Consequences of Paying Interest on Reserves
Marco Bassetto and Todd Messer

WP-13-04

Properties of the Vacancy Statistic in the Discrete Circle Covering Problem
Gadi Barlevy and H. N. Nagaraja

WP-13-05

Credit Crunches and Credit Allocation in a Model of Entrepreneurship
Marco Bassetto, Marco Cagetti, and Mariacristina De Nardi

WP-13-06

Financial Incentives and Educational Investment:
The Impact of Performance-Based Scholarships on Student Time Use
Lisa Barrow and Cecilia Elena Rouse

WP-13-07

The Global Welfare Impact of China: Trade Integration and Technological Change
Julian di Giovanni, Andrei A. Levchenko, and Jing Zhang

WP-13-08

Structural Change in an Open Economy
Timothy Uy, Kei-Mu Yi, and Jing Zhang

WP-13-09

The Global Labor Market Impact of Emerging Giants: a Quantitative Assessment
Andrei A. Levchenko and Jing Zhang

WP-13-10

3

Working Paper Series (continued)
Size-Dependent Regulations, Firm Size Distribution, and Reallocation
François Gourio and Nicolas Roys

WP-13-11

Modeling the Evolution of Expectations and Uncertainty in General Equilibrium
Francesco Bianchi and Leonardo Melosi

WP-13-12

Rushing into American Dream? House Prices, Timing of Homeownership,
and Adjustment of Consumer Credit
Sumit Agarwal, Luojia Hu, and Xing Huang

WP-13-13

The Earned Income Tax Credit and Food Consumption Patterns
Leslie McGranahan and Diane W. Schanzenbach

WP-13-14

Agglomeration in the European automobile supplier industry
Thomas Klier and Dan McMillen

WP-13-15

Human Capital and Long-Run Labor Income Risk
Luca Benzoni and Olena Chyruk

WP-13-16

The Effects of the Saving and Banking Glut on the U.S. Economy
Alejandro Justiniano, Giorgio E. Primiceri, and Andrea Tambalotti

WP-13-17

A Portfolio-Balance Approach to the Nominal Term Structure
Thomas B. King

WP-13-18

Gross Migration, Housing and Urban Population Dynamics
Morris A. Davis, Jonas D.M. Fisher, and Marcelo Veracierto

WP-13-19

Very Simple Markov-Perfect Industry Dynamics
Jaap H. Abbring, Jeffrey R. Campbell, Jan Tilly, and Nan Yang

WP-13-20

Bubbles and Leverage: A Simple and Unified Approach
Robert Barsky and Theodore Bogusz

WP-13-21

The scarcity value of Treasury collateral:
Repo market effects of security-specific supply and demand factors
Stefania D'Amico, Roger Fan, and Yuriy Kitsul
Gambling for Dollars: Strategic Hedge Fund Manager Investment
Dan Bernhardt and Ed Nosal
Cash-in-the-Market Pricing in a Model with Money and
Over-the-Counter Financial Markets
Fabrizio Mattesini and Ed Nosal
An Interview with Neil Wallace
David Altig and Ed Nosal

WP-13-22

WP-13-23

WP-13-24

WP-13-25

4

Working Paper Series (continued)
Firm Dynamics and the Minimum Wage: A Putty-Clay Approach
Daniel Aaronson, Eric French, and Isaac Sorkin
Policy Intervention in Debt Renegotiation:
Evidence from the Home Affordable Modification Program
Sumit Agarwal, Gene Amromin, Itzhak Ben-David, Souphala Chomsisengphet,
Tomasz Piskorski, and Amit Seru

WP-13-26

WP-13-27

The Effects of the Massachusetts Health Reform on Financial Distress
Bhashkar Mazumder and Sarah Miller

WP-14-01

Can Intangible Capital Explain Cyclical Movements in the Labor Wedge?
François Gourio and Leena Rudanko

WP-14-02

Early Public Banks
William Roberds and François R. Velde

WP-14-03

Mandatory Disclosure and Financial Contagion
Fernando Alvarez and Gadi Barlevy

WP-14-04

The Stock of External Sovereign Debt: Can We Take the Data at ‘Face Value’?
Daniel A. Dias, Christine Richmond, and Mark L. J. Wright

WP-14-05

Interpreting the Pari Passu Clause in Sovereign Bond Contracts:
It’s All Hebrew (and Aramaic) to Me
Mark L. J. Wright

WP-14-06

AIG in Hindsight
Robert McDonald and Anna Paulson

WP-14-07

On the Structural Interpretation of the Smets-Wouters “Risk Premium” Shock
Jonas D.M. Fisher

WP-14-08

Human Capital Risk, Contract Enforcement, and the Macroeconomy
Tom Krebs, Moritz Kuhn, and Mark L. J. Wright

WP-14-09

Adverse Selection, Risk Sharing and Business Cycles
Marcelo Veracierto

WP-14-10

Core and ‘Crust’: Consumer Prices and the Term Structure of Interest Rates
Andrea Ajello, Luca Benzoni, and Olena Chyruk

WP-14-11

The Evolution of Comparative Advantage: Measurement and Implications
Andrei A. Levchenko and Jing Zhang

WP-14-12

5

Working Paper Series (continued)
Saving Europe?: The Unpleasant Arithmetic of Fiscal Austerity in Integrated Economies
Enrique G. Mendoza, Linda L. Tesar, and Jing Zhang

WP-14-13

Liquidity Traps and Monetary Policy: Managing a Credit Crunch
Francisco Buera and Juan Pablo Nicolini

WP-14-14

Quantitative Easing in Joseph’s Egypt with Keynesian Producers
Jeffrey R. Campbell

WP-14-15

Constrained Discretion and Central Bank Transparency
Francesco Bianchi and Leonardo Melosi

WP-14-16

Escaping the Great Recession
Francesco Bianchi and Leonardo Melosi

WP-14-17

More on Middlemen: Equilibrium Entry and Efficiency in Intermediated Markets
Ed Nosal, Yuet-Yee Wong, and Randall Wright

WP-14-18

Preventing Bank Runs
David Andolfatto, Ed Nosal, and Bruno Sultanum

WP-14-19

The Impact of Chicago’s Small High School Initiative
Lisa Barrow, Diane Whitmore Schanzenbach, and Amy Claessens

WP-14-20

Credit Supply and the Housing Boom
Alejandro Justiniano, Giorgio E. Primiceri, and Andrea Tambalotti

WP-14-21

The Effect of Vehicle Fuel Economy Standards on Technology Adoption
Thomas Klier and Joshua Linn

WP-14-22

What Drives Bank Funding Spreads?
Thomas B. King and Kurt F. Lewis

WP-14-23

Inflation Uncertainty and Disagreement in Bond Risk Premia
Stefania D’Amico and Athanasios Orphanides

WP-14-24

Access to Refinancing and Mortgage Interest Rates:
HARPing on the Importance of Competition
Gene Amromin and Caitlin Kearns

WP-14-25

Private Takings
Alessandro Marchesiani and Ed Nosal

WP-14-26

6