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Private Takings
Ed Nosal
Federal Reserve Bank of Chicago
May 30, 2008

Abstract
This paper considers the implications associated with a recent Supreme Court
ruling that can be interpreted as supporting the use of eminent domain in transferring the property rights from one private agent— a landowner— to another
private agent— a developer. A potential bene…t of the ruling is that it e¤ectively eliminates a hold-out problem, i.e., the problem associated with potential
sellers withholding their property in an attempt to obtain a larger surplus. But,
when property rights are transferred via eminent domain, landowners’investments in their properties become more ine¢ cient and the level of redevelopment
may actually fall. Compared to voluntary exchange, when property rights are
transferred via eminent domain, social welfare will increase only if the hold-out
problem is signi…cant; otherwise, it will fall.

1

Introduction

A recent Supreme Court decision (Kelo v. New London) has e¤ectively given communities the green light for private takings, where local and state governments have the
authority to condemn private property for other private use. The ruling is controversial. Some observers believe the use of eminent domain in the Kelo case does not
ful…l the public-use criterion as stated in the …fth amendment to the U.S. constitution: “nor shall private property be taken for public use, without just compensation”
(my emphasis). They also might point out that the recent ruling seems to contradict
an earlier Court ruling (Hawaii Housing Authority v. Midki¤ ): “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 be void ... The court’ cases
s
I wish to thank Guillaume Rocheteau, Perry Shapiro and participants at the UCSB Takings
Conference for their comments and suggestions. 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

have repeatedly stated that ‘ person’ property may not be taken for the bene…t of
one
s
another private person without a justifying public purpose, even though compensation be paid,’.”Other observers, however, believe that Kelo ruling is fully consistent
with both the constitution and previous Court decisions. The Holmes Court ruled
in 1925 what constitutes public use should be determined by state legislatures; so if
legislatures deem that economic development of private property by private agents
provides bene…ts to the community at large— due to, say, higher employment levels
and tax base— then such a taking ful…ls the public-use criterion as stated in the constitution. Proponents of the Kelo ruling would point out that the Supreme Court
had no choice but to rule for the City of New London, since the taking was motivated
by the public bene…ts associated with economic development.
From a public policy perspective, attempting to assess whether a taking is “appropriate,” by determining whether or not it ful…ls the public use criterion in the
constitution, seems almost pointless: given the way the Court has interpreted public
use, “almost anything goes”in the sense that if a state government claims that there
is a public bene…t associated with a taking, then there is a public bene…t associated
with the taking. A more meaningful and relevant exercise would be assess the social
welfare implications associated with takings along the lines of Kelo, i.e., where the
government takes property from one private agent and gives it to another. In this
paper, I present a model where a developer has the opportunity to redevelop private property that is currently owned by another private party, a landowner. The
developer can obtain the property rights from the landowner directly— by voluntary
exchange— or indirectly— by having the government take the landowner’ property
s
rights and provide the landowner with just compensation. When the developer purchases property rights directly from the landowner, the price of the property rights
is determined as an outcome to a bargaining problem.1 Under voluntary exchange,
the developer may face the so-called “hold-out problem.”The problem here is that a
seller recognizes that the if buyer must assemble multiple plots of land, then he may
be able to extract a higher surplus for his property, by threatening to withhold or
delay its sale. It has been suggested that the hold-out problem may have negative
implications for redevelopment. If, however, the government takes the property from
the landowner, then, by construction, the hold-out problem does not arise. In this
case, the landowner receives “just compensation”for his taken property, which is paid
for by the developer.
I consider two alternative bargaining scenarios when the developer and landowners voluntarily exchange property rights. In one scenario, the developer has a …xed
bargaining weight, independent of how many landowners he bargains with. I interpret
this as a situation as one where there is no hold-out problem, since the developer’
s
share of the surplus is independent of the number of landowners he bargains with.
Here, the use of eminent domain will always lower social welfare compared to vol1

In practice, there does not exist a well-de…ned, competitive market for real estate. The selling
price for real estate is typically determined by some bargaining process between a buyer and a seller.

2

untary exchange. In the other bargaining scenario, the developer has a bargaining
weight that declines with the number of landowners he bargains with. And, for any
level of redevelopment, each landowner receives a bigger share of the surplus, compared to the “no hold-out”bargaining scenario. I interpret this as a situation where
the developer faces a hold-out problem. When the hold-out problem exists, the use
of eminent domain may increase or decrease social welfare compared to voluntary
exchange depending on the importance of he hold-out problem. Social welfare will
only increase if the hold-out problem is “signi…cant.”
The seminal economics paper on eminent domain and takings is Blume, Rubinfeld
and Shapiro (1984). This paper, and the rather sizeable literature that follows it—
e.g., Blume and Rubinfeld (1984), Fischel and Shapiro (1989), Miceli and Segerson
(1994), Innes (2000) and Nosal (2001)— focuses on issues related to optimal compensation and its e¤ect on private investment, when condemned property is converted
into a public good. The takings literature that addresses the condemnation of private
property for private use is quite small. Rolnik and Davies (2006) and Garrett and
Rothstein (2007), relying on solid economic reasoning, point out that when governments interfere with the market place, bad outcomes usually follow. Both of these
discussions, however, are not conducted within the context of an explicit model.
The remainder of the paper is as follows. The next section considers a simple
redevelopment and takings environment with one developer and one landowner. Since
there is only one landowner, a hold-out problem does not arise. In section 3, the
environment is extended so that there are many landowners and, as a result, a holdout problem may arise. The …nal section summarizes and concludes.

2

A Simple Model with One Landowner

There is a single landowner who is endowed with capital K` and property rights to
a tract of land. The landowner can invest his capital in two ways. He can invest in
a safe asset that provides a gross rate of return R and he can make an irreversible
investment x K` on his land, which gives a payo¤ of f (x), where f 0 > 0, f 00 < 0
and f 0 (0) = 1.
A developer is endowed with capital Kd . He can redevelop the landowner’ land
s
and invest in the safe asset. If land is redeveloped, then the investment x and its
potential payo¤, f (x), are destroyed. There are two states of the world for redevelopment: good and bad. The probability that the state is good is 1
. In the good
state, redevelopment spending by the developer y
y generates a payo¤ of Y and
redevelopment spending y < y gives a zero payo¤. In the bad state, any redevelopment expenditure y 0 gives a zero payo¤. Since there is only one landowner, there
is no hold-out problem.
In order to redevelop land, the developer must acquire the property rights from the
landowner. If the developer gets the landowner’ property rights through voluntary
s
exchange, then the purchase price, p, is determined by generalized Nash bargaining.
3

The developer’ generalized Nash bargaining weight is denoted by , where 0 < < 1,
s
and the landowner’ is 1
s
. Since 0 < < 1, both the landowner and the developer
have some bargaining power.
There exists a government that can condemn and expropriate, i.e., take, the
landowner’ property. When the government revokes the landowner’ property rights,
s
s
it sells them to the developer. The law requires the government provide “just compensation” to the landowner in the event that his land is taken. In this article, just
compensation will be de…ned as f (x)— the value of the property to the landowner in
the event that his property is not taken. The government must balance its budget.
Hence, if land 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 landowner is born; he invests x
in his property and K` x in the safe asset. In between dates 0 and 1, the state of
world— good or bad— is revealed. At date 1, the developer is born; he decides whether
or not to redevelop the landowner’ property. In the event that the redevelopment
s
takes place, the developer either bargains with the landowner or the government
takes the landowner’ property rights and sells them to the developer. The developer
s
spends either p or f (x) (at date 2) to acquire the property rights, where he spends
p if the he bargains with the landowner and f (x) if he gets the property rights, via
eminent domain, from the government. The developer invests (Kd y) in the safe
asset and spends y on redevelopment if he obtains the property rights to the land;
otherwise he invests Kd in the safe asset. At date 2 all investments pay o¤, payments
are exchanged, and the landowner and developer consume.
The objective of the landowner and the developer is to maximize their expected
payo¤s. The timing of the births of a landowner and the developer prevent them
from interacting before the landowner makes his investment decision. This timing
assumption is designed to re‡ the real world fact that developers enter the scene
ect
long after initial investments are undertaken.

2.1

Social Optimum

At date 0, the landowner invests x in his property. With probability , the state of the
world is bad and it is not e¢ cient to redevelop the land. In this situation the payo¤
to the landowner is f (x) + (K` x) R and the payo¤ to the developer is Kd R. With
probability (1
), the state is good and it will be e¢ cient to redevelop the land only
if the total payo¤ to redevelopment, Y + (Kd y) R + (K` x) R, exceeds the payo¤
to not redeveloping the land, f (x) + Kd R + (K` x) R; or if Y yR f (x). De…ne
a critical level of investment in land, xc , as
Y

yR = f (xc ) :

If x xc , then it is e¢ cient to redevelop the land in the good state; if x > xc , then
it is not. To make the redevelopment problem interesting, I will assume the e¢ cient
4

level of investment in land— described below— is strictly less than xc . If the e¢ cient
level of investment is greater than xc , then redevelopment is never socially optimal.
The e¢ cient level of investment in land is determined by the solution to
max (f (x) + Kd R) + (1

) (Y + (Kd

x

y) R) + (K`

x) R;

(1)

i.e., the e¢ cient level of investment in land maximizes total expected payo¤ to society. The e¢ cient level of investment in land, denoted x , is given by the …rst-order
condition to (1), which is
f 0 (x ) = R:
(2)
The social optimum is characterized by:
1. the landowner invests x at date 0;
2. the developer spends y on redevelopment in the good state; and
3. no redevelopment occurs in the bad state.

2.2

Redevelopment Under Voluntary Exchange

The developer has no incentive to obtain property rights in the bad state. In the
good state, the (date 2) payo¤ to the developer when he does obtain property rights
is Y
yR p and (date 2) the payo¤ to the landowner is p f . Note that the
developer spends y = y for redevelopment. At the time of bargaining, the investment
x is sunk for the landowner, but y is not; this is why the term “yR” shows up in
the developer’ payo¤ function and there is no comparable term in the landowner’
s
s
payo¤ function. Let S represent the total surplus associated with redevelopment in
the good state, where
S (x) = Y f (x) yR;
S 0 (x) < 0 for all x > 0 and S (xc ) = 0. If S > 0— or equivalently x < xc — then the
developer will want to redevelop the land; if S
0— or equivalently x
xc — then
he will not. If S > 0, then the price that the developer pays for the landowner’
s
property rights, p, is given by the solution to
max (Y
p

yR

p) (p

f )1

;

which is
p = f + (1

) S:

Suppose …rst that the landowner believes (correctly) that S 0 for his choice of
x; then the optimal level of investment in his property is given by the solution to
max f (x) + (1
x

) [f (x) + (1
5

) S (x)] + (K`

x) R:

(3)

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

( + (1

(4)

where “B” stands for “bargaining.”Comparing (4) with (2), note that xB > x ; the
landowner’ investment in his property is larger than what is socially optimal.
s
Suppose now the landowner believes (correctly) that S < 0 for his choice of x;
then his optimal level of investment is given by the solution to
max f (x) + (K`

(5)

x) R:

x

The solution of (5) is characterized by
f 0 (xN ) = R;

(6)

where the “N ” stands for “no redevelopment.” Comparing (6) with (4), note that
xN > xB > x . Since S 0 (x) < 0 for all x > 0,
S (x ) > S (xB ) > S (xN ) :
If S (xN ) > 0— or xN < xc — then the developer will always redevelop the landowner’
s
land in the good state. Hence, if S (xN ) > 0, then the relevant problem for landowner
is (3) and he invests xB .
If S (xB ) < 0— xB > xc — then developer will never redevelop the landowner’
s
property and relevant problem is given by (5). Hence, the landowner invests xN and
no redevelopment takes place.
Finally, if S (xB ) > 0 and S (xN ) < 0, then landowner’ level of investment
s
will determine whether or not there will be redevelopment in the good state. That
is, if the landowner believes that redevelopment will occur, then he will invest xB
and redevelopment will occur in the good state. If he believes that redevelopment
will not occur, then he will invest xN and in the good state, the developer will
have no incentive to redevelop the landowner’ land. How much will the landowner
s
invest at date 0, xB or xN ? While one might be tempted to conjecture that the
landowner will invest xB , since the surplus associated with investment xB is greater
than investment xN , the landowner may actually invest xN . This possible outcome is a
feature associated with generalized Nash bargaining: the generalized Nash bargaining
solution is not monotonic, which implies that although total surplus increases, the
landowner’ expected share (and payo¤) may decrease. So although S (xB ) > 0 and
s
S (xN ) < 0, it may be the case that
f (xN ) + (K`

xN ) R > f (xB ) + (1

) (1

) S (xB ) + (K`

xB ) R:

(7)

Therefore, if S (xB ) > 0 and S (xN ) < 0 and condition (7) holds, then the landowner
will invest xN ; if condition (7) does not hold, then he will invest xB .
6

Note that there are ine¢ ciencies associated with redevelopment under voluntary
exchange. First, the landowner always “overinvests”in his property since xN > xB >
x . Second there may be too little redevelopment. In the social optimum, it is always
e¢ cient to redevelop in the good state. If either S (xB ) < 0 or S (xB ) > 0, S (xN ) < 0
and condition (7), then redevelopment will not occur under voluntary exchange.

2.3

Redevelopment Under Eminent Domain

Under eminent domain, a government can take the landowner’ property but must
s
provide “just compensation,”f (x), to the landowner. The government then sells the
property rights to the developer for f (x). In terms of the model, eminent domain
can be interpreted as giving all of the bargaining power to the developer since the
landowner does not receive any of the surplus associated with redevelopment.
Proposition 1 Using eminent domain to transfer property rights never increases,
but can decrease, social welfare compared to voluntary exchange.
Proof. If x < xc , then social welfare can be written as
W (x) = f (x) + (1
If x

) S (x)

xR + (Kd + K` ) R:

xc , then social welfare is given by
~
W (x) = f (x)

xR + (Kd + K` ) R:

Note that if the landowner optimally chooses x = xB under voluntary exchange, then
necessarily, redevelopment occurs under voluntary exchange in the good state. Under
eminent domain, the landowner will always receive a payo¤ of f (x) + (K` x) R,
independent of the redevelopment outcome, which means that he always invests xN .
When x = xN , redevelopment may or may not occur under eminent domain depending
on whether xN < xc or xN xc , respectively. Hence, if xN < xc , we have
W (x ) > W (xB ) > W (xN ) > W (xc ) ;
since W (x) is strictly concave for all x 2 [0; xc ]. If xB < xc < xN , we have
~
~
W (x ) > W (xB ) > W (xN ) > W (xc ) = W (xc ) :
There are a number of cases to consider:
1. If S (xB ) < 0, then redevelopment does not take place under voluntary exchange
and the landowner invests xN ; in this case, eminent domain and voluntary
exchange generate the same level of welfare.

7

2. If S (xN ) > 0, then under voluntary exchange the landowner invests xB and
redevelopment occurs in the good state. Under eminent domain, the landowner
invests xN and the developer redevelops in the good state. In this case, the
overinvestment problem is exacerbated under eminent domain, compared to
bargaining— since xN > xB > x ; here social welfare is lower under eminent
domain compared to the voluntary exchange since W (xB ) > W (xN ).
3. If S (xB ) > 0 and S (xN ) < 0 and condition (7) does not hold, then under
voluntary exchange, the landowner will invest xB and redevelopment will occur
in the good state. In this case, welfare is W (xB ). Under eminent domain, the
landowner will invest xN > xc > xB ; there will be too much investment and too
~
~
little redevelopment. In this case welfare is W (xN ). Since W (xN ) < W (xB ),
the use of eminent domain strictly lowers welfare. If, however, S (xB ) > 0 and
S (xN ) < 0 and condition (7) holds, then the landowner will invest xN under
both eminent domain and voluntary exchange. Social welfare will be the same
under voluntary exchange and eminent domain.
From all of this we can conclude that the use of eminent domain will never increase
social welfare, but may lower it.

2.4

Discussion

Up to this point, the analysis seems to indicate that the recent Supreme Court decision
on Kelo v. New London is wrong-headed: eminent domain, in conjunction with just
compensation, can never increase social welfare and can only lower it. Eminent
domain, along with just compensation, e¤ectively gives all of the bargaining power
to the developer, i.e., eminent domain and just compensation e¤ectively sets = 1
in the landowner’ investment problem (3), making it equivalent to (5). It is true
s
that, absent eminent domain, the level of landowner investment x is too high, but
the use of eminent domain, along with just compensation, can only exacerbate the
overinvestment problem. Not only may there be too much investment, but the higher
level of landowner investment may result in no redevelopment at all in the good state.
The results here 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
landowner 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 eminent domain
is equivalent to a …rst-party damage rights regime. In this regime, the landlord 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 but there is less over-investment in a …rst-party injunctive rights
regime, which are precisely the results above. In addition, both parties will make
8

the same ex post decision,2 and this decision is ex post optimal. As we shall see
below, however, the nice equivalence between my results and the property rights and
nuisance literature results break down when a hold-out problem exists; redevelopment
decisions will no longer be e¢ cient, and landowners and the developer will disagree
on the level of redevelopment.
There are (at least) two ways to restore social e¢ ciency under government takings.3 One way has the government giving “more than just compensation” to the
landowner. To see this, suppose that government compensates the landowner by
transferring the entire net surplus to him; this is the solution suggested by Hermalin
(1985). Such a scheme is equivalent to the landowner having all of the bargaining
power.4 When the landowner has all of the bargaining power, then the landowner’
s
decision problem is given by (3) with = 0; the solution to this problem is x = x .
A second way to restore e¢ ciency is to give a …xed payment c— perhaps equal to
zero— to the landowner; this is the famous solution suggested by Blume, Rubinfeld
and Shapiro (1984), and further investigated by Blume and Rubinfeld (1984). In this
case, the landowner’ optimal level of investment problem
s
max f (x) + (1

) c + (K`

x

x) R;

which is x = x .
In practice, I would conjecture the neither one of these schemes would be implemented as a policy. In terms of the …rst policy— giving the entire surplus to the
landowner— there would probably be insu¢ cient support in a legislature to pass such
a law. By appealing to eminent domain, the legislature wants developers to redevelop properties; but, giving them zero surplus might have the opposite e¤ect. In
terms of the second policy, an arbitrary …xed payment c would probably not pass a
“just compensation”criterion. One might argue that compensation could be a …xed
payment, but need not be arbitrary; for example, why not set compensation equal
to c = f (x ). Such a compensation rule, however, requires intimate knowledge of
tastes and technology in order to determine x . In addition, the world is populated
with many di¤erent technologies, each requiring its own “just” …xed payment. If
c = f (x ), then policy makers would have to determine …rst-best levels of investment across many heterogeneous projects. It is not at all obvious that they have the
capacity or expertise to make these calculations. In the end, if compensation were
required to be just, in the sense that c = f (x ), then policy makers would probably
equate or correlate compensation with something they can actually observe, e.g., actual markets values. But this would not implement the e¢ cient level of investment,
x.
2

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.
3
Given that the landlord 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.
4
It is also equivalent to a second-party injunctive rights regime.

9

And …nally, parties who have their property taken by the government often claim
that they are under-compensated. In the context of the model, if a landowner is
compensated f (x) for his property rights, then there is some legitimacy to the claim
that he is under-compensated. In the real-world economy, the price for real estate is
typically determined by bargaining between a seller and buyers. The purchase price
of land via voluntary exchange, p, is always strictly greater than the level of just
compensation, f , as long as both parties to the bargain have some bargaining power,
i.e., f + (1
) S > f . So, in fact, sellers (landowners) receive a lower price for their
property via eminent domain than they could have obtained by dealing directly with
buyers (developers).

3

A Model with Many Landowners

In the model presented in section 2, the landowner has an interesting decision problem,
while the developer really doesn’ The developer simply decides whether or not to
t.
redevelop, since the level of redevelopment and the amount spent on redevelopment
are e¤ectively predetermined. In this section, the developer’ problem is made more
s
interesting and realistic by having him choose both the amount of land to redevelop
and the amount to spend on redevelopment. In addition, a hold-out problem can now
be introduced because redevelopment may involve more than one piece of property.
This richer environment can be obtained by making only slight modi…cations to the
model in section 2.
Now there are N landowners, each having property rights to their own tract
of land. The total value associated with property redevelopment is given by Y =
F (A; y), where A represents the tracts of land or properties used for redevelopment
and y is the total amount spent on redevelopment. I assume the function F (A; y) is
strictly concave and increasing in both of its arguments, with FA (0; y) = Fy (A; 0) !
1 for y; A > 0.5
The timing of events is as follows: At date 0, landowners are born and invest
x in their property and K` x in the safe asset. At date 1, the developer is born;
he decides how many properties he wishes to redevelop, A, and the total amount
that he will spend on redevelopment, y. The developer either bargains with a set
of A landowners or the government takes the landowners’property rights away from
A landowners and sells them to the developer, and the developer pays either Ap or
Af (x) (at date 2), respectively, to acquire the property rights. The developer invests
(Kd y) in the safe asset. At date 2, all investments pay o¤, payments are exchanged,
and the landowners and the developer consume.
5

One can assume, as in Nosal (2001), that only a fraction of properties are suitable for redevelopment and this is revealed only after landowners make their investments. Qualitatively speaking,
this would not a¤ect any of the results.

10

3.1

Social Optimum

Let W (A; x; y) represent the total payo¤ to society. The e¢ cient levels of property
redevelopment, A, property 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: (8)

All N landowners invest x in their property and the remainder of their capital in the
safe asset. Since A properties will be redeveloped, the total payo¤ to the landowners
investment is (N A)f (x). The developer spends y on redevelopment so the payo¤
to redevelopment is F (A; y). The developer invests (Kd y) in the safe asset. The
…rst-order conditions to problem (8) are,
N

A
N

f 0 (x) = R;

(9)

Fy (A; y) = R;

(10)

FA (A; y) = f:

(11)

and
Conditions (9) and (10) simply say that the expected returns to investment x
and spending y equal the opportunity cost of capital, R. In terms of property redevelopment, condition (11), properties continue to be redeveloped until the value last
redeveloped unit equals the (social) cost of redevelopment, which is the value of the
destroyed investment, f . Let (A ; x ; y ) represent the solution to (9)-(11).
For what follows, it will be useful to diagrammatically characterize the social
optimum in (x; A) space. The slope of the locus of points described by (9) is negative
and is given by
f 00
dA
= 0 (N A) < 0:
(12)
dx
f
Equation (9) is depicted in …gure 1 as `xN ; “`”for landowner. Note that the allocation
(xN ; 0) lies on locus `xN , where xN solves f 0 (xN ) = R, i.e., equation (6). As well,
since A ! N as x ! 0, allocation (0; N ) lies on locus `xN . The slope of the locus of
points described by equation in (11), conditional on e¢ cient redevelopment spending
y, is also negative and given by
f0
dA
=
dx
FAA

2
FAy
Fyy

< 0;

(13)

since, from (10), dy = FAy =Fyy dA and F is strictly concave. Figure 1 depicts equations (10) and (11) as dd0 ; “d ”for developer. For convenience, let Ae (x) represent the
e¢ cient amount of land redevelopment, conditional on x and assuming that spending
on redevelopment, y, is e¢ cient, i.e., equation (10) holds.
11

Social Optimum
Figure 1
Figure 2
In …gure 1, `xN and dd0 loci intersect twice; social welfare is maximized at point a ,
where the slope of `xN curve is steeper than that of the dd0 curve.6 Moving away from
the point of intersection a = (x ; A ) along either curve `xN or dd0 unambiguously
lowers social welfare. Assuming that condition (10) holds, the slope of a social welfare
indi¤erence curve is given by
(N
dA
=
dx

A) f 0 N R
:
f FA

For allocations on the `xN curve, the slope of the social welfare indi¤erence curve
is zero and for allocations on the dd0 curve, it is in…nite. A typical social welfare
~
indi¤erence curve that intersects allocation a (where A < A and x > x ) is given
~
~
g
by the ellipse denoted SW in …gure 1. Note that for allocations that are south-east
of allocation a = (x ; A ) and that lie in between (but not on) the `xN and dd0
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 xN a d0 and a line that connects the two allocations has a strictly negative
slope— such as allocations a and a in …gure 1— then the allocation that has higher
~
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.
~
6
The appendix constructs an example where the `^ and dd0 curves intersect twice— as in …gure
x
1— and demonstrates that a is the solution to problem (8).

12

3.2

Redevelopment Under Voluntary Exchange

I do not explicitly model the landowners’ hold-out problem; for treatments on this
topic, see, e.g., O’
Flaherty (1994) and Mendezes and Pitchford (2004). In this paper,
the hold-out problem— or the lack of it— will be implicitly modeled by the structure
of the various parties’ cooperative bargaining weights. For example, a no hold-out
problem is modeled by assuming that the developer’ share of the surplus— or bars
gaining weight— is independent of the number of landowners he bargains with; a
hold-out problem is modeled by assuming that the developer’ share declines with
s
the number of landowners he bargains with. (I discuss the relationship between bargaining weights and the hold-out problem in more detail below.) Of course, a more
complete treatment of the hold-out problem would generate these bargaining shares
as an equilibrium outcome to a game where landowners can threaten to withhold or
delay the sale of their properties.
Consider a generalized Nash Bargaining problem with n > 2 parties, see Osborne
and Rubinstein (1990, p. 23). The developer’ bargaining power or weight is denoted
s
0
by (A), where
0. Each landlord involved in the bargain is assumed to have
the same bargaining power, which is (1
) =A. If each landowner receives p for
transferring his property rights, then the net surplus received by the developer is
F yR pA and by each of the A landowners is p f . Hence, the total net surplus,
S, that the developer and landowners split is equal to F Af yR. The compensation,
p, that each landowner receives for transferring his property rights to the developer is
given by the solution to the generalized Nash bargaining problem with A + 1 players,
i.e.,
1

max (F

yR

pA) (p

f)

= max (F

yR

pA) (p

f )1

p

p

which is
p=f+

(p

A

f)

1
A

;

1

(14)

S:
A
Each landowner’ investment choice is given by the solution to
s
max
x

N

A
N

f (x) +

A
N

f (x) +

1
A

S (A; x; y) + (K`

x) R;

(15)

which is given implicitly by
N

A
N

+

A
N

f 0 (xB ) = R:

(16)

The developer’ choice of the level of property redevelopment, A, and spending
s
on redevelopment, y, is given by the solution to
max F (A; x; y)
A;y

pA + (Kd
13

y) R:

In light of (14), the developer’ problem can be rewritten as
s
max (A) S (A; x; y) + Kd R:
A;y

The solution to the developer’ problem is given by
s
(17)

Fy (A; y) = R;
and
FA (A; x; y) = f

0

(18)

S:

Note the following: Independent of the structure

(A),

1. for any given A, landowners invest an amount that is greater than what is
socially desirable, i.e., compare (16) to (9),7 and
2. for any given (A; x), developer’ redevelopment spending, y, is always e¢ cient,
s
i.e., equation (17).
3.2.1

No Hold-out Problem

Here, it is assumed that the developer’ bargaining weight is …xed and independent
s
0
of A, i.e., = 0. When the developer has a …xed bargaining weight, one can think of
landowners as being incapable of increasing their (collective) share of the surplus—
which is 1
— by threatening to withhold their properties. In this sense, a …xed
bargaining weight for the developer models a no-hold out problem. To reinforce the
idea that the developer’ bargaining weight is …xed, let
s
.
Note a few things. First, given the amount of investment undertaken by landowners, x, the amount of property redeveloped, A, is e¢ cient since 0 = 0 , i.e., compare
equations (18) with (11). Second, from equations (17) and (18), the developer’
s
choice of y and A does not depend directly on his bargaining strength; the choices do
depend indirectly on bargaining strength since the landowner’ choice of x depends
s
upon on the bargaining strengths and the developer’ choice variables depend on x.
s
Hence, the developer will choose A and y so as to maximize total surplus, since this
also maximizes his share of the surplus. This result mirrors that of Pitchford and
Synder (2003), i.e., conditional on the choice of x, the ex post decisions, A and y, are
e¢ cient. Diagrammatically speaking, the developer’ decision is described by locus
s
0
0
dd in …gure 2, which is identical to the locus dd in …gure 1.
7

Diagramatically speaking, the landowner’ investment locus will lie everywhere above locus `xN
s
in …gure 1, except at point (xN ; 0).

14

No Hold-out Problem
Figure 2
The locus of points that describe the landowner’ optimal investment decision,
s
(16), in (x; A) space is depicted in …gure 2 as `1 xN . From …gure 2, the equilibrium outcome aB = (xB ; AB ) is given by the lower intersection of the `1 xN and dd0
curves. It is evident that when the developer and landowners bargain over the price
of landowners’ property rights, there will be, from a social perspective, too much
investment in property, xB > x , and, as a result, too little redevelopment activity,
AB < A . (The total amount of investment associated with redevelopment, y, can be
higher than, lower than or equal to y , depending on the sign of FAy .)
The equilibrium outcome aB = (xB ; AB ) di¤ers from the socially e¢ cient levels
because landowners take account of the fact that if their property is purchased for
redevelopment, then, through the bargaining process, the purchase price will depend
positively on the amount of investment undertaken. Because of this, landowners will
tend to overinvestment in their properties.
3.2.2

Hold-out Problem

Here, it is assumed that the developer’ bargaining power, (A), falls with the number
s
of landowners, A, he bargains with, i.e., 0 < 0. Without loss of generality, I also
assume that (1) = . This bargaining scheme models the hold-out problem in a
rather direct, but simple, way. When A = 1; there cannot be a hold-out problem,
and both bargaining scenarios— the no-hold out and the hold out— give the developer
and the landowner bargaining weights of and 1
, respectively. However, as A
increases, the developer’ bargaining power strictly decreases, while the landowner’
s
s

15

Hold-out Problem
Figure 3
share of the surplus increases, compared to the no hold-out bargaining scenario. Here,
one can think of landowners as successfully holding out for higher surpluses as the
number of landowners involved in the bargain increases. It is in this sense that a
bargaining scheme where a developer’ weight (A) declines in A models a hold-out
s
problem.
The locus of points that describe the landowner’ investment decision (16) when
s
0
< 0 is depicted by `1 xN in …gures 3 and 4. Note that this locus lies below a “no^
hold out”locus for all A > 1, which is depicted in …gure 3 by `1 xN . (The equilibrium
outcome for the no hold-out problem is given by allocation aB .)
^
When 0 < 0, the level of development, A, is no longer socially e¢ cient. The developer now faces a trade o¤: although total surplus may increase with A, his share of
that surplus decreases. The end result may be that the developer “under-redevelops.”
By under-redevelop, I mean that, for a given x, the amount of redevelopment, A, is
less than what is e¢ cient, Ae (x). To see that there is, indeed, under-redevelopment,
for a large number of speci…cations of (A), note that equation (18) implies that
FA (Ae (x) ; y) < f (x)

0

S (Ae (x) ; x; y) :

(19)

This is because the second term on the right-hand side of (19) is strictly positive and,
by de…nition, FA (Ae (x) ; y) = f (x). Now note that a reduction in A always increases
16

the left-hand side of (18) since
dFA
= FAA
dA

FAy

dy
= FAA
dA

and does not increase the right-hand side of (18) if
h
i
0
2
00
d f
S (A; x; y)
( 0)
=
2
dA

2
FAy
< 0;
Fyy

0

(FA

(20)

f)

0:

(21)

The equilibrium will be characterized by under-redevelopment if inequality (21) holds,
(inequality (20) always holds). Inequality (21) will hold for sure when 00
0; it
00
also holds for some speci…cations of , where
> 0. A particularly attractive
speci…cation for along this dimension is (A) = 1= (A + 1), which that each party
to the bargain has an equal bargaining weight. When (A) = 1= (A + 1), the lefthand side of inequality (21) is equal to zero and, hence, the equilibrium will be
characterized by under-redevelopment. In what follows, I will assume that (A)
satis…es inequality (21), i.e., the developer under-redevelops.8
When 0 (A) < 0, the developer’ behavior— given by equations (17) and (18)— is
s
s
described in …gures 3 and 4 by locus d1 d01 ; the planner’ decision along these dimensions is represented by locus dd0 . The equilibrium aB = (xB ; AB ) is characterized
by the lower intersection of the d1 d01 and `1 xN loci. Compared to the social optimum, a = (x ; A ), landowners overinvest and the developer redevelops less than
A properties, which, qualitatively speaking, parallels the results when there was no
hold-out problem. But, when there is no hold-out problem, the developer’ level of
s
redevelopment is, conditional on x, e¢ cient. Although the existence of the holdout problem introduces a new ine¢ ciency, it is not necessarily the case that society
is made worse o¤ because of this.9 When a hold-out problem exists, the amount
of redevelopment is lower than an already ine¢ ciently low level when the hold-out
problem is absent. But the amount of landowner investment under the former can be
lower; this may be a good outcome because landowner investment in a no hold-out
environment is ine¢ ciently too high. Diagrammatically speaking, it is quite possible
to have social welfare higher at allocation aB , SWB , than at aB , see …gure 3. If,
^
however, the hold-out problem is more severe— meaning that under-redevelopment is
more pronounced— the “new” d0 d01 curve will shift down closer to the origin in …gure 3. In this scenario, landowner investment when the hold-out problem exists can
exceed that of when the hold-out problem does not exist. If this is the case, then,
unambiguously, social welfare will be lower when the hold-out problem exists.
8

In O’
Flaherty (1994), there exists an externality owing to the public good nature of land assembly, which results in an ine¢ ciently low level of redevelopment. Here, there exists an externality that
comes from the developer’ declining share of surplus associated with increasing levels of redevelops
ment. As in O’
Flaherty (1994), this externality generates ine¢ ciently low levels of redevelopment.
9
The theory of the second-best, tells us that this observation is not surprising.

17

3.3

Redevelopment Under Eminent Domain

Under eminent domain, landowners understand that their payo¤ will be f (x), independent of whether or not their property is taken. Therefore, the optimal behavior
for the landowner is given by f 0 (x) = R or x = xN . The locus of points that describe
the landowner’ optimal investment decision under eminent domain is given by `2 xN
s
in both …gures 2 and 4. The developer’ decision problem is to choose the level of
s
redevelopment, A, and spending on redevelopment, y, given that he must pay f for
each property, i.e.,
max F (A; y)
A;y

f A + (Kd

y) R

max S + Kd R:
A;y

The solution to this problem is
Fy (A; y) = R
and
FA (A; y) = f;
which is identical to (10) and (11), respectively. When property is transferred by
eminent domain, the developer’ decision regarding the level of redevelopment is
s
0
represented by then locus dd in …gures 2 and 4, (which also represents the planner’
s
locus along these dimensions).
The following two propositions demonstrate that although it gets the redevelopment decisions “right,” eminent domain may have some rather undesirable consequences.
Proposition 2 When there is no hold-out problem, if landowners believe that redevelopment will occur under eminent domain, then social welfare is strictly lower under
eminent domain than under voluntary exchange.
Proof. In …gure 2, the equilibrium under voluntary exchange, aB = (xB ; AB ), is
given by the intersection of the `1 xN and dd0 . The equilibrium under eminent domain,
aED = (xN ; AED ), is given by the intersection of the `2 xN and dd0 loci. Since social
welfare unambiguously falls as one moves away from a = (x ; A ) along the dd0
locus, the social welfare associated with allocation aB is strictly higher than that of
allocation aED .
Proposition 3 When there is a hold-out problem, if landowners believe that redevelopment will occur under eminent domain, then social welfare is strictly lower under
eminent domain than under voluntary exchange when the hold-out problem is not is
“signi…cant” when the hold-out problem is signi…cant, welfare under eminent domain
;
exceeds that of voluntary exchange.

18

Hold-out Problem
Figure 4
Proof. The equilibrium under eminent domain— whether or not a hold-out problem
exists— is given by allocation aED = (xN ; AED ), with associated social welfare SWED ,
see …gure 4. When a hold-out problem exists, the equilibrium allocation under voluntary exchange can lie anywhere on the locus a0B xN . Suppose the hold-out problem
is “not signi…cant”in that the curve d1 d01 intersects curve `1 xN locus above the lower
intersection of `1 xN and the SWED indi¤erence curve. In this situation, the level of
social welfare associated with allocation aB exceeds that associated with the eminent
domain allocation, aED . If, however, the hold-out problem is “signi…cant,” meaning
that curve d1 d01 locus intersects curve `1 xN below the lower intersection of `1 xN and
the SWED indi¤erence curve— this is suppressed in …gure 4— then the social welfare
associated with the eminent domain allocation, aED , will exceed that of voluntary
exchange allocation.

3.4

Discussion

When there is no hold-out problem, the conclusions regarding the use of eminent
domain mirror those of the one landlord case and the property rights and nuisance
literature (Pitchford and Synder (2003)). That is, compared to voluntary exchange,
the use of eminent domain exacerbates the landowners’overinvestment problem and
lowers social welfare. As well, the level redevelopment is lower than the socially
e¢ cient level, A ; but, given the level of landlord investment, redevelopment and
redevelopment spending are e¢ cient. When there is a hold-out problem, it is still
the case that the use of eminent domain exacerbates the overinvestment problem.
However, the amount of redevelopment is no longer e¢ cient for the level of landlord
19

investment; if inequality (21) holds, it is too low for any given x. If the hold-out
problem is not too severe, then social welfare under eminent domain is lower than
that associated with voluntary exchange. This observation is consistent with the
result that when there is no hold-out problem, i.e., the extreme case where the holdout problem is not at all severe, voluntary exchange dominates eminent domain.
If, however, the hold-out problem is signi…cant, then the use of eminent domain can actually increase social welfare, compared to voluntary exchange. In this
situation— compared to voluntary exchange— although the use of eminent domain
exacerbates the landowner’ overinvestment problem, it does increase the amount of
s
redevelopment from ine¢ ciently low levels. Hence, social welfare increases because
the latter (positive) e¤ect dominates the former (negative) e¤ect.
If policy makers could reliably and costlessly observe the magnitude of the holdout problem, then the selective use of eminent domain to transfer property rights for
redevelopment could be a social welfare enhancing policy. That is, eminent domain
would be used only when the hold-out problem is severe; otherwise, the developer
would bargain directly with landowners. Of course, the problem here is that one
cannot costlessly observe the magnitude of the hold-out problem. And one cannot
rely on developers or landowners to inform policy makers of the extent of the hold-out
problem. Developers have an incentive to claim that the hold-out problem is severe,
since the use of eminent domain implies that property can be purchased cheaper
than through direct bargaining. Landowners’would have an incentive to claim that
there is no hold-out problem and that they would bargain for the same price for their
parcel of land independent of how many parcels of land the buyer in interested in
purchasing.
In defending the state’ right to take property from one private agent and give
s
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 eminent domain 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 …gure 4 has a higher level
of redevelopment compared to allocation aB , but a lower level of social welfare. If
local governments equate higher levels employment and tax revenue— that usually
accompany higher levels of redevelopment— with a higher level of social welfare, then
allowing communities to use eminent domain to promote redevelopment can lead to
bad outcomes. For example, if local governments will use their power of eminent
domain when the hold-out problem is not particularly severe, then there will be a
negative impact on social welfare.
And …nally, it is not even obvious that the use of eminent domain will increase
the level of redevelopment. Recall that if there is no hold-out problem, then eminent
domain will have a lower level of redevelopment (and social welfare) than voluntary
exchange. By continuity, if the hold-up problem is not signi…cant, then the level of
20

redevelopment under eminent domain can be less than voluntary exchange.

4

Conclusion

One might think that a government policy that allows developers to purchase as many
properties that they want for “just”compensation would promote redevelopment and
enhance social welfare. If there is no hold-out problem, then such a policy will, in
fact, reduce both redevelopment and welfare. When a hold-out problem does exists,
such a policy need not promote redevelopment and increase social welfare. But even if
the policy does promote a higher level of redevelopment activity, it need not enhance
social welfare. It is only if the hold-up problem is signi…cant that both redevelopment
and social welfare will increase if local government’ power of eminent domain is
s
exercised.

21

5

References
1. Blume, L., Rubinfeld, D., 1984. Compensation for takings: An economic analysis. California Law Review 72, 569-628.
2. Blume, L., Rubinfeld, D., Shapiro, P., 1984. The taking of land: When should
compensation be paid? Quarterly Journal of Economics 99, 71-91.
3. Fischel, W., Shapiro, P., 1989. A constitutional choice model of compensation
for takings. International Review of Law and Economics 9, 115-128.
4. 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.
5. Hermalin, B,. 1995. An economic analysis of takings. The Journal of Law,
Economics & Organization 11, 64-86.
6. Innes, R. 2000. The economics of takings and compensation when land and its
public use value are in private hands. Land Economics 76, 195-212.
7. Menezes, F., Pitchford, R., 2004. The land assembly problem revisited. Regional Science & Urban Economics 34, 155-162.
8. Miceli, T., Segerson, K., 1994. Regulatory takings: When should compensation
be paid? Journal of Legal Studies 23, 749-776.
9. Nosal, E., 2001. The taking of land: Market value compensation should be
paid. Journal of Public Economics 82, 431-443.

10. O’
Flaherty, B., 1994. Land assembly and urban renewal. Regional Science &
Urban Economics 24, 287-300.
11. Osborne, M., Rubinstein, A., 1990. Bargaining and Markets. Academic Press.
12. Pitchford, R., Snyder, C., 2003. Coming to the nuisance: An economic analysis
from an incomplete contracts perspective. The journal of law, economics and
organization 19, 491-516.
13. Rolnick, A., Davies, P., 2006. The cost of Kelo. The Region, Federal Reserve
Bank of Minneapolis, 20 no. 2 12-17, 42-45.

22

6

Appendix

The necessary conditions for a maximum to problem (8) are given by (9), (10) and
(11). These conditions will identify a (local) maximum if the following second-order
conditions are satis…ed,
(22)
(23)

Fyy < 0
2
Fyy FAA FAy > 0
A) f 00 (x) Fyy FAA

(N

2
FAy

Fyy f 0 (x)2 < 0

(24)

Conditions (22) and (23) are satis…ed since F (A; y) is strictly concave. Condition
(24) can be rewritten as
f 0 (x)
FAA

2
FAy
Fyy

>

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

A) :

This condition has a nice interpretation; the …rst order conditions identify a (local)
maximum if the `^ curve is steeper than that of the dd0 curve, i.e., compare (12) and
x
(13).
To show that an equilibrium exists and is characterized by what is identi…ed in
the text, consider the following example. Let f (x) = x:5 and Y (A; y) = A:4 y :4 . For
these functional forms, the …rst-order conditions for problem (8) are
N A 0:5
x
= R
2N
:4A:4 y 0:6 = R
:4A 0:6 y :4 = x:5

(25)
(26)
(27)

The decision of a landlord is given by (25) and can be rewritten as
N A
= x:5 ;
2N R
this function is represented as `^ in …gure 1. The decision of the developer is given
x
by equations (26) and (27), which can be combined to read
10

:4 6 R

2
3

A

1

= x:5 :

Note that A ! 1 as x ! 0 and x ! 1 as A ! 0. This function is represented as dd0
in …gure 1. Together, the …rst-order conditions (25), (26) and (27) can be rewritten
as the quadratic equation
A2 + AN KN = 0;
2

1

where K = (0:8) (0:4) 3 R 3 . The solution to this quadratic is
p
N (N 4K)
A=N
:
2
23

If N > 4K, there will be two solutions, as depicted in …gure 1. If N > 4K, then the
maximum is given by allocation given by point a , since at point x the slope of the
`^ curve is steeper that that of the dd0 curve, (at point b the slope of the dd0 curve is
x
steeper that that of the `^ curve.) If N
x
4K, then the solution is A = N . In the
text, the more interesting case of N > 4K is assumed.

24


Federal Reserve Bank of St. Louis, One Federal Reserve Bank Plaza, St. Louis, MO 63102