Takings, the exit option and just compensation

ELSEVIER

Takings, the Exit Option and Just Compensation

SHUBHA G H O S H

Oklahoma City University School of Law, Oklahoma City, Oklahoma

I. Introduction

Even though the Fifth Amendment of the Constitution mandates the payment of just compensation for the taking of private property for a public use, economists have traditionally agreed that just compensation leads to inefficiency if capital and insurance markets are perfect, governments do not suffer from fiscal illusion, and the takings decision is based on social welfare maximization and not the result of rent seeking. Unless any of these imperfections exist, compensation for takings cannot be justified on efficiency grounds but could be justified through fairness or distributive goals. 1

The traditional economics position stands in stark contrast to the views of scholars like Richard Epstein and the recently expansionist reading of the takings clause by the U.S. Supreme Court. Although the traditional economics view allocates the property right to the government for its exercise of its eminent domain power, Epstein advocates allocating the property right to landowners and protecting the right through a property rule. For example, Epstein would prescribe full compensation for almost all government regulatory activity. 2 The conclusion of this paper resides in the middle ground between these two viewpoints: The government can take as long as it pays something, but an amount less than full compensation. This position can be interpreted as a liability rule protection for the governments exercise of eminent domain. 3

The author would like to thank A. Mitchell Polinksy and two anonymous referees for extensive c o m m e n t s on an earlier draft o f this paper.

1The most recent paper to discuss these issues is W.A. Fischel and P. Shapiro, "A constitutional choice mode l o f compensat ion for takings," 9 International Review of Law and Economics 115 (1989), which establishes results on how public decision making through majority voting will necessitate compensat ion for takings. Professor Fischel elaborates on the political e c o n o m y o f the takings problem in his exce l l ent book Regulatmy Takings (1995). For a discussion o f the points concern ing eff icient markets, see Lawrence Blume and Daniel L. Rubinfeld, "Compensation for takings: An e c o n o m i c analysis," 72 California Law Review 569 (1984) and Lawrence Bhune, Daniel L. Rubinfeld, and Perry Shapiro, "The taking of land: When should compensat ion be paid?," 99 QuarterlyJouTvzal of Economics 71 (1984). A discussion o f fairness justifications for takings can be found in William A. Fischel, The Economics of Zoning Law 150 (1985).

2Richard Epstein, Takings (1985). SThis distinction be tween property and liability rules is taken from Guido Calahresi and Douglas Melamed,

"Property rules, liability rules, and inalienability: One view o f the cathedral," 85 Harvard Law Review 1089 (1972). Liability rule protect ion for e m i n e n t domain is also prescribed by Blume and Rubinfeld (1984), supra note 2.

International Review o f Law and Economics 17:157-176, 1997 © 1997 by Elsevier Science Inc. 655 Avenue o f the Americas, New York, NY 10010

0144-8188/97/$17.00 PII S0144-8188 (97) 00001-X

158 Takings, the exit option and just compensation

A strong criticism of the economic approach to the takings p rob l e m is that the t radi t ional economic models of takings do not consider "demoral iza t ion costs," as def ined by Frank Michelman. 4 Demoral izat ion costs represent the costs to polit ical par t ic ipat ion and mora le associated with the failure to compensa te for takings. Mich- e lman ' s app roach to the takings p rob lem, which can be categorized as a modi f ied uti l i tarian one, bases the jus t compensa t ion quest ion on a compar ison of the benefits of government act ion with demoral iza t ion costs and se t t lement costs, the lat ter represent- ing the costs of compensa t ing the victims of a taking. Specifically, Miche lman concludes that governments should compensa te for the taking of private proper ty when the ne t benefits of the government action are greater than the se t t lement costs bu t the settle- men t costs are less than the demora l iza t ion costs. 5

Economic models have typically ignored demoral iza t ion costs because of the impos- sibility of quantifying them. As a result most economic models implicitly assume that demora l iza t ion costs are zero. This assumption provides a way to reconci le the economic pred ic t ion of no compensa t ion with Michelman 's conclusion. If demora l iza t ion costs are zero, then se t t lement costs can never be strictly less than demora l iza t ion costs and Michehnan ' s condi t ion for compensa t ion can never be satisfied. Al though the assumption of zero demoral iza t ion costs permits reconci l ing Michelman ' s prescr ipt ion with that of t radi t ional economists, this assumption has rarely been exp lored in the economics l i terature.

This pape r examines one possible way to justify the t radi t ional assumption of zero demora l iza t ion costs: the possibility of exit by regula ted bodies. Miche lman ' s demoral - ization costs arise essentially from the p rob lem of majori ty excess over minori ty interests. If the costs of major i tar ian decisions that regulate or take private proper ty interests is too high, Miche lman would r e c o m m e n d that compensa t ion be paid for a government taking. However, majori ty excess can be avoided th rough exit. Regula ted entities, such as developers, can simply move to a jur i sd ic t ion that offers more favorable regulat ion. Of course exit is not an opt ion if the costs of migra t ion are too high. But this observation suggests that demoral iza t ion costs should be equa ted with the costs of exercising the exit opt ion. If my a rgumen t about the exit-option is correct, the tradi- t ional economic models have implicitly been assuming that exit costs, and therefore demora l iza t ion costs, must be relatively low.

In a provocative article, Vicki Been has taken the s trong posi t ion that the possibility of exit militates against jus t compensa t ion for takings. 6 Her a rgumen t contradicts the ho ld ing of Nollan v. California Coastal Commission, 7 in which the Supreme Court adop ted a strict scrutiny s tandard for the review of exactions p laced on land developers by local municipali t ies. The Court ' s decision in Nollan reflects a concern with oppor tun i sm by munic ipa l bodies to exact private p roper ty from land developers. Been, on the o the r hand, is conce rned with the ability of land developers to bargain effectively with the state. Been 's posi t ion also contrasts with the view that compensa t ion is requi red to

4Frank 1. Michehnan, "Property,, utility, and fairness: Comments on the ethical ffmndations of just cmnpensat ion," 80 Harvard Law Review 1165 (1967).

5This part icular formulat ion is taken f rom William A. Fischel and Pert"/Shapiro, "Takings, insurance, and Michel- man: Commen t s on economic interpretat ions of 'just compensa t ion ' law," 17Journal of Legal Studies 269-293 (1988).

GVicki Been, "Exit as a constraint on land use exactions: Rethinking the unconsti tut ional conditions doctrine," 91 Colorado Law Review 473 (1991). For a critique, see Stewart Sterk, "Competi t ion a m o n g nmnicipalit ies as a constraint on land use exactions," 45 Vanderbilt Law Review 831 (1992).

7107 S. Ct. 3141 (1987).

S. GHOSH 159

ensure efficient regulat ion, a view endor sed by Thomas Merrill. s Al though, according to Merrill, cour t -manda ted payment of compensa t ion by legislative bodies is one way to make legislatures internal ize the costs of exercising the taking power, the exit opt ion, according to Been, provides a strategy that developers can use to reach an efficient barga in ing equi l ibr ium with the state. The purpose of this pape r is to provide a formal economic analysis of these confl ict ing doctr inal positions.

The controversy over compensa t ion for takings and the exit opt ion has a historical as well as a doctr inal d imension. The historical l i terature on the prevalence of jus t compensa t ion for takings contains a debate between Morton Horowitz, who argues that compensa t ion for takings by state governments was u n c o m m o n pr ior to the Civil War, and James Ely, who points to several examples of compensa t ion for the exercise of the state's eminen t domain in several contexts. Accord ing to Horowitz, colonial Massachu- setts seems rigidly to have followed the pr inciple of jus t compensa t ion in road building, and that the majori ty view at the time of the Amer ican revolut ion was that jus t compensat ion was a " ' b o u n t y . . . given by the State ' out of kindness and no t out of just ice. ''9 Ely responds:

The authority of government to take private property for public use by eminent domain was well established in the colonial and Revolutional T periods. Typically land was taken for the erection of public buildings and the construction of roads. Eminent domain was also used for the purpose of encouraging economic devel- opment. With limited exceptions, the usual practice was to compensate the landowners.l°

Al though this pape r does not add directly to the historical record , the economic analysis o f this pape r provides a basis by which to de te rmine the rat ionali ty of compensa t ion for takings by add ing an over looked d imens ion of the takings problem: state compet i t ion and the exit opt ion. This addi t ional d imens ion extends the applicabil i ty of t radi t ional economic analyses of the takings p rob lem to the historical deba te about the applica- bility of the jus t compensa t ion r equ i remen t to state governments .

The doctr inal and historical l i terature that I have cited so far focuses singly on takings by state ra ther than federal governments . On the surface, the quest ion of the effect of an exit op t ion on jus t compensa t ion seems to be appl icable only to takings by state governments . But the quest ion also arises in the context of federal regulat ion. For example , Justice O ' C o n n o r ' s concur rence in R u c k e l s h a u s v. M o n s a n t o al focused on the effect of federal envi ronmenta l disclosure rules on the re locat ion of U.S. companies overseas:

It is i m p o r t a n t to d i s t ingu i sh at the ou t se t pub l i c d i sc losure of t r ade secre ts f rom

use of these secre ts en t i re ly wi th in EPA. I n t e r n a l use may u n d e r m i n e M o n s a n t o ' s compe t i t i ve pos i t ion wi th in the U n i t e d States, bu t i t leaves M o n s a n t o ' s pos i t ion in

fo re ign marke t s u n d i s t u r b e d . . . . [T ]he l ikely i m p a c t on fo re ign m a r k e t pos i t ion is

one tha t M o n s a n t o wou ld we igh w h e n d e c i d i n g w h e t h e r to s u b m i t t rade secre ts to EPA. 12

~Thomas Merrill, "The economics of public use," 72 Co,'nell Law Review 61, 115-116 (1986). 9Morton J. Horowitz, The Transformation of American Law: 1780-1860 63, 65- 66 (1977). WJames W. Ely, "'That due satisfaction may be made:' the Fifth Amendment and the origins of the compensation

principle," 36 American Journal of Legal History 114 (1992). 1~467 U.S. 986 (1983). 42467 U.S. at 1021.


I I I I t

I r I I I I I I I

I I I I I

I I I I t

I I I I I

' I 1 I I I I I I

r I I I

I I I I I I

I I I I I I I I

F16. 1. Stage one: capital investment; stage two, takings policy announced; and stage three, migration and execution of takings policy.

In Ruckelshaus, the cour t he ld that a legal r equ i r emen t to disclose a t rade secret could be a compensab le taking. In he r concurrence , Justice O ' C o n n o r was squarely raising the issue of the exit opt ion in the takings context and her conclusion that compensa t ion should be paid for Congressional regula t ion even with the possibility of exit is consistent with the spiri t o f this paper .

The organizat ion of this pape r is as follows. The next section presents an extension of the mode l of takings by a Pigovian government deve loped by Fischel and Shapiro. I show that Fischel and Shapiro ' s mode l is equivalent to a two-stage game in which landowners make capital investments in the first stage and the legislature chooses how much land to take in the second stage. I then ex tend the two-stage game to include two jur isdic t ions each with its own legislature, which compete in the exercise of the takings power. Al though the in t roduc t ion of ano the r jur i sd ic t ion does not substantively al ter Fischel and Shapi ro ' s model , I also in t roduce a third stage to the game in which landowners make a migra t ion decision to move to that jur i sd ic t ion that offers the more favorable regulatory climate. The in t roduct ion of the th i rd stage, which explicitly captures the exit opt ion, does substantively al ter Fischel and Shapi ro ' s mode l and provides a basis for jus t compensa t ion for takings. In the th i rd section, I discuss three extensions of nay analysis to include o ther forms of government finance, thin markets, and government decis ion making th rough major i tar ian rule. In the final section, I summarize the results and suggest future avenues of research.

II . Takings as a Multistage Game: An Extension o f Fischel and Shapiro

In this section, I analyze the mode l of takings in two steps. First, I analyze a version of Fischel and Shapiro ' s mode l as a two-stage game. I then ex tend the mode l to allow for the exit opt ion and compet i t ion between states. The extensive form game dep ic ted in Figure 1 illustrates the e lements of the model . The game consists of three stages. In the first stage, landowners in each state choose the level of capital investment. In the second stage, the legislature in each state announces a takings policy. In the third stage, landowners migrate in response to the state's a n n o u n c e d takings policy, and the state executes its policy after migra t ion has occurred. As I explain in greater detail below, Fischel and Shapiro 's mode l is a special case of this three-stage game in which there is only o n e State.

S. GHOSH 161

N

N, =

A i =

X i =

A . ) = Q ( A ) =

The following notation 13 will apply to each version of the model:

Total populat ion of the economy; Total populat ion in state I, where I = 1, 2 and N 1 + N 2 = ~, Total number of parcels taken by the legislature in state L Each landowner is assumed to own one parcel; Capital invested in state I by a typical landowner; Output as a function of capital invested. This function is identical in each state; A concave function capturing per capita value of public good produced by government using A;

r = Exogenous market interest rate; s = Proport ion of output f( • ) that is compensated to each landowner whose parcel

of land is taken.

The model will be analyzed in terms of the following variables:

Pi = Ai/N, the number o f landowners in s t a t e /whose parcel land is taken as a propor- tion of the total population;

n = N 1 / N , the propor t ion of the total populat ion who lives in state 1. (1 - n) is the propor t ion living in state 2.

I will be making the usual assumption that landowners are profit maximizing in their choice of capital investment and migration decision. I will also be assuming that each landowner is atomistic. Therefore, each landowner does not take into consideration the effect of his decision on other landowners. Specifically letting x_ 1 represent the capital investment o f each of the other landowners, the total amount of compensat ion that would be paid is s" A i ' f ( x - i ) . In state i, each landowner then will be charged his equal share of the total bill, or s" A i / N i • f(x_i). This expression equals, after normalization by N, s ' p l / n "f(x_i) in state one and s ' p 2 / ( 1 - n) -f(x_i) in state 2.

In the special cas e where there is only one state, the takings problem can be described as follows. In the first stage, each landowner chooses the level of capital investment to maximize expected profit, holding the probability o f a taking and the compensat ion ruled fixed. The expected profit function is:

p " s ' J ( x ) + (1 - p ) " f ( x ) - r" x + Q ( p " N) - p " s" f ( x _ i ) . (1)

The elements of the expected profit function can be interpreted as follows. The first expression represents the output to the landowner in the event his land is taken discounted by the probability of a taking. The second expression represents the output to the landowner in the event his land is not taken. The third expression is the cost of capital. The fourth is the per capita benefit from the public good. Finally, the fifth element is each landowner 's per capita share of the cost of compensat ing all the landowners whose land has been confiscated. The quantity xi represents the amount of capital invested by the other landowners, which is independent of the amount of capital invested by the typical landowner. Because landowners are atomistic in this model, each individual landowner 's choice of x does not affect x i.

In the second stage of the game, the legislature makes its decision on how much to take to maximize the net value of the public project. The total output from the public

lSFor the purposes of comparison, I follow the notation used by Fischel and Shapiro, see note 1.


project is given by N" Q(A). The total cost is the loss in value from the confiscated land or A "f(x). The ne t value of the public project is

U" [Q(p" N) - p "f( x)], (2)

after making the appropr ia t e substi tutions for A. In this paper , I follow Fischel and Shapiro and call this the objective funct ion for a Pigovian government .

The two-stage game can be solved by backward induct ion. In the second stage of the game, the legislature chooses p, taking the capital investment of the landowner as given. This maximizat ion p rob lem yields the following first-order condi t ion:

Q' " U - f ( x ) = 0. (3)

This implicit ly defines the react ion funct ion p(x). In the first stage each landowner takes the react ion fnnct ion p(x) as given. However since each landowner is small relative to the rest of the economy, p ' (x) will equal zero. Therefore , the first-order condi t ion for the landowner ' s maximizat ion p rob lem is

(1 - p - p , ) ' f ( x ) = r. (4)

Because each landowner is identical , in equi l ibr ium each landowner will choose the identical level of capital investment x.

The two-stage version of the mode l has a s t rong pred ic t ion for the opt imal choice of the compensa t ion rule. Following Fischel and Shapiro, suppose a cour t or a constitu- t ional convent ion is to choose the opt imal level of s to maximize the ne t revenues of landowners. In equi l ibr ium, after substi tut ing for the maximizing values p and x, the cr i ter ion funct ion faced by a cour t or a convent ion would be:

(1 - p ) ' J ( x ) - r x + Q ( p " N ) . (5)

The first-order condi t ion for the choice of s is

[N" Q' - j ~ x ) ] " p , + [(1 - p ) ' f ( x ) - r ] - x , = 0, (6)

where p, and x, are the effects of a change in s on the opt imal choices of p and x. Substi tut ing the first-order condi t ions for the legislature and the landowners, this expression simplifies to

- p " s ' j e (x ) • x~ = 0. (7)

As Fischel and Shapiro show, x~ > 0. Therefore , the court ' s choice of s is maximized when s equals 0. In o the r words, economic efficiency as measured by wealth maximization would require zero compensat ion , consistent with the results of Blume, Rubin- feld, and Shapiro.

The t radi t ional result of no compensa t ion is very sensitive to the structure of the game. In the next two subsections, I p resen t extensions of the basic two-stage game by first in t roduc ing the exit opt ion as the third stage of the game and by next in t roduc ing compet i t ion between states.

Modeling Exit

There are several possible ways to mode l the exit opt ion. In this section, I discuss the implicat ions of different mode l ing strategies. To bet ter facilitate the discussion, I will first clarify two major factors that drive the results demons t ra t ed in the previous section.

S. GHOSH 163

The first factor is the sequencing of the moves of capital investment and takings. In the Fischel-Shapiro model , it is impor t an t that landowners move before the government does. If the gove rnmen t moves first, it must take into considera t ion the effect of its takings decis ion on the capital investment of the landowner. Specifically, the first-order condi t ion becomes

Q' . N - J(x) - p . f ( x ) " x:o = 0. (8)

Substi tut ing this expression into the f irst-order condi t ion of the social p lanner , equa- t ion (6), yields

p ' f " x p ' p ~ - p" s ' f " x~= 0. (9)

Therefore , if the government moves first, the first-order condi t ion is no longer necessarily sat isf ied at s equals zero o r at s equals one. Jus t c o m p e n s a t i o n that is non-ze ro will in gene ra l be a p p r o p r i a t e .

This result should not be too surprising. If the government ' s use of takings can affect capital investment, compensa t ion will be n e e d e d to address the possibility of moral hazard on the par t of the government . The r equ i r emen t of compensa t ion will l imit the government ' s a t tempt to change the level of capital investment by landowners.

The pred ic t ion (and hence prescr ipt ion) about jus t compensa t ion will d e p e n d upon the sequencing of moves between the landowner and the government . Arguably, the game in which the landowner moves first seems to bet ter fit our intuitive mode l of the takings problem: The landowner has sunk capital investment into a deve lopmen t project when the government changes the rules or exercises the eminen t domain power. However, this intuitive mode l may not fit reality. As p roponen t s of the exit opt ion demonst ra te , the government does not necessarily have the last move. The landowner could still take his capital investment elsewhere. But as I argue in greater detail below, sequencing is not the ent i re story. Even if landowners move last, the a rgumen t for jus t compensa t ion will still d e p e n d upon the mobil i ty of capital after the government has a n n o u n c e d its taking policy.

A second factor that is driving the economic pred ic t ion of zero compensa t ion is the implici t assumption of full capitalization. In the first stage, the landowner was assumed to know the probabi l i ty of a taking. But suppose the landowner acted solely on his bel ief that a taking would occur. Call this belief, b. Then the landowner ' s investment will be based on the following first-order condi t ion:

(1 - b + b . s ) . f = r. ( 1 0 )

In this variat ion the landowner is still moving first so that the legislature 's f irst-order condi t ion is not al tered. However, the social p lanner ' s f irst-order condi t ion becomes

[ ( b - p) - b" s ] ' f • x, = 0. (11)

In this case zero compensa t ion does not satisfy the first-order condi t ion unless b equals p, in o ther words unless the landowner has rat ional expectat ions and the rental rate of capital fully capitalizes the legislature 's actions. In fact without full capitalization, full compensa t ion will be opt imal as long as b > 0. To see this, note that the f irst-order condi t ion for max imum to occur at s = 1 is

[ ( b - p ) - b ' s ] ' f ' x ~ < O . (12)


If s equals one the left-hand side reduces to p" f • xs, which is positive for all positive p. Therefore , if the l andowner does not have rat ional expectat ions and full capital izat ion does not occur, full compensa t ion may be optimal . 14 Of course rat ional expecta t ions and full capital izat ion are c o m m o n assumptions. But as this discussion shows, the assumption is crucial for the zero compensa t ion result.

These observations are directly relevant to the mode l ing strategy for the exit opt ion. If the exit op t ion is to really upset the t radi t ional economic pred ic t ion of zero compensat ion, the exit opt ion has to affect e i ther the sequencing of moves or the full capital izat ion assumption. One immedia te impl ica t ion is that exit must occur after the gove rnmen t moves. If exit occurs before and all o ther e lements o f the mode l remain the same, then exit only serves to equalize the ne t re turns between the two regions. The zero compensa t ion result will no t be affected. Therefore , for exit to make a difference, it must occur after the government has moved.

If landowners have the last move, the quest ion of capital mobil i ty still exists. We can imagine two possibilities, descr ibed as a story abou t (David) Lucas. Suppose Lucas plans to bui ld on the South Carol ina coast. He has not sunk any investment yet in South Carolina, bu t has made contracts with bui lders and suppliers in South Carolina. After the contractual outlays are made, South Carol ina announces p roposed bui ld ing restrictions on coastal proper ty . Lucas as a result decides to move the project to Nor th Carolina, but still maintains his contracts with bui lders and suppliers in South Carolina. This cor responds to the case where capital is fully mobi le upon the exit of the landowner. Even though Lucas has exi ted and moved last, this scenario obviously does no t require compensa t ion for Lucas: He has no t had anything taken f rom him except the rents that may have accrued if he could have bui l t un regu la ted in South Carol ina ra ther than Nor th Carolina, his second choice. Fur the rmore , South Carol ina does no t need to pay compensa t ion to people like Lucas to fully internal ize the cost of its taking power. The cost has already been in ternal ized because of lost potent ia l tax revenue from Lucas ' investment in South Carolina.

The scenario jus t descr ibed captures Vicki Been 's a rgumen t about exit and compensation. If capital is fully mobile , then compensa t ion will not be necessary. But as this version of the Lucas story shows, the case for compensa t ion is trivial. Lucas has no t sunk any investment in South Carolina; no cour t would grant him s tanding to sue the state of South Carol ina u n d e r the takings clause. This result in fact makes intuitive sense.

The intui t ion can be suppor t ed by economic analysis. If capital is fully mobi le , then rental rates of capital will be equal ized across all regions. Fur the rmore , if all rental rates capitalize the government ' s takings activity, then it doesn ' t mat te r at the margin whether Lucas invests in Nor th Carol ina or South Carolina. To see the effects of full capital mobil i ty on the takings game, cons ider Figure 1 which depicts an ex t ended version of the game discussed above. In the first stage, the l andowner invests capital in his region. In the second stage, the government announces the takings decision. In the third stage, the landowner moves his capital to a more favorable climate. The third stage essentially serves to integrate all the regions. Once all the regions are integrated, however, the game reduces to the two-stage version of the takings game and the zero compensa t ion result follows.

For exit to be interes t ing not only must it occur after the government moves, but it

14Note that if b is greater than zero and equal to p, then both s = 0 and s = 1 will be local maxima. A full

consideration o f all the parameters in the social p lanner ' s objective funct ion would have to be considered to de termine which is the global maximum.

S. GHOSH 165

must also occur with capital that is not fully mobile. In fact, this depic t ion cor responds be t te r to our intuitive priors about the takings problem. Lucas has bough t a house on the South Carol ina coast that he in tends to develop. South Carol ina imposes develop- m e n t restrictions. Lucas could move to Nor th Carol ina and develop there. But should he be compensa ted? And if so, for what? Should the house be viewed solely as a sunk cost i r relevant to his exit decision? These questions become relevant only if Lucas has an exit op t ion and has sunk his investment in immobi le capital.

The final mode l ing issue is that of descr ibing the env i ronment to which Lucas and o the r landowners can move. In this p a p e r I will consider two possibilities: exit to an un regu la t ed f ront ie r in which the government does not exercise its takings power and exit to a regula ted state in which the government does take. In each case I will be assuming that exit occurs after the government acts and that part of the landowner ' s capital is immobile . The pr incipal result is that the s t rong economic pred ic t ion of zero compensa t ion no longer holds.

The Exit Option and the Frontier Model of Takings

Suppose that residents of the state descr ibed in the two-stage mode l have the op t ion of exit ing after the state has a n n o u n c e d its takings decision and moving to an unregu la ted f ront ie r where they can settle with their capital investment. The in t roduc t ion of this strategy changes the mode l in three ways. First, a third stage is a d d e d to the game in which the migra t ion equi l ibr ium is de te rmined . Second, the government ' s objective funct ion, which is def ined in pe r capita terms, must take into account the possibility of exit. Third , the possibility of migra t ion affects the capital investment decision in the first stage of the game.

The first stage of the game must be modi f ied to take into considera t ion the possibility of exit in the th i rd stage. Specifically, if p is the probabi l i ty of a taking without the exit opt ion, the probabi l i ty with the exit opt ion must take into considera t ion the fact that the size of the popu la t ion may change. If N is the size of the total popula t ion initially res iding in the state, then let n be def ined as the p ropor t ion of the ent ire popu la t ion res iding in the state after migra t ion and 1 - n be the p ropor t ion residing in the frontier . Therefore , p/n must be the probabi l i ty of a taking. The objective funct ion in the first stage of the game becomes

( 1 - p / n ) - J ( x ) + p / n ' s ' J ( x ) - r ' x + Q ( p ' N ) - p / n ' s ' A x ) , (13)

where p must be less than or equal to n. This inequali ty places ano the r const ra int on the model , which is discussed more fully in the Appendix .

The government ' s objective funct ion must take into account the possibility of migration. Using the same nota t ion f rom the previous section, the pe r capita value of the publ ic pro jec t is Q(p" N). The total value of the project is n" N" Q(p" N). Because the government ' s objective is to maximize the total value of the project ne t of the lost ou tpu t of confiscated land, the objective funct ion is

N" In" Q(p" N) - p'j '(x)], (14)

which the government maximizes with respect to p taking x, N, and n as given. It should be emphas ized that "n" is a funct ion of all the parameters of the mode l that is d e t e r m i n e d in the th i rd stage of the game. Note that u n d e r full capitalization, the gove rnmen t takes x as given in its opt imizat ion problem. There fo re the f irst-order condi t ion for the choice of p is given by


np" Q + n ' N " Q' - f ( x ) = 0, (15)

where n is derived from the react ion funct ion for n in the third stage of the game. U n d e r condi t ions discussed in the appendix , the f irst-order condi t ion for the government ' s p rob lem becomes:

n ' N " Q' - j ' (x) = 0, (16)

which is analogous to the legislature 's f irst-order condi t ion in the mode l without exit. Finally, migra t ion occurs in the third stage of the game. I assume that at the

beg inn ing of the game all landowners reside in the regula ted state and that the unregu la ted f ront ier is unpopula ted . Once the government reveals how much it in tends to take in the second stage. The landowner has two options: to e i ther remain in the regula ted state and adjust his capital investment or a ba ndon the regula ted state, move to the frontier , and pick a new level of capital investment. If he remains in the regula ted state, u n d e r the assumption of perfect capitalization, the landowner will simply retain the level of capital chosen in the first stage of the game. If he moves, he chooses the capital stock x to maximize f (x ) - r" x. Call the profi t maximizing level of capital investment in the unregu la ted f ront ier x u. In equi l ibr ium profits in the two regions will be equal ized net the costs of migrat ion, which will equal c" (1 - n). The equi l ibr ium condi t ion for migra t ion is given by

( 1 - p / n ) ' f ( x ) - r ' x + Q ( p ' N ) = J ( x , ) - r ' x , , - c . ( 1 - n ) . (17)

This expression defines n( • ), the funct ion the government takes as given in the second stage of the game. ~5

I discuss the technical aspects of the mode l in greater detail in the Appendix . What is impor tan t to emphasize is that the possibility of exit alters the conclusion that zero compensa t ion is efficient.

RESULT 1: In the model of takings with exit to an unregulated frontier, the optimal level of compensation no longer occurs at s = O.

This result follows f rom the objective funct ion of the social p lanner , modi f ied to take into account of both jurisdict ions. Once again it is assumed that the social p l anne r cares about total re turns to all landowners. The p lanner ' s objective funct ion is

N" { n - [ ( 1 - p / n ) ' J ( x ) - rx + Q(p" N)] + (1 - n)" I f ( x ) - r" x]}, (18)

which the p l anne r maximizes with respect to s. Taking the derivative of this expression with respect to s and substi tuting the equi l ibr ium condi t ion for migra t ion and the first-order condi t ions f rom the landowner ' s and legislature 's p roblems yields the following first-order condi t ion for the choice of s in the interior:

- p ' s / n ' f ( x ) ' x ~ + [ p l / n Z ' J ( x ) - Z ' c ' ( 1 - n ) ] ' n ~ = O , (19)

15This condition is similar to the equilibrium condition for migration used in Joseph E. Stiglitz, "Public goods in open economies with heterogeneous individuals," in Locational Analysis of Public Facilities (].F. Thisse and H.G. Zoller, eds.), pp. 55, 58 (1983) and in Dennis Mueller, Public Choice II, p. 157 (1990). These two authors, however, express the equilibrium condition in terms of utility levels rather than profits.

S. GHOSH 167

where xs and ns are both greater than zero. As can be seen f rom the first o lder condi t ion , the opt imal level of compensa t ion occurs ne i the r at s equals 0 nor at s equals 1.

The intui t ion for this result rests on how popu la t ion size affects the spreading of the takings risk among all landowners. If there is no compensat ion , all landowners would migrate to the unregu la ted jur isdic t ion, result ing in a loss of the publ ic project in the regula ted jur i sd ic t ion and a loss in the ability of the takings risk to be spread across all landowners. If there is full compensat ion , no landowners will migrate, which will result in the takings risk to be spread across the ent ire popula t ion . Because the takings risk is spread broadly, the incentive will be for the legislature to take too much. Social op t imum, which is def ined in terms of the c o m b i n e d profits of the regula ted state and the frontier , occurs somewhere between full compensa t ion and no compensa t ion to balance the effects of loss in the publ ic project and the spreading of the takings risk.

It may seem unintuit ive to speak of risk spreading when all landowners are assumed to be risk neutral . But the spreading of risk occurs th rough a change in the probabi l i ty of a taking occurr ing. In the modi f ied model , the probabi l i ty of a taking is p /n , where bo th p and n are endogenous and are functions p (n, s) and n(p, s), respectively. As n changes, the probabi l i ty of a taking changes. In the extreme, as n approaches zero, the risk that any one landowner will have his land taken increases. Similarly, as n approaches one, the risk diminishes. Therefore , migra t ion enters into the mode l essentially as a means of spreading the risk of a taking within a jur isdict ion.

The mode l p resen ted in this section in t roduced a second jur isdic t ion, that is unregulated. In the next section, I general ize the mode l fur ther to allow for two states that compete in the exercise of the respective taking power.

State Competition and Takings

Consider now the more genera l game in which there are two states and a third stage in which the al locat ion of popu la t ion between the states is de te rmined . In stage one, each landowner in each state still initially picks the level of capital investment. In this game, the expec ted profi t funct ion is compl ica ted by the fact that the popu la t ion of the state can change, causing a change in the value of both the per capita benefi t of the publ ic good and the per capita costs of compensat ion . Fur the r compl ica t ing the analysis is that the capital investment in the two states can differ. Taking into cons idera t ion all of these changes, the expec ted prof i t funct ion can be derived as follows for a landowner in state one.

First, the probabi l i ty of a taking in state one is given by A a / N P This expression can alternatively be written as p l / n l after normal iz ing by the size of the ent ire popula t ion N.

In the second stage of the game, each legislature decides how much land to take. This involves a choice of the variable A i, which has been normal ized in this mode l by the size of the ent i re popula t ion N t o Pi. Each legislature seeks to maximize the ne t value of the public good, which is given by the following expression:

N i. Q(A~) - A i . f (x i ) . (20)

Normal iz ing by the size of the ent i re popula t ion N, the legislature 's objective funct ion is

N" [ni" Q(Pi" N) - pi. f(x~)], (21)


which the legislature maximizes with respect to p. The legislature 's objective funct ion differs in two ways from that in (2). First, the funct ion depends on ni, which is endogenous and is de t e rmined by the migra t ion decision in the third stage of the game. As I show below n i is a funct ion of Pa, P2, and s. Therefore , the objective funct ions for the legislatures are in t e rdependen t , and the solut ion to the takings p rob l e m will d e p e n d upon the game theory solut ion concept , which for the purposes of this p a p e r will be the Nash equi l ibr ium concept .

Finally, the equi l ibr ium al locat ion of popu la t ion between the two states will be de te rmined . I will mainta in the same assumption about mobil i ty as in the mode l of the unregu la ted frontier: Landowners can e i ther reside in their native state and adjust their level of local capital investment or move to the o the r state and pick ano the r level. At equi l ibr ium, the expec ted profits in the two states will be the equal ized ne t of migra t ion costs c" (1 - n). The equi l ibr ium condi t ion will be given by

( 1 - pa/n)"~Xl) - - T " X 1 + Q(p,-N) = ( 1 - - p 2 / ( 1 - n ) )

• ] ( x 2 ) - - r ' x 2 + Q ( p 2 " N ) - c ( 1 - n). (22)

This condi t ion defines the react ion funct ion for n as a funct ion of Pl, P2, Xa, x2, and s. Each legislature takes this react ion funct ion as given in the second stage of the game.

As in the mode l of the unregu la ted frontier , restrict ions on c are n e e d e d to derive unambiguous comparat ive statics results. U n d e r the restrict ions discussed in the Ap- pendix, the legislature 's f irst-order condi t ions are

n " Q' ( Pl " N) " N - J( xa) = 0

(1 - n)" Q'(P2" N ) . N - f (x2) = 0, (23)

assuming Nash behavior If the legislature acted collusively a maximized the j o i n t sum of the net surplus f rom the public project the f irst-order condi t ions would be

npa " Q( Pa " N) + n " Q' ( Pl " PO " N - f ( x 1) = npl " Q( P2 " N)

-np2" Q(P2" N) + (1 - n)" Q'(P2" N)" N - J r ( x 2 ) = - np2" Q(Pa" N). (24)

A compar ison of the f irst-order condi t ions for the collusive solut ion and the Nash solut ion allows us to prove the following result

RESULT 2: A symmetric Nash equilibrium exists.

The p r o o f follows f rom rewrit ing the first-order condi t ions for the collusive solut ion as follows

n" Q'(Pa" N)" N - J ' ( x l ) = npl" [Q(P2" N) - Q(Pl" N)]

(1 - n)" Q ' ( p 2 " N ) ' N - f (x2) = n p z ' [ Q ( p 2 " N ) - Q(plN)] . (25)

If Pl = P2, the symmetric case, then the expressions become

n " Q' ( pl " N) " N - J( Xl) = 0

(1 - n ) ' Q ' ( p l " N ) - N - f (xz) = 0, (26)

which are the first-order condi t ions for a symmetric Nash equi l ibr ium. Notice that at a symmetric Nash equi l ibr ium, the popu la t ion need no t be symmetric. In fact the pop-

S. GHOSH 169

ulations may vary in size in equilibrium even if the legislative game results in a symmetric equilibrium. However, the following relationship exits among symmetric Nash equilibria.

RESULT 3: Within the set of symmetric Nash equilibria, the region with higher population will have a higher level of capital investment.

The proof follows from the first-order conditions for a symmetric Nash equilibrium. Rearranging equation (26) and rewriting it in terms of ratios, we obtain the following relationship:

n / (1 - n) = ~ xl) / f ( x2) , (27)

f rom which Result 3 immediately follows. Again this result is consistent with the risk spreading explanation discussed in the context of the unregulated frontier.

As I discuss in the Appendix, there are several possible Nash equilibria to this game, some of them non-symmetric. Even without further specification o f the Nash equilibrium, it is possible to derive the following result on optimal compensation.

RESULT 4: The social planner will

1. choose zero compensation in the case of the symmetric Nash equilibrium with symmetric distribution of population, and

2. choose a positive level of compensation in the nonsymmetric case.

The first part of this result follows from the social welfare function of the social planner, which can be written as follows:

U" [ n ' { ( 1 - p / n ) j ~ X l ) - r" x 1 + Q(Pl" N)} + (1 - n)

• { ( I - p / ( 1 - n ) ' J ( x 2 ) - r ' x 2 + Q(p2"N)}]. (28)

In the symmetric case with symmetric population, the objective function becomes

N / 2 - [(1 - 2 " p ) - f ( x ) - r ' x + Q ( p ' N ) ] , (29)

which is the social welfare function in the model without exit. The second part o f the result follows from the first-order condit ion o f the social

planner 's problem, obtained from differentiating (28) with respect to s:

- p l . s / n ' f " x l s + [ p l / n z ' f ( x l ) - Z ' c ' ( 1 - n ) ] ' n s = O . (30)

This expression is not necessarily satisfied at s equal to zero. Result 1 derived in the context of the unregulated frontier carries over in the model of state competition.

This section has extended the model of takings to incorporate both exit and state competi t ion The results generalize f rom the model of the unregulated frontier: When landowners are able to exit, zero compensat ion is no longer optimal. What is instructive from the state competi t ion is that zero compensat ion is still optimal in the special case of the symmetric Nash equilibrium with symmetric population. The latter result should not be too surprising inasmuch as the fully symmetric case reduces the original Fischel and Shapiro model. The principal result of this section is that Fischel and Shapiro's model without exit is just a special case of a more general model in which exit is possible.


III. Exit Options, Takings, and Compensation

Legal rules can serve as exit opt ions that affect the structure of private bargaining. 16 Analogously, exit opt ions can affect the structure of legal rules. The takings p rob lem has tradit ionally been analyzed by economists as a p rob lem of the government f inance of publ ic projects. Both Blume, Rubinfeld, and Shapiro and Fischel and Shapiro start with the premise that the government finances its publ ic project by taking proper ty from private landowners. The policy quest ion of opt imal compensa t ion is made assuming that landowners make their investment decision incorpora t ing the risk of a govern- men t expropr ia t ion . The two papers differ in how the risk is character ized. In Blume, Rubinfeld, and Shapiro, the risk of a government expropr ia t ion is not different from the risk of p roper ty loss result ing from o ther hazards. In Fischel and Shapiro, the risk arises from major i tar ian decision making that acts more systematically than natura l disasters. In both papers, however, compensa t ion acts as a form of insurance when private insurance markets fail.

This pape r extends the mode l of takings as a form of government f inance one step fur ther to show that the Fischel and Shapiro mode l is a special case of a genera l mode l in which landowners are given an exit opt ion to move to a more favorable regulatory climate. The in t roduc t ion of an exit opt ion changes the incentives of both landowners and legislatures. Compensa t ion in the ex tended mode l acts not only as a form of insurance but also a means to control the legislative game. The s t rong impl ica t ion is that the t radi t ional economic conclusion of the efficiency of uncompensa t ed takings is sensitive to the structure of the mode l of the takings problem.

The exit op t ion in the takings game is re la ted to the role of demora l iza t ion costs in de t e rmin ing the need for compensa ted takings. Tradit ionally, economic models have ignored demora l iza t ion costs and exit options. This oversight can be exp la ined by a view of the takings p rob lem as one of government f inance ra ther than one of polit ical decision making. Fischel and Shapiro ' s pape r pushed the f ront ier of economic analyses of takings by expressly consider ing majori ty voting, or voice, as de t e rmin ing the takings decision. This pape r adds to the work of Fischel and Shapiro by expressly inc luding the exit opt ion.

There are several ways to s t rengthen and ex tend the results of this paper . Specifically, the mode l p resen ted in this pape r does not cons ider o ther means of f inancing publ ic projects, such as taxat ion or purchase. Fur the rmore , the mode l implicit ly assumes a thick marke t for land. Takings decisions, however, are often made in thin marke t contexts. Finally, the mode l includes an exit opt ion but not the voice opt ion. The results however can be s t r eng thened to allow landowners to exercise both voice and exit. I analyze each of these three extensions in turn.

Taxation, Purchase, and Takings

A comple te mode l of the effects of exit and compensa t ion on the legislative choice among taxation, purchase, and takings is beyond the scope of this paper . But the mode l p resen ted in this pape r suggests that the exit op t ion affects opt imal compensa t ion and takings rules as strongly as it affects opt imal tax and expend i tu re rules. The exit op t ion

1°See Douglas G. Baird, Robert H. Gertner, and Randall C. Picker, Game "l'heo~y and the Law 224 (1994).

S. GHOSH 171

descr ibed in this pape r is a species of tax avoidance analyzed by Joe l Slemrod. ~ In my model , the taking of land entails a 100% tax levied by lottery on the capital p laced on the confiscated land. The r andom "takings tax" can be avoided by changing the locat ion of capital. Once the exit op t ion is unde r s tood as a form of tax avoidance, many of the insights from the tax avoidance l i terature can be app l ied to unde r s t and the legislative choice among takings, taxation, and purchase.

Joel S lemrod has a rgued that opt imal tax theory with its focus on opt imal colnmodi ty taxat ion and product ive efficiency is incomple te because "it has not yet come to terms with taxat ion as a system of coercively collecting revenues from individuals who tend to resist. ' ' is He urges a shift in the focus of economic research f rom opt imal taxat ion to opt imal tax systems and specifically to the issue of the technology of tax collection.

The analysis of this pape r presents the government ' s takings power as one possible technology of tax collection that taxpayers can avoid by change of citizenship. The possibility of change of cit izenship creates strategic incentives for the legislature in its exercise of the takings power. The r equ i r emen t of compensa t ion mitigates the strategic incentives when landowners can migrate to a f ront ier that is unregula ted . When landowners can migrate to a ju r i sd ic t ion that also f inances public projects th rough eminen t domain , the existence of state compet i t ion also serves as a way to mit igate an excessive use of the takings power.

Thin Markets versus Thick Markets

It is impor t an t to dist inguish the results of this pape r from the results of takings in a thin marke t context . In this paper I have assumed that each landowner has an equa l l ike l ihood of having his land confiscated and that the l ike l ihood changes as the size of the popu la t ion changes. Often, however, the government will expropr ia te one partic- ular parcel or set of parcels because of its un ique value to a public project. In this si tuation the takings decision of the government is made in the context of a bi lateral monopo ly si tuation in which the threat of exit may adequately protect the landowner more than a liability rule enforced by the courts. 19 Suppose for example that the government dec ided to condemn a large parcel of land owned by a landowner who p l anned to use it for a mall. If the landowner th rea tened to take its project to ano the r jur i sd ic t ion and this threat were credible, the government may be de t e r r ed from exercis ing its taking power. The exit threat works if the landowner provides a suffi- ciently large benef i t to the jur i sd ic t ion that its exit would genera te more harm to the jur i sd ic t ion than any publ ic benefits from the public project. In the mode l p resen ted in this paper , there are a large n u m b e r of landowners, and therefore the costs imposed on a ju r i sd ic t ion by exit were relatively small. The natural quest ion is whether the results ex tend to a mode l in which there is a thin marke t for land so that the landowner and the government engage in bi lateral bargaining.

Miceli and Segerson ~° have deve loped a vm T compel l ing mode l with which to discuss takings in a thin marke t context . Thei r mode l contains three stages: the capital invest-

J7See, e.g.,Joel Slemrod, "Optimal taxation and optimal tax systems," 4JouTv~al of Economic Perspectives 157 (1990) and articles cited therein.

lSld. at 157. mRichard Epstein, Bargaining with the State (1993) provides an excellent discussion of thin market problems and

takings. 2°Thomas J. Miceli and Kathleen Segerson, "Regulatory takings: When should compensation be paid?," 23.lourvzal

of Legal Studies 749 (1994).


ment stage, the regula t ion stage, and the compensa t ion stage. The i r main result is that in the thin marke t case in which the government singles out a few parcels for condem- na t ion compensa t ion should be based on the ex ante efficiency of the land use. Al though they do no t cons ider exit, their results may be sensitive to the possibility and t iming of exit. For example , if exit occurs after the compensa t ion stage, their basic result is no t a l tered because landowners would be made indif ferent between compensa t ion for their c o n d e m n e d parcel and re locat ing their capital to ano the r jur isdic t ion. However, even if the land use is efficient, exit after the regula t ion stage and before the compensa t ion stage may mili tate against compensa t ion if landowners can change cit izenship to a jur i sd ic t ion with less restrictive regulat ion. Incorpora t ion of the exit op t ion in Miceli and Segerson 's r ich-model of regulatory takings is a fruitful area of research.

Majoritarian Rule and the Exit Option

Compensa t ion for takings is of ten argued to be a means of pro tec t ing polit ical minor- ities from the excesses of majori tar ianism. 21 This a rgumen t has typically over looked the possibility of exit as a response to majori tar ianism. If minor i ty groups can leave the jur i sd ic t ion and establish a separate jur i sd ic t ion in which they consti tute a majority, the need for compensa t ion may be diminished. A modi f ied version of the mode l of the unregu la ted f ront ier p resen ted in this p a p e r can be used to answer the quest ion of whether exit can substitute for voice with compensat ion .

Fischel and Shapiro consider a mode l of major i tar ian government that does not allow for the exit opt ion. In their model , the legislature 's objective funct ion is no t the Pigovian funct ion used in the analysis in Section II but a funct ion that captures the total benef i t of the public project ne t the tax costs of f inancing the taking. The major i tar ian objective funct ion is:

N" Q(p" N) - p / ( 1 - p)" s ' J ( x ) . (31)

The first-order condi t ion for the choice of p unde r this major i tar ian funct ion is:

lV 2. Q'; - s . J ( x ) / ( 1 - p)2 = 0. (32)

I will call the value of p that satisfies the f irst-order condi t ion "Pro'" If a third stage is in t roduced in the mode l in which landowners can exit to an

unregu la ted jur isdic t ion, the objective funct ion must be modi f ied in two ways. First, the aggregate size of the popu la t ion is no longer N but n" N, to reflect the fact that a fraction (1 - n) has migra ted to ano the r jur isdic t ion. Second, the probabi l i ty of a taking is no t p but p / n . After incorpora t ing these changes, we obta in the following objective function:

n" N • Q(p" N) - p / ( n - p)" s ' J ( x ) . (33)

The first-order condi t ion for the choice of p is given by

n t , ' [ N ' Q + s ' f ( x ) ' p / ( n - p ) 2 ] + n ' N 2 " Q ' s ' f ( x ) ' n / ( n - p ) 2 = O . (34)

I will call the value of p that satisfies the f irst-order condi t ion "p~."

21John Hart Ely, Democracy and Distrust (1980), p. 97.

S. GHOS~q 173

Two useful results can be derived by compar ing the Fischel and Shapiro model o f majoritarian government without exit and the model with exit.

RESULT 5: I f landowners have the exit option, the majoritarian government will take less than i f the landowners do not have an exit option (i.e., Pine < Pro)"

The proof is in the Appendix and follows from the concavity o f the objective function. The result shows that exit limits the use of the takings power. However, exit does not necessarily limit the need for compensation.

RESULT 6: The optimal level of compensation in the model of majoritarian government with exit may be greater or less than the optimal level in the model of majoritarian government without exit.

The result follows from the social welfare function in equation (18) and the first- order condit ion from equation (34). After substituting the migration equilibrium condit ion and the first-order conditions for the government and landowners in the first-order condit ion for the social welfare function maximized with respect to "s," we obtain the following:

- p . s / n . f ( x ) . Xs + Q(p . 5 0 . n s= - K . p s . K 1. K 2 (35)

where K is an expression that does not depend on s and

K 1 = n" N" Q' - n" s ' f ( x ) / ( n - p)2

K 2 = p" s ' J ( x ) / ( n - p)2 + N" Q. (36)

As in the model of takings with exit to the unregulated frontier discussed in Section II, the first-order condit ion is not satisfied when s is either equal to 1 or 0. Furthermore, Fischel and Shapiro derive the following expression for the first-order condit ion for the optimal choice of s for the model of majoritarian government without exit:

[(1 - p ) - 2 . s ' J ( x ) - J ( x ) ] p ~ - p" s ' f ( x ) ' x s = 0. (37)

To compare the optimal choice of s under the two models, we need to be able to compare these two first-order conditions. Unfortunately, without further restrictions on the expressions constituting the right-hand side of (36), we cannot make such a comparison. Therefore, in general, the introduction of the exit option in the majoritarian model of government may either increase or decrease the optimal level of compensation.

The main conclusion of this section is that exit does not necessarily substitute completely for voice. Although the exit option reduces the optimal level of takings, the exit option does not necessarily reduce the optimal level of compensat ion in the majoritarian model. The latter result should not be surprising. As Fischel and Shapiro explain, the need for compensat ion in the majoritarian government model stems from the fiscal illusion created by including the level of compensat ion in the government 's objective function. The exit option does not mitigate fiscal illusion and therefore does not limit the need for full compensation.

IV. Summary and Conclusion

This paper started with a discussion of the omission of demoralization costs in traditional economic models of takings. I suggested that this omission in part has to do with the difficulty of incorporat ing political context in simple models of condemnat ion. This


paper addresses this omission and contributes to the growing literature on the political economy of takings by exploring the effect of the exit option on optimal takings and compensat ion rules. The introduction of the exit option changes the traditional model of takings in two ways. The first is by making the probability of a taking a function of population. This change allows for an additional strategic dimension to the legislative decision to take. The second is by allowing for state competi t ion in the takings decision. This change allows for the takings decisions of states to be interdependent .

An important result of this paper is that the possibilities of exit and state competi t ion significantly alter traditional conclusions of the optimal compensat ion rule for takings. The model developed in this paper adds an important wrinkle to the seminal model of Blume, Rubinfeld, and Shapiro, which focused singly on the insurance aspect of compensation. Although the exit option prmddes one way to insure against government confiscation, this paper shows that exit cannot provide full insurance because of the strategic effect that exit has on the legislative decision to take; this is the meaning of Results 1, 4, and 5. However, competi t ion between states in the use of the takings power will limit its exercise as each state internalizes the effects of takings on the size of the populat ion in its jurisdiction; this is the meaning of Result 3.

The model in this paper suggests other avenues for future research. For example, the model developed artificially restricted the powers available to state governments. States can finance public projects in many ways other than through eminent domain, such as taxation and purchase. Consideration of the broader question of whether states should take, purchase, or tax to finance a public project when citizens have the exit option requires a richer game theoretic model that allows state legislatures to have a broader range of strategies. The model developed in this paper provides the necessary first step to develop a richer, more complete model of takings, taxation, state competition, and exit.

Appendix Existence of Equilibrium

The existence of an equilibrium in the model of unregulated frontier follows from the existence of a solution for the optimization problems faced, respectively, by the landowners and the legislature. There are two complicating factors. First, the legislature must choose p subject to the constraint that p is less than n(p, s), which is derived from equation (17). Although this constraint has not been explicitly stated in the optimization problem discussed in the text, the constraint will not be binding, as can be seen from equation (13). I f p exactly equals n, then the probability of a taking is effectively 100% and all capital will migrate to the unregulated frontier.

Second, the legislature's objective function incorporates the migration equilibrium condit ion (17). The first-order condition for the legislative choice of p (obtained by taking the first derivative of (14) with respect to p) is

nf," Q+ n" Q " N - J( x) = 0, (A1)

where np can be derived by totally differentiating (17). The expression for np derived from the total differential of (17) is

In" N" Q' - J ( x ) ] / [ n ' c - p ' J ( x ) /n ] . (A2)

S. GHOSn 175

The d e n o m i n a t o r is positive if n" c > p" f l x ) / n . This expression has a simple economic explanat ion. The r ight-hand side is the expec ted cost of a taking to the typical landowner. The left-hand side is the cost of migra t ing into the regula ted state. In equilib- r ium, we would expect the ant ic ipated cost of sett l ing in the regula ted state to be grea ter than the ant ic ipated cost of a taking, otherwise there would be migra t ion into the regula ted state. After substi tuting the expression for nt, into the legislature 's f irst-order condi t ion and simplifying and applying the condi t ion on costs, the legislature 's first- o rde r condi t ion reduces to

n" Q' " N - f ( x) = 0. (A3)

The existence of an opt imal value of p follows from the concavity of Q. The existence of equi l ibr ium in the mode l of state compet i t ion is compl ica ted by the

fact that a Nash game between the legislatures is e m b e d d e d within the larger game. Once again equi l ibr ium to the game exists if solutions exist to the opt imizat ion p rob lem for the landowners and the legislatures. For the legislatures, the equi l ibr ium is given by the solut ion to a Nash game. The first-order condi t ions for each legislature 's choice of p is given by equat ion (23). Once again each legislature takes the funct ion n(p 1, p.~, s) as given in the respective opt imizat ion problem. Each legislature 's opt imizat ion prob- lena also contains the inequali ty const ra int Pl < n(pl, P2, s), which is non-b ind ing for the reasons discussed above.

However, condi t ions must be establ ished for the existence of a Nash equi l ibr ium for the legislative game. The existence of equi l ibr ium can be established by consider ing the react ion functions of the two legislatures. The slope of the react ion functions can be ob ta ined from the expressions for nt, 1 and np2. Totally different ia t ing the equi l ibr ium condi t ion for migrat ion, we f ind that

nt, 1 = In" Q " N - f ( x l ) ] / { n c - p l / n - p 2 / n " (1 - n)], (A4)

and a similar expression can be der ived for nl, 2. For the reasons discussed above, restrict ions on the cost of se t t lement can ensure that the d e n o m i n a t o r is always positive. Substi tut ing the expressions for np~ and np2 into the first-order condi t ions for the legislature 's p rob lem in the Nash game, we find the following expressions:

n . Q' . N - J( xi) = O.

( 1 - n ) ' Q " N - J ( x 2 ) = 0 (A5)

both of which must be true at the Nash equil ibr ium. The first-order condi t ions def ine react ion functions for state 1 and state 2. Slopes of the two react ion functions can be der ived by total d i f ferent ia t ion and can be expressed as follows:

d p l / d p z = - np2" Q / [ Q . nt, , + N" Q']

dpz / dp, = np, " Q / I N " Q' - Q" nt,2]. (A6)

Because the slope of the react ion funct ions differ in sign, existence can be establ ished by the intersect ion of the react ion functions.


Proof of Result 5

Substituting the expression for np derived from (17) into (37) and simplifying, the first-order condition for social welfare for social welfare maximization in the model with the possibility for exit becomes:

K ' [ n " Q" N - ~x)] + n.[N2" Q ' - s . j ~ x ) / ( n - p) 2] = O, (a7)

(part 1) (part 2)

where x is a positive constant. From the first-order condition for the model without exit [equation (32)], we can see that (part 2) differs from equation (32) only in the denomina tor (n - p). Because Pm is the value that satisfies (32) and because n < 1, it must be the case that ifpm were substituted into (part 2) of (A7), (part 2) would be less than zero. Furthermore, compar ing (part 1) with the expression in (32), (part 1) will also be negative if

(a8 ) s /N" (1 - p)2 < 1/n.

The condition in (A8) is satisfied if s equals 0. If s equals 1, it is also satisfied if N" (1 - p)2 > n, which will always be true if N is big enough. Condit ion (A8) will always be satisfied and (part 1) and (part 2) are both less than zero at p = Pm" Because the objective function must be concave for a maximum, the value of p that satisfies (34) must be less than Pm, as Result 5 states.

Takings, the exit option and just compensation

Documents

Transcript of Takings, the exit option and just compensation