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Optimal regulation of land development through price and fiscal controls
JOURNAL
OF URBAN
ECONOMICS
30, 64-82 (1991)
Optimal Regulation of Land Development through Price and Fiscal Controls J. VERNONHENDERSON Department of Economics, Brown University, Providence, Rhode Island 02912 Received September 14, 1988;revised September 11,1989 This paper examines the effectiveness of instruments existing residents of a community might use to regulate developers of vacant land in a community. Instruments examined include zoning laws, price regulation, and the shifting of fiscal burdens between existing residents and the developer. Traditional instruments such as zoning are not efficient. In a world of perfect certainty, price controls and creative fiscal arrangements produce efficient outcomes. With uncertainty over future prices, only by restructuring fiscal arrangements can the community efficiently control the developer. 0 1991 Academic Press, Inc.
This paper analyzes the effectiveness of instruments residents might use to regulate developers of vacant land in a community. Developers propose development projects. The community can accept or refuse permission to develop. It also collects at least a portion of any excess, or so-called monopoly profits, from community development, by effectively selling these permissions. The introduction discussesjust how and why this is the case. The central focus of the paper, however, is on how the community might regulate developers, who have paid for and been given permission to develop. Why is such regulation desirable? What methods of regulation might produce optimal outcomes? This paper shows that traditional methods of regulation cannot produce first best outcomes. However, there are nontraditional methods which can do so. Consider a small homogeneous suburban community with some undeveloped land, in a growing metropolitan area. Several perceptions about such a situation are in the literature (see, for example, the essaysin Mills and Oates [16], Ellickson [3], Edelson [2], Hamilton [9], and Epple, Filimon and Romer [4]). First, such communities generally have some “monopoly” power. This can mean the demand curve to enter is downward sloping. However, monopoly can simply mean (see Ellickson 131)that some entrants view this community as more desirable than others, perhaps because of some special amenity particularly valued by these people. They are willing to pay in excess of opportunity costs to live in this community relative to others: This paper does not choose an interpretation of 64 0094-1190/91 $3.00 Copyright All rights
0 1991 by Academic Press, Inc. of reproduction in any form reserved.
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monopoly power and avoids the general issue of determining the optimal number and type of entrants at each point in time and their optimal sequencing. That would require a separate paper. Rather the paper assumes that a number of people enter in a given period for whatever reason (free or restricted entry), each of whom is willing to pay an entry premium. The next issue concerns who profits from the monopoly position-the current residents or developers/owners of vacant land. In a traditional community, vacant land is typically competitively owned. Since atomistic developers compete for entrants, they cannot exploit the community’s potential monopoly power. However, through the political process (as with an optimal tariff), residents may force realization of the monopoly position and perhaps profit from it. That involves two questions. Does the community have the instruments to force and profit from the monopoly position? Can they politically and bureaucratically carry this out? In the U.S., a community can inhibit development by setting growth quotas on new houses built, imposing stringent and costly zoning regulations on undeveloped land, and refusing or delaying utility hook-ups and building permits (see Ellickson [3] for a revealing discussion). In some other countries (e.g., Canada), property and development rights are legally separated and developers must apply for development permits, because development rights are vested in the local public sector. Given the ability to prohibit development, a community can collect any expected excess development profits, by setting fees for development rights, permits, hook-ups, and/or waivers of zoning regulations (Ellickson [3]). This process in the U.S. is subject to legal challenges and the ability of the community to profit from development varies by state. However, the results in the paper hold under any overall split of profits between developers and communities, as long as communities can claim marginal profits. All this presumes the community can act democratically as an effective collective. Elected officials and community agencies carry out the wishes of the electorate. This model is plausibly applicable in the context of small homogeneous residential suburbs (Komesar [15], Ellickson [3], Fischel[5]). If residents of a community extract surplus development profits, why should they further try to regulate developers? They shouldn’t, if developers provide Pareto-efficient levels of housing and any public services they are responsible for. However, because of property tax externalities (Aaron 111)and/or neighborhood externalities (Schall [20]), there is a divergence between the level of housing that is Pareto-efficient and what incoming residents and developers agree upon. If developers have responsibilities for certain public services, they account only for the tastes of incoming residents who they have yet to sell to, and not for existing residents. These
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divergences for both housing and public services bring up issues of regulation. Ceteris paribus, Pareto-efficient provision leads to higher development profits and hence is sought by the community. Regulation of developers is typically attempted by quantity restrictions (e.g., fixing housing quality). These work in theory (Hamiliton [8]), but are difficult to implement efficiently. The community may not know, or at least may not be able to document for legal purposes, the precise quality of housing and infrastrucure constructed by the developer. Housing services are derived from a bundle of characteristics and many combinations of housing attributes produce a given level of services. Services themselves are a hypothetical construct and cannot be quantified. Not all attributes can be enumerated, let alone measured and checked following construction. Thus courts cannot assesswhether some level of services has been provided. The best a community can do in terms of quantity regulation is to specify the levels of those few attributes which are readily measurable and observable. While this is the common method of regulation, it is inefficient and can be ineffective (Grieson and White [61, Henderson [12]). While quantities cannot be efficiently regulated, sales prices of housing, taxes, and other monetary magnitudes officially recorded are generally observable. For example, in the U.S., given the institutionalization of land markets (real estate listings, deeds, mortgage financing) sales prices are observed, and cannot be readily misrepresented. Similarly, tax assessments and liabilities can be structured to be difficult to misrepresent. Thus, a potential instrument of regulation involves regulation of sales prices or tax liabilities, for example by constraining developers to charge a particular price for housing that forces them to provide a certain quality level of housing in order to be able to sell it. Or, by shifting tax liabilities to the developer, it may be possible to internalize the tax externality problem, so the developer faces the correct incentives. In the U.S., some of these regulations are not generally legally permitted-they may be interpreted as violating the state zoning enabling acts. The paper advocates their permitted use by pointing out the benefits of such regulation. It explains their historical use in the U.S. and in countries where they are legally permitted. A second purpose is to isolate forms of regulation which both are legal and can induce first best outcomes. The regulation problem is specified as a variant of a principal-agent problem (Mirrlees [17], Harris and Raviv [lo], and Grossman and Hart [7]). The community is the principal, indirectly having “ownership” of profits from land development as well as choosing instruments to influence the actions of the agent(s), or land developer(s). In adopting the principal-agent paradigm we use the first-order approach to demonstrate how the agent’s behavior constrains outcomes, as an expositional device.
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While under uncertainty the first-order approach can be shown to be correct only under restrictive (sufficiency) conditions (see, in particular, Rogerson [18]), in the paper our focus is generally on first best outcomes, which themselves are unique and where we are not constrained by the agent’s optimizing behavior. Our propositions about first best solutions hold, whether or not the first-order approach is valid. 1. REGULATION UNDER CERTAINTY This section formally specifies the problem and develops several propositions about the regulatory process in a world characterized by certainty. This isolates several important features of the regulatory process. A one shot, or single-period development problem is examined. We look at an existing community with a stock of existing residents and examine in a single period model their policies for dealing with incoming residents who have a one-period horizon. The period of development of vacant land could, for example, be the second period of a two-period model. The basic regulation principles can all be developed in this context, although the extension to multiple period development processes where entrants have extended horizons raises second-order problems. Multi-period models with finite and infinite horizons are developed in Henderson [ll] and in Henderson and Miceli [14] in the context of reputational issues. 1.1 The Model To examine regulation issues we specify the maximization problems of developers and community members. The incomes of both depend on taxes and profits from housing sales to entrants. To determine potential profits, we must solve for the willingness-to-pay for housing on the part of entrants. Potential Entrants, Public Services, Assessments Potential entrants, or consumers of vacant land in the community have a quasi-concave utility function v = v(x, h, g), where h is individual housing consumption, g individual consumption of public services which are provided equally to all residents, and x all other goods. Entrants have a fixed best alternative utility level IJ, achievable in equilibrium in some other community(ies), which this community hence must offer them. This is is the same throughout the paper whether the internal community solution is first best or not. It is simply a partial equilibrium device to exposit solutions. If in general equilibrium all communities moved internally from inferior to first best solutions that would affect Z’s, facing developers in different communities. They might plausibly rise everywhere. Entrants spend income, y, on housing purchased at price R, the numeraire X, and on taxes T. Thus y - n - R - T = 0. Substituting into
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J. VERNON HENDERSON
E - u(e) = 0 for x and solving the implicit function for R yields R = R(h, g, T; Y, 6)
(1)
where - aT/dh)(
aR/ah = (vJv,
1 + dT/dR) -’
aR/ag = ( v~/v, - aT/ag)( i + aiyazq - ’ aRiaiS = -~;l(i
+ aT/aR)-‘.
(2)
The tax terms in (2) come from the public sector. Public expenditures equal cg(fi + N), where c is the unit cost of public services g provided to N existing residents and N new entrants. If c is constant (independent of A + N) which is not necessary, at the margin g is a Samuelson private good in terms of cost or provision. In fact, there will be services particular to existing residents, particular to entrants, and common to both. Examples of the last can be parks, schools, shopping centers, water and sewage treatment plants, police protection, artery roads, etc. Since it is only common services that present externalities in provision they are what are formally specified here. Defining a=c(Af+N),
(3)
public expenditures are ug. Taxes are the tax rate c times the community tax base, b. Assuming a balanced public budget, t = ag/b.
(4)
One issue in evaluating (2) given (4) concerns how to define the community tax base and that is important for the later implementation of regulation schemes. There are two common practices. Our results hold under both. We use uniform assessment where all property is assessedon the same basis, regardless of purchase date. The other procedure is sales price assessment.’ Uniform assessmentis based on the true quality/quantity of housing services as observed by an independent authority. In that ‘Under sales price assessment
where t is then simply a tax rate. For entrants and existing residents respectively T = tR = Rag/b, f = tk = kag/bR In Eq. (21, aT/aR = ag&?/bi
and aT/ah = 0.
OPTIMAL
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OF LAND DEVELOPMENT
case the community tax base is b&i++hN,
(5)
where t is then a combined assessment price-tax rate. & is the true individual consumption level of existing residents. For entrants and existing residents taxes are respectively T = th = hag/b f=
Then in (2), aT/aR = 0, aT/ah = agh??/b2, and af/ah Community
(6)
ti =iag/b. = -agiN/b2.
and Developer: A First Best Benchmark
Given (l)-(6), we can specify the relationship between the community and developers. The community as principal hires developers as agents to develop vacant land. For expositional purposes, developers are collapsed into a single agent. That agent chooses h, which is unobservable by the community. The sale of h to entrants produces per entrant revenue of R, which is observable. The agent is paid a fee per house, f, based on R. The fee could, for example be the sales price less the ex ante cost D of a zoning waiver. For the community the issue is how the regulate the developer, by regulating R or certain other observable inputs or magnitudes. Existing residents have preference functions V = V(Z’, g; * 1, where Z is consumption of the numeraire good and g the common level of public services. Housing consumption h is fixed. Nonidentical existing residents can also be incorporated.2 Existing residents have a budget constraint jl-++(N/ti)(R-f)-f=O,
(7)
which defines consumption of all other goods, f, in their utility function V(& g; * >. Substituting for 2 from (7) into V(* 1 yields the objective function of an existing resident of V($ - f + (N/fiXR - f), g; * >. NCR - f) is the total net revenue to the community from the land development projec_t,which is divided equally (for identical existing residents) among the N existing residents. An issue not explicitly dealt with, in say Ellickson [3], is whether this direct transfer of money to community residents can occur. It is not enough, for example, for the money to go into the general Treasury to ‘Then efficiency will require a nonidentical splitting of the community’s revenue, to compensate for differential demand for public services.
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lower tax rates for existing plus new residents-that would rule out first best solutions. The money must go just to the existing residents. Several alternative means exist. First in a dynamic context, it could be transferred by lowering taxes of existing residents prior to sale of developed land, given the time between payment for zoning waivers and sales of new housing could be a year. Lowering taxes means either the developer makes contributions to the Treasury or that he actually provides services for existing residents. It could be a rebate to which, again given residency timing, only existing residents are entitled. Finally, it could go to pay for privately or fee financed services of existing residents such as certain utility levies. The agent has some best alternative utility level, u, that he can achieve in a different occupation or undertaking in this time period. For this project his income is N(f - ph), where f is the fee per house he receives from the community for his services and p is the opportunity cost to him of providing housing, assuming no regulation of inputs. Thus the utility from development is U(N(f - p/z)), which must at least equal 0. It is not necessary that the agent be reduced to p. A court on equity grounds could give the developer a part of the “excess profits,” so long as at the margin his income depends on the fee, f. In summary, the community’s first best optimization problem is to hMfaxgV(f- ~+(N/~)(R-f),g;.)+A(~--(N(f-ph))). , ,
(8)
A first best solution which ignores how the actions of agents constrain communities yields relevant Pareto-efficiency conditions. It is obtained by optimizing with respect to h, f, and g and recalling that entrants’ preferences are embedded in R. Maximizing under the definitions of T and f in either (6) or footnote 1 yields
‘h/‘x
-p=o
I’?V~/V, + Nv,/v,
(9) = a.
(10)
Equation (9) sets the housing marginal rate of substitution equal to opportunity cost. Equation (10) is the Samuelson condition for a public good provided equally to all residents. In practice we do not expect (9) to be satisfied, given that the developer, not the community, sets h. In maximizing utility the developer sets h to
OPTIMAL
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71
maximize U(N(f - ph)) so that N(af/ah
- p) = N[ f,$R/ah
- p]
= N [ fR( uJu, = N[ f,&/v,
aT/ah)
- agh#/b’)
- p] = 0 -p]
= 0,
(11)
where fn = af/aR is the increase in fees offered as sales revenue rises and is a tax externality term. The tax externality term distorts the agent’s choice of h and inhibits the attainment of a Pareto-efficient solution. Can regulation overcome this distortion?
aT/ah
1.2 Quantity Controls If all community-developer financial exchanges must occur ex ante (i.e., no community imposed fines or fiscal transfers can occur ex post), the only forms of regulation are quantity controls. Regulation via fee alterations (through fines, contingent fiscal transfers, and so on) requires ex post financial exchanges based on outcomes. Ex ante fees with quantity control are to extract expected surplus profits. These fees can be monetary or in-kind (as long as in-kind transfers such as public services do not exceed the demand for these services which would prevail under monetary transfers (see Henderson 113, Section 1.41)). The inefficiency of quantity controls has been explored elsewhere (Henderson [12] and Grieson and White 161)and here we simply summarize the results. Quantity controls typically are zoning laws governing observable and documentable inputs into the housing construction process. For example, assume there are just two inputs in the housing production function: lot size, 1, and capital, K. Only 1 is observable and hence can be quantity controlled. In this situation we have PROPOSITION 1. Quantity controls where the community sets public services and zones but does not manipulate prices result in a second best solution under regular production conditions with the following charactektics : (1) For any given K and g, 1 is raised relative to what the agent would freely choose. By raising 1, the community forces h up nearer the otherwise Pareto e#icient level, at the cost of increased ineficiency in factor proportions. (2) For any given g, h is raised relative to what the agent would freely choose (Henderson [121X (3) For any given h, g is lowered relative to the level satisfying the Samuelson condition. This lowers tax rates and hence the magnitude of the tax externality distortion in setting h.
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HENDERSON
Remark 1. If housing is produced with hxed proportions then a first best solution results since zoning directly controls housing quality.
1.3 Fee Schedule Controls Unlike quantity controls, in a world of certainty, ex post control over fees paid to the agent permit attainment of first best solutions. However, their construction is nontrivial especially as it relates to the attainment of first best solutions under uncertainty later in the paper. We consider two types of fee schedules, one a forcing schedule and the other a regular differentiable fee schedule. Both yield first best outcomes under certainty but produce different results under uncertainty. Forcing Fee Schedules
PROPOSITION 2. If R( * 1 is strictly increasing in h in the interval [0, !I ] then a first best solution is realized if the developer announces a fee schedule f=6
such that 0 - U( N( 6 - pi))
f=O
ifR #I?.
= 0,
ifR=R
R is ihe v+e of the willingness-to-pay function R(g, h; a) for g = g and h = h. 2, h are the pair satisfying Eqs. (9) and (10) for *a given fi. A sufficient condition for R(* > to be strictly increasing in [0, h] is that unit opportunity cost of housing exceed the efective property tax rate (with 100% evaluation ). Remark 2. Any version of this fee schedule works where the developer officially retains R paymen$s ex* post (paying an ex ante development rights* charge of D (= NCR - C)), but face a “large” fine ex post if R # R.
Th$ community sets g at d. To transact business the developer must set R = R. Otherwise, he collects no revenue, or faces l?rge fines. The question is whether that constrains him to set h at the h satisfying (9). Providing R is strictly increasing up to h, then for each h there is a unique R in the interval, so by setting R appropriately any desired h can be realized. By diminishing marginal rate of*substitution in the interval [O,h] - p L 0 given strict equality at h. Therefore, it is sufficient for ‘hi% aR/dh > 0 that aR/ah = uh/u, - @t/b > v,,/v, - p in [O,&I. In turn a sufficient condition for that (given Nh < b for N, h > 0) is that t < p. In most tax areas in the U.S., the effective tax-assessmentrate t is under 4%
while the comparable opportunity cost including interest and depreciation presumably exceeds 5.5%. In the U.S., the legality of regulating sales price, R, is connected with the legal ownership structure. If the community owns vacant land the
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OF LAND DEVELOPMENT
transfer of money to it is direct and the agent can be paid a fee ex post according to some contractual fee schedule, based upon sales revenue per house. If the community only implicitly commands the profits, sales revenue goes directly to the landowners. It is then beyond the scope of zoning enabling acts in the U.S. for communities to regulate R. As a normative proposition, in a world of perfect certainty (only), this is an unfortunate restriction which could eliminate the ability to realize Paretoefficient solutions. Differentiable
Fee Schedules
There is another fee schedule which produces a first best outcome under certainty. It involves fiscal regulations; we examine two, each with differing degrees of legal feasibility. These schedules are important in a world with uncertainty. Note that the developer chooses to maximize profits N(f - ph). The FOC is from (11)
If we can construct a fee schedule where all components of f are documentable and
fR = W~,>Wv,
-WW-'>
by substituting into (11) we can see that in (12) u,,/u, = p will be met. Thus we can use such a schedule to obtain a first best solution. PROPOSITION 3. A first best solution can be realized under community provision of public services, if the community announces the following fee schedule : f=R-fti/N-D/N.
In Proposition 3 fR = (u,/v,Xu,/u, - aT/ah)-‘. Community memb_ershave a budget-constraint jj ; 2 -
th - Nf/Z'? +
RN/N+=?-x’-th-(N/tiXR-thN/N)+D/N+RN/ti=jX, + D/N = 0. Accordingly, the community’s problem is to pgah V( h + D/& , , + A2[ fR( Gu,
g; *) + A,( 5 - U( N( R - thfi/N - a&$/b2)
- ph) - D)
- P] .
Maximization with respect to h shows the A, constraint is not binding. The expression in the A, constraint reduces to (uII/u, - p> when the
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J. VERNON HENDERSON
expression for fR is substituted. Maximization with respect to g and D yields (10). Thus under the specified fee schedule, (9) and (10) are satisfied. Note this implies it does not pay the community to overprovide g, just because the developer is paying his taxes. That would directly and negatively impact the D they receive. Given developers and entrants are held at 0 and fi, respectively, the resulting solution is identical to that in Proposition 2. In Proposition 3 the developer pays the community an ex ante lump-sum fee D (2 0) plus assumes all ex post tax liabilities (2%) of existing residents. The community sells its tax liabilities to the developer. In return the developer gets development rights and keeps all housing sale revenues. By paying the tax liabilities of existing residents, the developer directly (for existing residents) or indirectly (through R reductions for entrants) faces all tax liabilities in the community and hence internalizes the property tax externality, so a first best solution results. Remark 4. Any version of the fee schedule in Proposition 3 would work where the developer assumes marginal tax liabilities of existing residents. For example, if f” were the prior to development tax liabilities of an existing resident then f could be given as f = R - (f - f’)l\j/N D/N. Remark 5. The essence of the optimal fee schedule is that fR = (~,/u~Xu,Ju, - U/C%)-‘. In theory any specification of the fee schedule with this property will do. The form (only) in Proposition 3 does not require the principal to explicitly specify how f varies with R. Nor does it require ex post transfers directly between the developer and residents.
There is a potential documentation problem here. How _is I’?F = + N/z) determined for developers given h and N are not observable. The developers simply pay the tax bill for existing residents as issued by the tax office. Should developers be concerned that existing residents may infuluence the assessor’s office and bias assessments to increase the burden of the developers? ,The answer depends on whether the developer and entrants know how new property will be assessed before R is paid. If they do, biased assessment has no impact on profits, since &r/ah = (da/dTXdT/dh) + @~/afXaf’/ah) = 0, where &r/aT = NaR/aT; and similarly for A. Since the developers face all tax liabilities implicitly, shifting their composition has no impact. Thus it does not alter D. This means the community has no incentive to bias assessmentsand the developer is indifferent. However, if assessmentsare done after R is paid and are uncertain, the attainment of first best solutions will generally be eliminated. For example, entrants might require risk premiums, lowering realized profits and D.
i’&ag/(&%
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That problem suggests a further adjustment involving an institutional change, so assessmentsdo not matter. Moreover, this new specification may be more attractive from a legal point of view. PROPOSITION 4. A first best solution will be realized if (9 the community sets public expenditure levels (ag), (ii) there are no property taxes, (iii) the developer pays for public expenditures (ag) and (iv) the community announces the fee schedule f=R-D/N.
This arrangement directly gives the developer all fiscal costs. Now there is no property tax distortion, so in choosing h to maximize U(N(R D/N - ph) - ag), the developer voluntarily satisfies Q/U, - p = 0, given 8R/ah in (1) now equals uJu,. Second, the community chooses h, D, and g (and hence ag) to maximize V( 9 + D/l’?, g;) + A,(I!? - U( N( R - D/N + A*( %/%
- P) *
- ph) - ag)) (14)
Optimizing, we see that A, = 0 and g is chosen to meet the Samuelson condition (10). The community sets g optimally because failure to do so lowers D nonoptimally. Remark 6. If the developer sets public service levels (so the community does not control ag) and finances them, no fee schedule produces a first best outcome (given g and h are note observable. In particular, regulation of sales prices is ineffective.3 30nce the community gives up control of g, its only instrument of control is pricing. Fixing R = k fixes x = I given without property taxes i = y - i for entrants. However, in ij - v(i, g, h) = 0 both g and h are free to vary and the pricing constrain! only forc+esthe agent onto one indifference curve in g and h space. Given a fixed payment D (ii R = R), the agent’s goal can be restated as minimizing Nph + cg(i + N), their housing and public service costs, subject to g - u(i, g, h) = 0. Minimizing with respect to h and g yields the inefficient marginal rage of substitution between g and x of
N+.
(14)
The problem of agents ignoring the tastes of existing residents in setting g persists uncorrected.
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While the fee schedules in Propositions 3 and 4 work, it would be unusual for the developer to officially pay either the tax liabilities of existing residents or the fiscal burden of a community if the community sets public service levels. The latter, however, appears to be contractually feasible in the U.S. As a normative statement, if state legislations in the U.S. permitted more creative fiscal arrangements and pricing regulations, there would be gains in efficiency. Such gains in efficiency could improve the welfare of everyone across all communities. That is, in a general equilibrium context, Z’s and V( *l’s would rise everywhere. 2. LAND USE CONTRACTS UNDER UNCERTAINTY Land use contracts are typically made in the face of uncertainty about the willingness-to-pay of future entrants or numbers of future entrants. For illustrative purposes we focus on the former type of uncertainty, where now the state of nature affects willingness-to-pay by altering ii, the alternatives facing entrants (i.e., market conditions elsewhere). Such uncertainty affects the types of viable contracts. In specifying the process, for simplicity, we assume h and g are chosen before the state of nature is revealed. That is, housing and public service facilities are built and service provision contracts signed before marketing occurs, and the willingness-to-pay of entrants dependent on the l? drawing is revealed. The state of nature is continuously distributed between 5, and Z2. Note, fiz > Z1. A court cannot distinguish whether a low R is associated with a bad state of nature (high a) or low level of housing services. It also means that state contingent contracts cannot be written, which rules out first best forcing contracts. Direct regulation of R now cannot yield a first best h. The problem is not simply that R is no longer uniquely associated with h. Given h and g are fixed before 5 is known, fixing R also fixes the maximum x attainable, where x = y - R - T. This fixes maximum potential utility u(x, h, g> of entrants before developers know what utility level, Z, must be provided. For example, to ensure sales in all states of nature, then R would have to set (at its lowest value) to meet ij2. If R was simply fixed at this level, then in general realized utility (U,) would exceed the required alternative fi, implying large foregone profits. Setting a minimum R instead eliminates that aspect of the problem, since higher R’s can be charged if lower 5’s are drawn.4 But if the minimum R is low enough to ensure sales in all states of nature, no control over h is exercised, since that allows the developer to charge any feasible price. To exercise control, as we will see 41t is sufficient for the utility function to have the general form u = f(h; g) + x as in the principal-agent literature for a minimum R to always dominate a tixed R.
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below, R will be set such that sales do not occur in the worst states of nature. But that alone rules out a first best world. Before proceeding to consideration of specific schedules we present as a benchmark the first best solution, where the principal acts without constraints, in terms of either developer behavior or documentation. We assume the developer is risk neutral, which presents the only possibility of inducing an equilibrium first best solution (so we must only worry about moral hazard problems not risk sharing [lo]). A Pareto-efficient solution requires that the community choose f, g, and h to
y + $(R
-f)
- f,g;
)I
+ @-@((f+)N)l].
This results in three conditions:
~b,/%l -P
= 0
tig + NE[ug/u,]-a=0 A + V,/(U’iq
= 0.
(16)
(17)
(18)
The first two are the expected value versions of (9) and (10) relevant to this problem. The third is the usual optimal risk-sharing condition (Shave11 [20]). If the developer is risk neutral so U’ is constant, then satisfying (18) requires V, and hence x’ to be fixed ex ante. Hence any first best solution requires all variables affecting income of existing residents be set before E is known. With this benchmark we can analyze when, if ever, fee schedules induce the criteria defining first best solutions. If left unregulated the developer chooses h according to the expected value version of (111, or E[ u,/u,]
- agk’?/b’ -p = 0.
(19)
Uncertainty does nothing to alleviate the inefficiency of quantity controls. It simply generates expected value versions of the second best first-order conditions. So we focus just on price or fiscal regulations.
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2.1 Price Regulation As we noted earlier, price regulation under uncertainty cannot induce first best outcomes. However, it is helpful to our understanding to specify the second best problem and characterize solutions. We do so for the more reasonable case, where the community sets a floor on R, e. Corresponding to an effective & is a state of nature Zc, which is the maximum utility the community can offer. For E > EC, the houses built are not sold because a low enough price cannot be charged. An effective & where houses are sold for some states of nature is one where 5, s cc = u(y - & - T, h, g) < U2. If so regulated the developer then chooses h to maxN
u(y-R--T7h’g)R( 6; g, h)m( is) dE - ph
I D1
m( *) is the p.d.f. for U. Maximizing yields agiN FM&)
-p
+ R(~c;g,h)m(iY,)~
= 0.
(21) : .z fit = LXy - & - T, h, g), where i is the housing level chosen by the developer, and the then implied f. M(E,) is the cumulative up (from M(ij,) = 0) to EC. In (21), the first term is the expected value of the marginal rate of substitution in consumption where compared to (191, the expectation is only over is’s up to a, since no sales occur at higher E’s. The second term is the corresponding expected value of the tax externality term. So the first three terms are similar to (19). The fourth term indicates a new marginal benefit to the agent of increasing h. Increasing h for a given B increases the range of states of nature over which sales occur. As we argue below, the main gross benefit to the community of raising & (lowering potentially the range of states in whichZsales occur) is to induce the developer to raise h. The developer raises h so as to partially offset the redugtion in range of states where sales occur paused by raising & Raising h per se benefits the community by moving h nearer to the level where (16) is satisfied. Given the agent’s behavior, we can now specify the community’s optimization problem. We do so assuming the first-order approach is valid here. Given we are dealing with the incentive properties of a specific nondecreasing fee schedule, the conditions for validity may be weaker
OPTIMAL
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than those in [18]. The community’s problem is to max V( y’ + D/ti
- ug/(fi
+ Nh/il),
+ (1 - M( 5,))V( jj + D/N
g;)M( a,)
- a&,
g;)
1 a)dE -(agilrS/b2)M Z,) -p +*2u,/u,)m( +R( h,g;a,)m( iY,)aa,/ah I. + A,
%(h,g;v)m(u)
dv -phN
- D - U”
(22)
The objective function reflects the difference in taxes for existing entrants according to whether sales occur or not -assuming new housing remains tax free until sold but g is already provided. The community chooses B (which affects a,>, D, g, and implicitly h, subject to the individual rationality constraint (given the developers alternative of Uo> and self selection. If we maximize, the FOC conditions are not the ones for Paretoefficiency, as footnoted.’ In setting 8, one aspect of the problem is that
in the vicinity of equilibrium, where { a) is the expression accompanying A, 5Maximizing with respect to _R(where ~~,/~~ = -u,) and rearranging we get
+'(F
+D/N-
ag/(ti+M/h),g;)-
V(i, +D/N-
ag/iir,g;)]m(&)o,
- AINR(~,)m(E,)u, - h2~(.}/d& = 0, where (.) is a term associated with A, in (22). The first two terms reflect the costs to the community of raising Jj and eliminating states in which sales occur-the tax loss from not having new houses in the tax base and the transfer loss (lower D because of lower expected revenue) from the developer not selling houses in those states. This implies that aI.)/@ > 0, given A, > 0 (revealed by optimizing with respect to D) and A, > 0. We know A2 > 0 from V$zgl;N/(fi a[.]/&
+ N/I)~)N(Q
+ A,c~[.]/c#I + A,8{*}/&
= 0 and s{.)/ah < 0 by second-order conditions for the agent.
= 0.
80
J. VERNON HENDERSON
in (22). Footnote 5 shows the signs of derivatives of { *1. This is the result noted above. The community, by setting minimum sales prices, is very much in a second best world. In fact, there is an issue of whether some price regulation versus none is better. It appears that for utility functions of the form u = f(h; g) + X, no regulation is never better. The remaining concern is whether price regulation or quantity controls are now superior; and that is unclear. Consider two extremes. In the first example assume fixed proportions in production so by Remark 1 a Pareto-efficient solution can be realized with quantity con901s. Then consider the price regulation solution for that situation and the h and i optimal under regulation,given 5. Zone and set public services with quantity controls to mimic h and 2. Then with quantity controls (given no deadweight loss from nonoptimal factor combinatior$ the revenue in each state has the relationship to regulation revenue R that
R=R
for ii 5 fit
R>li=O
for fi > 6,.
Thus expected land sale profits are unambiguously larger under quanity control than under price regulation for the general price regulation solution where sales do not occur in some states of nature. This raises the D that developers can pay the community for a given 0. Second, existing residents will have an improved tax position, because with quantity con$rols the objective function in (22) is replaced V(Y + D/Q - hag/(&G + hN), i;). In total, existing residents’ utility will be unambiguously larger under quantity controls both because D will rise (given larger expected developer profits and the same 01 and because of smaller expected tax payments. Second, better levels of g and h can be set than 2 and i. In the second example assume factor substitutability in production so quantity controls distort factor proportions with the associated deadweight loss. Consider the case where fir + & or the amount of price variation approaches zero. At the limit the price regulation solution is Pareto-efficient while the quantity control solution is not. Therefore given appropriate continuity properties, for sufficiently “small” price variations, price regulation dominates. 2.2 Differentiable Fee Schedules Price regulation fails under uncertainty because it restricts a variable which must vary over the range of E to achieve efficiency. However, it also fails because of nonoptimal risk sharing, where in (22) utility varies
OPTIMAL
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81
ex post. With risk neutral agents, satisfaction of optimal risk sharing in (18) requires that V, and hence i be constant, given U’ is constant by assumption of risk neutrality. That is, the income and consumption of all other goods Z of existing residents cannot vary with Z. This requires 2 = y + RN/fi - ? - D/G to be invariant with respect to 6. This means the developer must absorb variations in both sales revenue (RN/& and taxes f. The fee schedule in Proposition 3 met this criterion and is thus potentially consistent with optimal risk sharing. Since it also has good incentive properties, this leads to PROPOSITION 5. Zf there is uncertainty about i, and agents are risk neutral, a first best outcome will be realized if the community announces the following fee schedule:
f=R-ffi,/N-D/N. Since h and g are set before E is revealed, in fact tax liabilities are set ex ante so only R (based on v,,/v, variations with C) varies ex post .6 The proof of the proposition is direct. Remark 7. The uncertainty equivalent of Proposition 4 also holds.
3. SUMMARY Under general conditions of uncertainty and asymmetric information in the land regulation process, regardless of tax assessmentprocedures, it is still possible for existing residents of a community to control the development process and achieve Pareto-efficient outcomes, assuming developer risk neutrality. Regulation requires the community to set public service expenditures and the developer to pay (a) an ex ante development fee and (b) the ex post tax liabilities of at least existing residents. In return the developer keeps all sales revenue. In general, allowing communities to regulate prices or be fiscally creative by selling tax liabilities could improve the land development process and social welfare. ACKNOWLEDGMENTS The support of the National Science Foundation (Grant No. SES-8517414)for this work is gratefully acknowledged. This paper is derived from a longer technical working paper (Brown University No. 87-11) methodically examining various types of regulation under different institutional circumstances. 6The more interesting case occurs when tax liabilities vary ex post under sales price assessmentas R varies with fi. The proposition can be proved for the more difficult case (see Henderson [13]).
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REFERENCES 1. H. J. Aaron, “Who Pays the Property Tax?” Brookings Institute, Washington (1975). 2. N. M. Edelson, Voting equilibria with market based assessments,J. Pub. Econom., 5, 269-84 (1976). 3. R. Ellickson, Suburban growth controls: An economic and legal analysis, Yale Lnw J., 86, 385-511 (1977). 4. D. Epple, R. Filimon, and T. Romer, “Community Development with Land Use Controls,” mimeo, Carnegie-Mellon (1985). 5. W. A. Fischel, “The Economics of Zoning Laws,” Johns Hopkins University Press, Baltimore, MD (1985). 6. R. Grieson and J. White, The effects of zoning on market structure and land markets, J. Urban Econom., 10, 271-285. 7. S. Grossman and 0. Hart, An analysis of the principal-agent problem, Econometrica, 51, 7-45. 8. B. Hamilton, Zoning and property taxation in a system of local governments, Urban Stud., 12, 205-211. 9. B. W. Hamilton, Zoning and the exercise of monopoly power, J. Urbun Econom., 5, 116-30 (1978). 10. M. Harris and A. Raviv, Optimal incentive contracts with imperfect information, J. Econom. Theory, 20, 231-259 (1979). 11, J. V. Henderson, Community development: The effects of growth and uncertainty, Amer. Econom. Reu., 70, 894-910 (1980). 12. J. V. Henderson, The impact of zoning regulations which regulate housing quality, J. Urban Econom., 18, 302-312 (1986). 13. J. V. Henderson, “Land Development Regulations,” Working Paper No. 87-11, Brown University (1987). 14. J. V. Henderson and T. Miceli, Reputation in land development markets, J. Urban Econom., in press. 15. N. Komesar, Housing zoning and the public interest, in “Public Interest Law” (B. Weisbrod, Ed.), University of California, Berkeley (1978). 16. E. S. Mills and W. E. Oates, Eds., “Fiscal Zoning and Land Use Controls,” HeathLexington, Lexington (1975). 17. J. Mirrlees, The optimal structure of incentives and authority within an organization, Bell J. Econom., 7, 10.5-131(1976). 18. W. P. Rogerson, The first order approach to principal-agent problems, Econometricu, 53, 1357-1367 (1985). 19. L. Schall, Urban renewal policy and economic efficiency, Am. Econom. Reu., 66, 612-628 (1976). 20. S. Shavell, Sharing risks of deferred payment, J. Polit. Econom., 84, 161-68 (1976).
OF URBAN
ECONOMICS
30, 64-82 (1991)
Optimal Regulation of Land Development through Price and Fiscal Controls J. VERNONHENDERSON Department of Economics, Brown University, Providence, Rhode Island 02912 Received September 14, 1988;revised September 11,1989 This paper examines the effectiveness of instruments existing residents of a community might use to regulate developers of vacant land in a community. Instruments examined include zoning laws, price regulation, and the shifting of fiscal burdens between existing residents and the developer. Traditional instruments such as zoning are not efficient. In a world of perfect certainty, price controls and creative fiscal arrangements produce efficient outcomes. With uncertainty over future prices, only by restructuring fiscal arrangements can the community efficiently control the developer. 0 1991 Academic Press, Inc.
This paper analyzes the effectiveness of instruments residents might use to regulate developers of vacant land in a community. Developers propose development projects. The community can accept or refuse permission to develop. It also collects at least a portion of any excess, or so-called monopoly profits, from community development, by effectively selling these permissions. The introduction discussesjust how and why this is the case. The central focus of the paper, however, is on how the community might regulate developers, who have paid for and been given permission to develop. Why is such regulation desirable? What methods of regulation might produce optimal outcomes? This paper shows that traditional methods of regulation cannot produce first best outcomes. However, there are nontraditional methods which can do so. Consider a small homogeneous suburban community with some undeveloped land, in a growing metropolitan area. Several perceptions about such a situation are in the literature (see, for example, the essaysin Mills and Oates [16], Ellickson [3], Edelson [2], Hamilton [9], and Epple, Filimon and Romer [4]). First, such communities generally have some “monopoly” power. This can mean the demand curve to enter is downward sloping. However, monopoly can simply mean (see Ellickson 131)that some entrants view this community as more desirable than others, perhaps because of some special amenity particularly valued by these people. They are willing to pay in excess of opportunity costs to live in this community relative to others: This paper does not choose an interpretation of 64 0094-1190/91 $3.00 Copyright All rights
0 1991 by Academic Press, Inc. of reproduction in any form reserved.
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monopoly power and avoids the general issue of determining the optimal number and type of entrants at each point in time and their optimal sequencing. That would require a separate paper. Rather the paper assumes that a number of people enter in a given period for whatever reason (free or restricted entry), each of whom is willing to pay an entry premium. The next issue concerns who profits from the monopoly position-the current residents or developers/owners of vacant land. In a traditional community, vacant land is typically competitively owned. Since atomistic developers compete for entrants, they cannot exploit the community’s potential monopoly power. However, through the political process (as with an optimal tariff), residents may force realization of the monopoly position and perhaps profit from it. That involves two questions. Does the community have the instruments to force and profit from the monopoly position? Can they politically and bureaucratically carry this out? In the U.S., a community can inhibit development by setting growth quotas on new houses built, imposing stringent and costly zoning regulations on undeveloped land, and refusing or delaying utility hook-ups and building permits (see Ellickson [3] for a revealing discussion). In some other countries (e.g., Canada), property and development rights are legally separated and developers must apply for development permits, because development rights are vested in the local public sector. Given the ability to prohibit development, a community can collect any expected excess development profits, by setting fees for development rights, permits, hook-ups, and/or waivers of zoning regulations (Ellickson [3]). This process in the U.S. is subject to legal challenges and the ability of the community to profit from development varies by state. However, the results in the paper hold under any overall split of profits between developers and communities, as long as communities can claim marginal profits. All this presumes the community can act democratically as an effective collective. Elected officials and community agencies carry out the wishes of the electorate. This model is plausibly applicable in the context of small homogeneous residential suburbs (Komesar [15], Ellickson [3], Fischel[5]). If residents of a community extract surplus development profits, why should they further try to regulate developers? They shouldn’t, if developers provide Pareto-efficient levels of housing and any public services they are responsible for. However, because of property tax externalities (Aaron 111)and/or neighborhood externalities (Schall [20]), there is a divergence between the level of housing that is Pareto-efficient and what incoming residents and developers agree upon. If developers have responsibilities for certain public services, they account only for the tastes of incoming residents who they have yet to sell to, and not for existing residents. These
66
J. VERNON HENDERSON
divergences for both housing and public services bring up issues of regulation. Ceteris paribus, Pareto-efficient provision leads to higher development profits and hence is sought by the community. Regulation of developers is typically attempted by quantity restrictions (e.g., fixing housing quality). These work in theory (Hamiliton [8]), but are difficult to implement efficiently. The community may not know, or at least may not be able to document for legal purposes, the precise quality of housing and infrastrucure constructed by the developer. Housing services are derived from a bundle of characteristics and many combinations of housing attributes produce a given level of services. Services themselves are a hypothetical construct and cannot be quantified. Not all attributes can be enumerated, let alone measured and checked following construction. Thus courts cannot assesswhether some level of services has been provided. The best a community can do in terms of quantity regulation is to specify the levels of those few attributes which are readily measurable and observable. While this is the common method of regulation, it is inefficient and can be ineffective (Grieson and White [61, Henderson [12]). While quantities cannot be efficiently regulated, sales prices of housing, taxes, and other monetary magnitudes officially recorded are generally observable. For example, in the U.S., given the institutionalization of land markets (real estate listings, deeds, mortgage financing) sales prices are observed, and cannot be readily misrepresented. Similarly, tax assessments and liabilities can be structured to be difficult to misrepresent. Thus, a potential instrument of regulation involves regulation of sales prices or tax liabilities, for example by constraining developers to charge a particular price for housing that forces them to provide a certain quality level of housing in order to be able to sell it. Or, by shifting tax liabilities to the developer, it may be possible to internalize the tax externality problem, so the developer faces the correct incentives. In the U.S., some of these regulations are not generally legally permitted-they may be interpreted as violating the state zoning enabling acts. The paper advocates their permitted use by pointing out the benefits of such regulation. It explains their historical use in the U.S. and in countries where they are legally permitted. A second purpose is to isolate forms of regulation which both are legal and can induce first best outcomes. The regulation problem is specified as a variant of a principal-agent problem (Mirrlees [17], Harris and Raviv [lo], and Grossman and Hart [7]). The community is the principal, indirectly having “ownership” of profits from land development as well as choosing instruments to influence the actions of the agent(s), or land developer(s). In adopting the principal-agent paradigm we use the first-order approach to demonstrate how the agent’s behavior constrains outcomes, as an expositional device.
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While under uncertainty the first-order approach can be shown to be correct only under restrictive (sufficiency) conditions (see, in particular, Rogerson [18]), in the paper our focus is generally on first best outcomes, which themselves are unique and where we are not constrained by the agent’s optimizing behavior. Our propositions about first best solutions hold, whether or not the first-order approach is valid. 1. REGULATION UNDER CERTAINTY This section formally specifies the problem and develops several propositions about the regulatory process in a world characterized by certainty. This isolates several important features of the regulatory process. A one shot, or single-period development problem is examined. We look at an existing community with a stock of existing residents and examine in a single period model their policies for dealing with incoming residents who have a one-period horizon. The period of development of vacant land could, for example, be the second period of a two-period model. The basic regulation principles can all be developed in this context, although the extension to multiple period development processes where entrants have extended horizons raises second-order problems. Multi-period models with finite and infinite horizons are developed in Henderson [ll] and in Henderson and Miceli [14] in the context of reputational issues. 1.1 The Model To examine regulation issues we specify the maximization problems of developers and community members. The incomes of both depend on taxes and profits from housing sales to entrants. To determine potential profits, we must solve for the willingness-to-pay for housing on the part of entrants. Potential Entrants, Public Services, Assessments Potential entrants, or consumers of vacant land in the community have a quasi-concave utility function v = v(x, h, g), where h is individual housing consumption, g individual consumption of public services which are provided equally to all residents, and x all other goods. Entrants have a fixed best alternative utility level IJ, achievable in equilibrium in some other community(ies), which this community hence must offer them. This is is the same throughout the paper whether the internal community solution is first best or not. It is simply a partial equilibrium device to exposit solutions. If in general equilibrium all communities moved internally from inferior to first best solutions that would affect Z’s, facing developers in different communities. They might plausibly rise everywhere. Entrants spend income, y, on housing purchased at price R, the numeraire X, and on taxes T. Thus y - n - R - T = 0. Substituting into
68
J. VERNON HENDERSON
E - u(e) = 0 for x and solving the implicit function for R yields R = R(h, g, T; Y, 6)
(1)
where - aT/dh)(
aR/ah = (vJv,
1 + dT/dR) -’
aR/ag = ( v~/v, - aT/ag)( i + aiyazq - ’ aRiaiS = -~;l(i
+ aT/aR)-‘.
(2)
The tax terms in (2) come from the public sector. Public expenditures equal cg(fi + N), where c is the unit cost of public services g provided to N existing residents and N new entrants. If c is constant (independent of A + N) which is not necessary, at the margin g is a Samuelson private good in terms of cost or provision. In fact, there will be services particular to existing residents, particular to entrants, and common to both. Examples of the last can be parks, schools, shopping centers, water and sewage treatment plants, police protection, artery roads, etc. Since it is only common services that present externalities in provision they are what are formally specified here. Defining a=c(Af+N),
(3)
public expenditures are ug. Taxes are the tax rate c times the community tax base, b. Assuming a balanced public budget, t = ag/b.
(4)
One issue in evaluating (2) given (4) concerns how to define the community tax base and that is important for the later implementation of regulation schemes. There are two common practices. Our results hold under both. We use uniform assessment where all property is assessedon the same basis, regardless of purchase date. The other procedure is sales price assessment.’ Uniform assessmentis based on the true quality/quantity of housing services as observed by an independent authority. In that ‘Under sales price assessment
where t is then simply a tax rate. For entrants and existing residents respectively T = tR = Rag/b, f = tk = kag/bR In Eq. (21, aT/aR = ag&?/bi
and aT/ah = 0.
OPTIMAL
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case the community tax base is b&i++hN,
(5)
where t is then a combined assessment price-tax rate. & is the true individual consumption level of existing residents. For entrants and existing residents taxes are respectively T = th = hag/b f=
Then in (2), aT/aR = 0, aT/ah = agh??/b2, and af/ah Community
(6)
ti =iag/b. = -agiN/b2.
and Developer: A First Best Benchmark
Given (l)-(6), we can specify the relationship between the community and developers. The community as principal hires developers as agents to develop vacant land. For expositional purposes, developers are collapsed into a single agent. That agent chooses h, which is unobservable by the community. The sale of h to entrants produces per entrant revenue of R, which is observable. The agent is paid a fee per house, f, based on R. The fee could, for example be the sales price less the ex ante cost D of a zoning waiver. For the community the issue is how the regulate the developer, by regulating R or certain other observable inputs or magnitudes. Existing residents have preference functions V = V(Z’, g; * 1, where Z is consumption of the numeraire good and g the common level of public services. Housing consumption h is fixed. Nonidentical existing residents can also be incorporated.2 Existing residents have a budget constraint jl-++(N/ti)(R-f)-f=O,
(7)
which defines consumption of all other goods, f, in their utility function V(& g; * >. Substituting for 2 from (7) into V(* 1 yields the objective function of an existing resident of V($ - f + (N/fiXR - f), g; * >. NCR - f) is the total net revenue to the community from the land development projec_t,which is divided equally (for identical existing residents) among the N existing residents. An issue not explicitly dealt with, in say Ellickson [3], is whether this direct transfer of money to community residents can occur. It is not enough, for example, for the money to go into the general Treasury to ‘Then efficiency will require a nonidentical splitting of the community’s revenue, to compensate for differential demand for public services.
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lower tax rates for existing plus new residents-that would rule out first best solutions. The money must go just to the existing residents. Several alternative means exist. First in a dynamic context, it could be transferred by lowering taxes of existing residents prior to sale of developed land, given the time between payment for zoning waivers and sales of new housing could be a year. Lowering taxes means either the developer makes contributions to the Treasury or that he actually provides services for existing residents. It could be a rebate to which, again given residency timing, only existing residents are entitled. Finally, it could go to pay for privately or fee financed services of existing residents such as certain utility levies. The agent has some best alternative utility level, u, that he can achieve in a different occupation or undertaking in this time period. For this project his income is N(f - ph), where f is the fee per house he receives from the community for his services and p is the opportunity cost to him of providing housing, assuming no regulation of inputs. Thus the utility from development is U(N(f - p/z)), which must at least equal 0. It is not necessary that the agent be reduced to p. A court on equity grounds could give the developer a part of the “excess profits,” so long as at the margin his income depends on the fee, f. In summary, the community’s first best optimization problem is to hMfaxgV(f- ~+(N/~)(R-f),g;.)+A(~--(N(f-ph))). , ,
(8)
A first best solution which ignores how the actions of agents constrain communities yields relevant Pareto-efficiency conditions. It is obtained by optimizing with respect to h, f, and g and recalling that entrants’ preferences are embedded in R. Maximizing under the definitions of T and f in either (6) or footnote 1 yields
‘h/‘x
-p=o
I’?V~/V, + Nv,/v,
(9) = a.
(10)
Equation (9) sets the housing marginal rate of substitution equal to opportunity cost. Equation (10) is the Samuelson condition for a public good provided equally to all residents. In practice we do not expect (9) to be satisfied, given that the developer, not the community, sets h. In maximizing utility the developer sets h to
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71
maximize U(N(f - ph)) so that N(af/ah
- p) = N[ f,$R/ah
- p]
= N [ fR( uJu, = N[ f,&/v,
aT/ah)
- agh#/b’)
- p] = 0 -p]
= 0,
(11)
where fn = af/aR is the increase in fees offered as sales revenue rises and is a tax externality term. The tax externality term distorts the agent’s choice of h and inhibits the attainment of a Pareto-efficient solution. Can regulation overcome this distortion?
aT/ah
1.2 Quantity Controls If all community-developer financial exchanges must occur ex ante (i.e., no community imposed fines or fiscal transfers can occur ex post), the only forms of regulation are quantity controls. Regulation via fee alterations (through fines, contingent fiscal transfers, and so on) requires ex post financial exchanges based on outcomes. Ex ante fees with quantity control are to extract expected surplus profits. These fees can be monetary or in-kind (as long as in-kind transfers such as public services do not exceed the demand for these services which would prevail under monetary transfers (see Henderson 113, Section 1.41)). The inefficiency of quantity controls has been explored elsewhere (Henderson [12] and Grieson and White 161)and here we simply summarize the results. Quantity controls typically are zoning laws governing observable and documentable inputs into the housing construction process. For example, assume there are just two inputs in the housing production function: lot size, 1, and capital, K. Only 1 is observable and hence can be quantity controlled. In this situation we have PROPOSITION 1. Quantity controls where the community sets public services and zones but does not manipulate prices result in a second best solution under regular production conditions with the following charactektics : (1) For any given K and g, 1 is raised relative to what the agent would freely choose. By raising 1, the community forces h up nearer the otherwise Pareto e#icient level, at the cost of increased ineficiency in factor proportions. (2) For any given g, h is raised relative to what the agent would freely choose (Henderson [121X (3) For any given h, g is lowered relative to the level satisfying the Samuelson condition. This lowers tax rates and hence the magnitude of the tax externality distortion in setting h.
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HENDERSON
Remark 1. If housing is produced with hxed proportions then a first best solution results since zoning directly controls housing quality.
1.3 Fee Schedule Controls Unlike quantity controls, in a world of certainty, ex post control over fees paid to the agent permit attainment of first best solutions. However, their construction is nontrivial especially as it relates to the attainment of first best solutions under uncertainty later in the paper. We consider two types of fee schedules, one a forcing schedule and the other a regular differentiable fee schedule. Both yield first best outcomes under certainty but produce different results under uncertainty. Forcing Fee Schedules
PROPOSITION 2. If R( * 1 is strictly increasing in h in the interval [0, !I ] then a first best solution is realized if the developer announces a fee schedule f=6
such that 0 - U( N( 6 - pi))
f=O
ifR #I?.
= 0,
ifR=R
R is ihe v+e of the willingness-to-pay function R(g, h; a) for g = g and h = h. 2, h are the pair satisfying Eqs. (9) and (10) for *a given fi. A sufficient condition for R(* > to be strictly increasing in [0, h] is that unit opportunity cost of housing exceed the efective property tax rate (with 100% evaluation ). Remark 2. Any version of this fee schedule works where the developer officially retains R paymen$s ex* post (paying an ex ante development rights* charge of D (= NCR - C)), but face a “large” fine ex post if R # R.
Th$ community sets g at d. To transact business the developer must set R = R. Otherwise, he collects no revenue, or faces l?rge fines. The question is whether that constrains him to set h at the h satisfying (9). Providing R is strictly increasing up to h, then for each h there is a unique R in the interval, so by setting R appropriately any desired h can be realized. By diminishing marginal rate of*substitution in the interval [O,h] - p L 0 given strict equality at h. Therefore, it is sufficient for ‘hi% aR/dh > 0 that aR/ah = uh/u, - @t/b > v,,/v, - p in [O,&I. In turn a sufficient condition for that (given Nh < b for N, h > 0) is that t < p. In most tax areas in the U.S., the effective tax-assessmentrate t is under 4%
while the comparable opportunity cost including interest and depreciation presumably exceeds 5.5%. In the U.S., the legality of regulating sales price, R, is connected with the legal ownership structure. If the community owns vacant land the
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OF LAND DEVELOPMENT
transfer of money to it is direct and the agent can be paid a fee ex post according to some contractual fee schedule, based upon sales revenue per house. If the community only implicitly commands the profits, sales revenue goes directly to the landowners. It is then beyond the scope of zoning enabling acts in the U.S. for communities to regulate R. As a normative proposition, in a world of perfect certainty (only), this is an unfortunate restriction which could eliminate the ability to realize Paretoefficient solutions. Differentiable
Fee Schedules
There is another fee schedule which produces a first best outcome under certainty. It involves fiscal regulations; we examine two, each with differing degrees of legal feasibility. These schedules are important in a world with uncertainty. Note that the developer chooses to maximize profits N(f - ph). The FOC is from (11)
If we can construct a fee schedule where all components of f are documentable and
fR = W~,>Wv,
-WW-'>
by substituting into (11) we can see that in (12) u,,/u, = p will be met. Thus we can use such a schedule to obtain a first best solution. PROPOSITION 3. A first best solution can be realized under community provision of public services, if the community announces the following fee schedule : f=R-fti/N-D/N.
In Proposition 3 fR = (u,/v,Xu,/u, - aT/ah)-‘. Community memb_ershave a budget-constraint jj ; 2 -
th - Nf/Z'? +
RN/N+=?-x’-th-(N/tiXR-thN/N)+D/N+RN/ti=jX, + D/N = 0. Accordingly, the community’s problem is to pgah V( h + D/& , , + A2[ fR( Gu,
g; *) + A,( 5 - U( N( R - thfi/N - a&$/b2)
- ph) - D)
- P] .
Maximization with respect to h shows the A, constraint is not binding. The expression in the A, constraint reduces to (uII/u, - p> when the
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expression for fR is substituted. Maximization with respect to g and D yields (10). Thus under the specified fee schedule, (9) and (10) are satisfied. Note this implies it does not pay the community to overprovide g, just because the developer is paying his taxes. That would directly and negatively impact the D they receive. Given developers and entrants are held at 0 and fi, respectively, the resulting solution is identical to that in Proposition 2. In Proposition 3 the developer pays the community an ex ante lump-sum fee D (2 0) plus assumes all ex post tax liabilities (2%) of existing residents. The community sells its tax liabilities to the developer. In return the developer gets development rights and keeps all housing sale revenues. By paying the tax liabilities of existing residents, the developer directly (for existing residents) or indirectly (through R reductions for entrants) faces all tax liabilities in the community and hence internalizes the property tax externality, so a first best solution results. Remark 4. Any version of the fee schedule in Proposition 3 would work where the developer assumes marginal tax liabilities of existing residents. For example, if f” were the prior to development tax liabilities of an existing resident then f could be given as f = R - (f - f’)l\j/N D/N. Remark 5. The essence of the optimal fee schedule is that fR = (~,/u~Xu,Ju, - U/C%)-‘. In theory any specification of the fee schedule with this property will do. The form (only) in Proposition 3 does not require the principal to explicitly specify how f varies with R. Nor does it require ex post transfers directly between the developer and residents.
There is a potential documentation problem here. How _is I’?F = + N/z) determined for developers given h and N are not observable. The developers simply pay the tax bill for existing residents as issued by the tax office. Should developers be concerned that existing residents may infuluence the assessor’s office and bias assessments to increase the burden of the developers? ,The answer depends on whether the developer and entrants know how new property will be assessed before R is paid. If they do, biased assessment has no impact on profits, since &r/ah = (da/dTXdT/dh) + @~/afXaf’/ah) = 0, where &r/aT = NaR/aT; and similarly for A. Since the developers face all tax liabilities implicitly, shifting their composition has no impact. Thus it does not alter D. This means the community has no incentive to bias assessmentsand the developer is indifferent. However, if assessmentsare done after R is paid and are uncertain, the attainment of first best solutions will generally be eliminated. For example, entrants might require risk premiums, lowering realized profits and D.
i’&ag/(&%
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That problem suggests a further adjustment involving an institutional change, so assessmentsdo not matter. Moreover, this new specification may be more attractive from a legal point of view. PROPOSITION 4. A first best solution will be realized if (9 the community sets public expenditure levels (ag), (ii) there are no property taxes, (iii) the developer pays for public expenditures (ag) and (iv) the community announces the fee schedule f=R-D/N.
This arrangement directly gives the developer all fiscal costs. Now there is no property tax distortion, so in choosing h to maximize U(N(R D/N - ph) - ag), the developer voluntarily satisfies Q/U, - p = 0, given 8R/ah in (1) now equals uJu,. Second, the community chooses h, D, and g (and hence ag) to maximize V( 9 + D/l’?, g;) + A,(I!? - U( N( R - D/N + A*( %/%
- P) *
- ph) - ag)) (14)
Optimizing, we see that A, = 0 and g is chosen to meet the Samuelson condition (10). The community sets g optimally because failure to do so lowers D nonoptimally. Remark 6. If the developer sets public service levels (so the community does not control ag) and finances them, no fee schedule produces a first best outcome (given g and h are note observable. In particular, regulation of sales prices is ineffective.3 30nce the community gives up control of g, its only instrument of control is pricing. Fixing R = k fixes x = I given without property taxes i = y - i for entrants. However, in ij - v(i, g, h) = 0 both g and h are free to vary and the pricing constrain! only forc+esthe agent onto one indifference curve in g and h space. Given a fixed payment D (ii R = R), the agent’s goal can be restated as minimizing Nph + cg(i + N), their housing and public service costs, subject to g - u(i, g, h) = 0. Minimizing with respect to h and g yields the inefficient marginal rage of substitution between g and x of
N+.
(14)
The problem of agents ignoring the tastes of existing residents in setting g persists uncorrected.
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While the fee schedules in Propositions 3 and 4 work, it would be unusual for the developer to officially pay either the tax liabilities of existing residents or the fiscal burden of a community if the community sets public service levels. The latter, however, appears to be contractually feasible in the U.S. As a normative statement, if state legislations in the U.S. permitted more creative fiscal arrangements and pricing regulations, there would be gains in efficiency. Such gains in efficiency could improve the welfare of everyone across all communities. That is, in a general equilibrium context, Z’s and V( *l’s would rise everywhere. 2. LAND USE CONTRACTS UNDER UNCERTAINTY Land use contracts are typically made in the face of uncertainty about the willingness-to-pay of future entrants or numbers of future entrants. For illustrative purposes we focus on the former type of uncertainty, where now the state of nature affects willingness-to-pay by altering ii, the alternatives facing entrants (i.e., market conditions elsewhere). Such uncertainty affects the types of viable contracts. In specifying the process, for simplicity, we assume h and g are chosen before the state of nature is revealed. That is, housing and public service facilities are built and service provision contracts signed before marketing occurs, and the willingness-to-pay of entrants dependent on the l? drawing is revealed. The state of nature is continuously distributed between 5, and Z2. Note, fiz > Z1. A court cannot distinguish whether a low R is associated with a bad state of nature (high a) or low level of housing services. It also means that state contingent contracts cannot be written, which rules out first best forcing contracts. Direct regulation of R now cannot yield a first best h. The problem is not simply that R is no longer uniquely associated with h. Given h and g are fixed before 5 is known, fixing R also fixes the maximum x attainable, where x = y - R - T. This fixes maximum potential utility u(x, h, g> of entrants before developers know what utility level, Z, must be provided. For example, to ensure sales in all states of nature, then R would have to set (at its lowest value) to meet ij2. If R was simply fixed at this level, then in general realized utility (U,) would exceed the required alternative fi, implying large foregone profits. Setting a minimum R instead eliminates that aspect of the problem, since higher R’s can be charged if lower 5’s are drawn.4 But if the minimum R is low enough to ensure sales in all states of nature, no control over h is exercised, since that allows the developer to charge any feasible price. To exercise control, as we will see 41t is sufficient for the utility function to have the general form u = f(h; g) + x as in the principal-agent literature for a minimum R to always dominate a tixed R.
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below, R will be set such that sales do not occur in the worst states of nature. But that alone rules out a first best world. Before proceeding to consideration of specific schedules we present as a benchmark the first best solution, where the principal acts without constraints, in terms of either developer behavior or documentation. We assume the developer is risk neutral, which presents the only possibility of inducing an equilibrium first best solution (so we must only worry about moral hazard problems not risk sharing [lo]). A Pareto-efficient solution requires that the community choose f, g, and h to
y + $(R
-f)
- f,g;
)I
+ @-@((f+)N)l].
This results in three conditions:
~b,/%l -P
= 0
tig + NE[ug/u,]-a=0 A + V,/(U’iq
= 0.
(16)
(17)
(18)
The first two are the expected value versions of (9) and (10) relevant to this problem. The third is the usual optimal risk-sharing condition (Shave11 [20]). If the developer is risk neutral so U’ is constant, then satisfying (18) requires V, and hence x’ to be fixed ex ante. Hence any first best solution requires all variables affecting income of existing residents be set before E is known. With this benchmark we can analyze when, if ever, fee schedules induce the criteria defining first best solutions. If left unregulated the developer chooses h according to the expected value version of (111, or E[ u,/u,]
- agk’?/b’ -p = 0.
(19)
Uncertainty does nothing to alleviate the inefficiency of quantity controls. It simply generates expected value versions of the second best first-order conditions. So we focus just on price or fiscal regulations.
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2.1 Price Regulation As we noted earlier, price regulation under uncertainty cannot induce first best outcomes. However, it is helpful to our understanding to specify the second best problem and characterize solutions. We do so for the more reasonable case, where the community sets a floor on R, e. Corresponding to an effective & is a state of nature Zc, which is the maximum utility the community can offer. For E > EC, the houses built are not sold because a low enough price cannot be charged. An effective & where houses are sold for some states of nature is one where 5, s cc = u(y - & - T, h, g) < U2. If so regulated the developer then chooses h to maxN
u(y-R--T7h’g)R( 6; g, h)m( is) dE - ph
I D1
m( *) is the p.d.f. for U. Maximizing yields agiN FM&)
-p
+ R(~c;g,h)m(iY,)~
= 0.
(21) : .z fit = LXy - & - T, h, g), where i is the housing level chosen by the developer, and the then implied f. M(E,) is the cumulative up (from M(ij,) = 0) to EC. In (21), the first term is the expected value of the marginal rate of substitution in consumption where compared to (191, the expectation is only over is’s up to a, since no sales occur at higher E’s. The second term is the corresponding expected value of the tax externality term. So the first three terms are similar to (19). The fourth term indicates a new marginal benefit to the agent of increasing h. Increasing h for a given B increases the range of states of nature over which sales occur. As we argue below, the main gross benefit to the community of raising & (lowering potentially the range of states in whichZsales occur) is to induce the developer to raise h. The developer raises h so as to partially offset the redugtion in range of states where sales occur paused by raising & Raising h per se benefits the community by moving h nearer to the level where (16) is satisfied. Given the agent’s behavior, we can now specify the community’s optimization problem. We do so assuming the first-order approach is valid here. Given we are dealing with the incentive properties of a specific nondecreasing fee schedule, the conditions for validity may be weaker
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than those in [18]. The community’s problem is to max V( y’ + D/ti
- ug/(fi
+ Nh/il),
+ (1 - M( 5,))V( jj + D/N
g;)M( a,)
- a&,
g;)
1 a)dE -(agilrS/b2)M Z,) -p +*2u,/u,)m( +R( h,g;a,)m( iY,)aa,/ah I. + A,
%(h,g;v)m(u)
dv -phN
- D - U”
(22)
The objective function reflects the difference in taxes for existing entrants according to whether sales occur or not -assuming new housing remains tax free until sold but g is already provided. The community chooses B (which affects a,>, D, g, and implicitly h, subject to the individual rationality constraint (given the developers alternative of Uo> and self selection. If we maximize, the FOC conditions are not the ones for Paretoefficiency, as footnoted.’ In setting 8, one aspect of the problem is that
in the vicinity of equilibrium, where { a) is the expression accompanying A, 5Maximizing with respect to _R(where ~~,/~~ = -u,) and rearranging we get
+'(F
+D/N-
ag/(ti+M/h),g;)-
V(i, +D/N-
ag/iir,g;)]m(&)o,
- AINR(~,)m(E,)u, - h2~(.}/d& = 0, where (.) is a term associated with A, in (22). The first two terms reflect the costs to the community of raising Jj and eliminating states in which sales occur-the tax loss from not having new houses in the tax base and the transfer loss (lower D because of lower expected revenue) from the developer not selling houses in those states. This implies that aI.)/@ > 0, given A, > 0 (revealed by optimizing with respect to D) and A, > 0. We know A2 > 0 from V$zgl;N/(fi a[.]/&
+ N/I)~)N(Q
+ A,c~[.]/c#I + A,8{*}/&
= 0 and s{.)/ah < 0 by second-order conditions for the agent.
= 0.
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in (22). Footnote 5 shows the signs of derivatives of { *1. This is the result noted above. The community, by setting minimum sales prices, is very much in a second best world. In fact, there is an issue of whether some price regulation versus none is better. It appears that for utility functions of the form u = f(h; g) + X, no regulation is never better. The remaining concern is whether price regulation or quantity controls are now superior; and that is unclear. Consider two extremes. In the first example assume fixed proportions in production so by Remark 1 a Pareto-efficient solution can be realized with quantity con901s. Then consider the price regulation solution for that situation and the h and i optimal under regulation,given 5. Zone and set public services with quantity controls to mimic h and 2. Then with quantity controls (given no deadweight loss from nonoptimal factor combinatior$ the revenue in each state has the relationship to regulation revenue R that
R=R
for ii 5 fit
R>li=O
for fi > 6,.
Thus expected land sale profits are unambiguously larger under quanity control than under price regulation for the general price regulation solution where sales do not occur in some states of nature. This raises the D that developers can pay the community for a given 0. Second, existing residents will have an improved tax position, because with quantity con$rols the objective function in (22) is replaced V(Y + D/Q - hag/(&G + hN), i;). In total, existing residents’ utility will be unambiguously larger under quantity controls both because D will rise (given larger expected developer profits and the same 01 and because of smaller expected tax payments. Second, better levels of g and h can be set than 2 and i. In the second example assume factor substitutability in production so quantity controls distort factor proportions with the associated deadweight loss. Consider the case where fir + & or the amount of price variation approaches zero. At the limit the price regulation solution is Pareto-efficient while the quantity control solution is not. Therefore given appropriate continuity properties, for sufficiently “small” price variations, price regulation dominates. 2.2 Differentiable Fee Schedules Price regulation fails under uncertainty because it restricts a variable which must vary over the range of E to achieve efficiency. However, it also fails because of nonoptimal risk sharing, where in (22) utility varies
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ex post. With risk neutral agents, satisfaction of optimal risk sharing in (18) requires that V, and hence i be constant, given U’ is constant by assumption of risk neutrality. That is, the income and consumption of all other goods Z of existing residents cannot vary with Z. This requires 2 = y + RN/fi - ? - D/G to be invariant with respect to 6. This means the developer must absorb variations in both sales revenue (RN/& and taxes f. The fee schedule in Proposition 3 met this criterion and is thus potentially consistent with optimal risk sharing. Since it also has good incentive properties, this leads to PROPOSITION 5. Zf there is uncertainty about i, and agents are risk neutral, a first best outcome will be realized if the community announces the following fee schedule:
f=R-ffi,/N-D/N. Since h and g are set before E is revealed, in fact tax liabilities are set ex ante so only R (based on v,,/v, variations with C) varies ex post .6 The proof of the proposition is direct. Remark 7. The uncertainty equivalent of Proposition 4 also holds.
3. SUMMARY Under general conditions of uncertainty and asymmetric information in the land regulation process, regardless of tax assessmentprocedures, it is still possible for existing residents of a community to control the development process and achieve Pareto-efficient outcomes, assuming developer risk neutrality. Regulation requires the community to set public service expenditures and the developer to pay (a) an ex ante development fee and (b) the ex post tax liabilities of at least existing residents. In return the developer keeps all sales revenue. In general, allowing communities to regulate prices or be fiscally creative by selling tax liabilities could improve the land development process and social welfare. ACKNOWLEDGMENTS The support of the National Science Foundation (Grant No. SES-8517414)for this work is gratefully acknowledged. This paper is derived from a longer technical working paper (Brown University No. 87-11) methodically examining various types of regulation under different institutional circumstances. 6The more interesting case occurs when tax liabilities vary ex post under sales price assessmentas R varies with fi. The proposition can be proved for the more difficult case (see Henderson [13]).
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