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Zoning rights and land development timing.

Zoning Rights and Land Development Timing

I. INTRODUCTION

Zoning assigns property rights concerning land use in a community. It circumscribes the private rights of landowners and establishes collective rights to community environment. A change in zoning simply reapportions property rights. Reapportionment occurs for many reasons but voluntary exchange on mutually advantageous terms is not often one of them. In ordinary experience we seldom observe communities buying up landowners' rights to intensive development in order to preserve pastoral surroundings, or selling collective rights to pastoral surroundings to developers intent on disrupting things.

The failure of zoning to accommodate voluntary exchange between landowners and communities is understood to impair efficient land use. To the extent local governments can identify in advance the approximate collective gain or loss caused by land-use changes, land market performance would be improved if zoning could be bought and sold (Fischel 1985, 1987; Mills 1989a; Nelson 1977, 1986).

Let us suppose, counterfactually, that there were no legal or institutional barriers to the sale of zoning in communities. In this environment would it make any difference how property rights are apportioned between private landowners and the community? The answer, of course, is supplied by the Coase Theorem, which holds that in the absence of transaction costs, the assignment of property rights has no effect on social welfare - any apportionment of property rights between private landowners and the community leads to efficient land use.

The division of property rights makes a difference in whether land use is efficient when transaction costs prevent landowners and the community from capturing gains from trade. Prominent examples of transaction costs involving zoning are the costs to communities of eliciting preferences and assessing the gain or loss stemming from a land-use change (Fischel 1985, 1987). But even if the collective valuation problem can be surmounted, other transactional problems may remain that keep the property rights assignment from being a matter of indifference.

Consider a land use that imposes external costs on a community. Suppose the external damage cannot be undone by the community without incurring still greater costs. Further suppose that there are many landowners in the community who would plausibly find the offending land use to be the most remunerative option for their site, if sufficiently few other landowners make a similar choice.

If the community owns development rights to the offending land use, then landowners (developers) may not impose external costs on the community without first acquiring development rights. The community's rights may be protected by either a liability rule or a property rule (Calabresi and Melamed 1972). If the rights are protected by a liability rule then landowners may buy them for a price equal to the damage caused by development. If they are protected by a property rule then the city may agree or refuse to sell them at any price. In either case, if the community sells development rights for a price equal to the external damage caused by development, then efficient land use is achieved.

But consider what happens if landowners are given development rights to the offending land use. Suppose first that landowners' rights are protected by a property rule. With this it may not possible to achieve efficient land use because of transaction costs imposed by landowners who strategically hold out (Calabresi and Melamed 1972). The same result probably holds even if landowners' rights are only protected by a liability rule since the number of sites whose owners require compensation is large relative to the number of sites that would be employed in the offending use, and since eminent domain proceedings involve substantial transaction costs (Munch 1976).

In this example social welfare is greater if property rights to the offending land use are assigned to the community rather than to landowners. This paper explores a dynamic version of this example to see whether the assignment of property rights can have effects on resource allocation and welfare that are masked by static analysis because it overlooks development timing.

The analysis of development timing and zoning rights in a growing city is straight-forward where technology permits development to proceed continuously. The previous result that social welfare is greater when the community holds property rights to the offending land use is preserved. But when scale economies and indivisibilities prevail in construction, as undoubtedly they do for many kinds of development (e.g., hotels, shopping centers, theaters, and commercial office buildings), land development is lumpy and does not proceed continuously. Instead it proceeds in strategically timed fits and starts. In this environment property rights assignments have some unexpected effects on development timing and welfare. Sometimes the land market's performance is better with community-held rights to the offending land use and sometimes, depending on conditions of technology and demand, performance is better when landowners possess these property rights.

The paper utilizes an apt example of lumpy development. It presents a model of a growing office market in a city with mixed land uses where intensive commercial development imposes external costs of one kind or another on the community. The timing of commercial office development projects in response to growing demand is governed by preemptive competition among landowners.(1) Commercial land rents are dissipated by "premature" development and the schedule of development times for commercial projects is inefficient.

II. CONTINUOUS DEVELOPMENT

The effect of zoning on development timing is illustrated by a model of a growing city in which land can be developed either residentially or commercially. Land in the city is homogeneous and scarce, although contiguous and nearby cities supply sites that are close substitutes for residents and firms.

Assume that the demand for commercial office space is small in relation to the demand for residences, and assume that residential development is supplied by a competitive industry. Vacant or undeveloped land produces no income. Under these conditions, undeveloped land appreciates at the interest rate r such that the price a residential developer must pay for one unit of land at time t is [he.sup.rt], where h is the market value of a unit of land at time 0. Developers who buy land to build commercial office buildings must compete with residential development, so they too must pay [he.sup.rt] at t for a unit of land.

Let l denote the number of units of homogeneous commercial office space in the city. The demand for l grows over time but is asymptotically stable. Formally, let p(l, t) be the inverse demand function for l at t and assume:

[p(l, t) [is greater than to equal to] O, [p.sub.l] [is less than] O, [p.sub.t] [is greater than] O for all l and t, [A1]

lim p(l,t) = [phi](l), where [phi.sub.l] [is greater than] 0, for all l. [A2] [Mathematical Expression Omitted]

Assume further that the marginal revenue produced by an increment of office space l is positive for all relevant times and all values of l:

[Mathematical Expression Omitted]

Entry into the commercial development industry in the city is free. Commercial building technology is such that office space can be added in infinitesimal increments but can only be produced with a constant ratio of one unit of office space per unit of land. Once built, office buildings are infinitely durable and cannot be converted to residential use. Similarly, residences are long-lived and cannot be converted to commercial use.

The cost net of land to a developer of erecting an office building is C per unit of land. This cost is incurred at the time of construction and is sunk. Assume that maintenance costs are zero. Thus, amortized over an infinite lifetime the long-run marginal cost of l is rC net of land.(2)

Suppose commercial development imposes external costs on city residents. Let the damage evaluated at the time of development be D per unit of commercial office space. Assume there are no measures the city can take to mitigate these damages for a cost less than D.

The city supplies municipal services to residents and firms with constant returns to scale. Assume that these services are wholly financed by property taxes or service charges equal to their long-run marginal cost. With this there are no distortions in development timing stemming from local public finance.

The supply of office space in the city is controlled by competition among developers. With free entry and monotonic demand growth, l expands continuously and is denoted by l(t), where [l.sub.t] [is greater than or equal to] 0 for all t. The rental rate p for office space at t depends on demand and supply and equals p(l(t), t).

The time path of l also depends on the apportionment of property rights in the city.(3) Two scenarios are examined. In the first scenario landowners possess all rights to commercial and residential development of sites in the city. In the second scenario the city holds commercial development rights - which means landowners may not build office buildings - and landowners retain residential development rights. In both scenarios property rights may be exchanged between landowners and the city. Suppose landowners' property rights are protected by a property rule and the city's property rights are protected by a liability rule. With this the city relinquishes commercial development rights to any landowner who compensates the city for external damage by paying a development fee of D.

When landowners hold commercial development rights, they disregard the external costs imposed by the offices they build unless the city contrives to compensate them for their restraint. Since the commercial sector of the city is small in relation to the total supply of land, the number of potential recipients of such compensation is vast. Because of this it is likely that strategic holdouts would raise transaction costs and thwart the city's effort to offer compensation of this kind. Assume this is so.

To derive the time path of commercial development l(t) that emerges when landowners hold commercial development rights, define [l.sub.1](t) for any t as the value of l for which

p([l.sub.1](t), t) = rC.

If p(0, t) [is less than] rC, then let [l.sub.1](t) = 0. Now define [T.sub.1] to be the solution to

[Mathematical Expression Omitted]

The time path of commercial development that emerges when landowners hold commercial development rights is

[Mathematical Expression Omitted]

Equation [1] indicates that development proceeds continuously at a rate that keeps p equal to rC, the amortized cost of commercial improvements, up until [T.sub.1]. At [T.sub.1] commercial development halts once and for all and p rises above rC, approaching [phi]([l.sub.1]([T.sub.1])) as t [right arrow] [symbol omitted]. This enables all commercial developers to recoup their investments in land.

Now suppose instead that the city owns all commercial development rights and sells them to landowners for a price of D per unit of l built (or, equivalently, per unit of land developed). Under this arrangement landowners must incur the external cost of their development activity.

To derive the time path of commercial development l(t) that emerges when the city holds commercial development rights, define [l.sub.2](t) for any t as the value of l for which

p([l.sub.2](t), t) = r(C + D).

If p(O, t) [is less than] r(C + D), then [l.sub.2](t) = 0. Now define [T.sub.2] to be the solution to

[Mathematical Expression Omitted]

The time path of commercial development that emerges here is

[Mathematical Expression Omitted]

Equation [2] indicates that development proceeds continuously until [T.sub.2] at the rate that keeps p = r(C + D), which covers the amortized cost of improvements plus the development fee paid the community. At [T.sub.2] development halts and p rises so that developers can recoup their investments in land.

Demand assumptions [A1] and [A2] imply that at any t where p(O, t) [is greater than or equal to] rC, l(t) is greater for equation [1] than for equation [2]. This means that commercial development is slowed by assigning commercial development rights to the city. Similarly, as demand growth and commercial development slows, [lim.sub.t] [right arrow] [symbol omitted] l(t) is less in the scenario where the city owns commercial development rights than where landowners retain these property rights.

Assigning commercial development rights to the city retards commercial development in this model for the evident reason that it forces landowners to bear external costs produced by their activity. It is equally evident, comparing equations [1] and [2], that land market performance is superior in the model when the city, rather than landowners, owns commercial development rights. In this model, social welfare is improved by assigning commercial development rights to the city.(4)

III. LUMPY DEVELOPMENT AND

PRIVATE RIGHTS

The main implications of the previous model do not carry over to the case where development is lumpy. It is no longer true that assigning commercial development rights to the city always retards the pace of commercial development. Sometimes assigning rights to the city has the opposite effect. Neither is it true that assigning commercial development rights to the city rather than landowners necessarily increases social welfare. Depending on conditions of technology and demand, either of the property rights regimes described above can be better in terms of social welfare.

To see how indivisibilities affect development timing and welfare, we will first consider the case where landowners possess commercial development rights and where transaction costs prohibit the city from transferring the external costs of commercial development onto landowners. Section IV examines the scenario where the city holds commercial development rights.

Suppose office buildings are constrained by technology to be unit sized. Each unit of l requires exactly one unit of land. This constraint means the commercial development process is a sequence of discrete development projects and that l(t) is integer valued.

The rental rate p for office space at t depends on demand and supply, where supply depends on the number of office buildings and the occupancy levels (0 to 1) sought by commercial developers. Suppose developers' decisions about occupancy levels are determined by Cournot behavior conditional on the current supply of office buildings. With this it is easily seen that developers always seek to keep buildings fully occupied with tenants. This is because assumption [A3] implies that the marginal revenue produced by higher occupancy is always positive while the zero-maintenance-cost assumption implies that the marginal cost of higher occupancy is always zero. Full occupancy holds no matter how many buildings there are in the city and no matter how concentrated or diffuse is their ownership. It even holds if the commercial office market is monopolized by a single developer.

Because demand for commercial office space is asymptotically stable, the process has a finite number of building projects and ends when the last building is built. The timing of building projects is governed by competition among developers who seek to preempt each other by building first. The resulting equilibrium is one in which each building is built at the earliest time when a loss can be averted.

The result is easiest to see in the case where conditions of technology and demand support only one office building. In this case a second building will never be built because it is certain to produce a loss for its developer. The earliest time at which a developer can build and avert a loss, assuming no subsequent commercial development, is [t.sub.1]. [t.sub.1] is found by solving

[Mathematical Expression Omitted]

At [t.sub.1], the cost of land and construction are exactly offset by the discounted stream of future revenues from development.

More generally the office market in the city supports multiple office buildings. Let n designate the final number of office buildings that will be built in the city under prevailing conditions of technology and demand. n is the maximum number of office buildings that can be built without imposing a loss on the last developer:

[Mathematical Expression Omitted]

Preemptive competition among developers assures that the nth building is built as soon as it becomes remunerative, just as in the n = 1 case above. Call this time [t.sub.n], where [t.sub.n] is found by solving

[Mathematical Expression Omitted]

The times at which buildings 1, 2, . . . , n - 1 are built are found by recursing backwards from [t.sub.n]. For instance, [t.sub.n -1], the time at which building n - 1 is built, is the earliest time when building n - 1 can be built and a loss averted when developers anticipate that building n will be built at [t.sub.n]. Thus [t.sub.n - 1] must satisfy

[Mathematical Expression Omitted]

Between [t.sub.n]-1 and [t.sub.n] the rental rate p for office space rises but the developer of building n - 1 only recovers the amortized cost of the building. There is no return on the developer's investment in land during this time interval. It is not until after the last building is built that developer n - 1 recovers the cost of land. This is shown by equation [5].

The times when buildings 1, 2, . . . , n - 2 are built, [t.sub.1], [t.sub.2], . . . , [t.sub.n - 2], are found similarly using the equation

[Mathematical Expression Omitted]

At each of these times the supply of office space expands by one unit and the rental rate falls discontinuously. During each of the intervals ([t.sub.i], [t.sub.i + 1]), the rental rate rises and developers of buildings 1, 2, . . . , i recover the amortized cost of their buildings; no developer recovers land costs until after the development process is completed.

The sequence of equilibrium development times in this process does not preclude the simultaneous development of two or more buildings. Two or more buildings are built simultaneously when there is no earlier time a loss can be averted by building one of them earlier, given the building time of the other(s).

There are two main features of this equilibrium. The first is that preemptive development timing dissipates all the rents from commercial land development. Even when the number of commercial office buildings is small, developers have no market power and earn no economic profit.

The second main feature of the equilibrium is that preemptive development timing is suboptimal. The optimal or surplus-maximizing development process can have fewer or more buildings than n. It may be that the optimal number is less than n since developers neglect the external cost D their action imposes on the city. Alternatively, if D is sufficiently small it may be that the optimal number of buildings is greater than n. In this instance the shortfall in supply is caused by the indivisibility of l.(5)

In any case, the sequence of development times [t.sub.1], t.sub.2, . . . , t.sub.n] is not optimal. Any of these times can be either too early or too late when compared to the optimal development times. This is because optimal timing of office buildings involves building when the incremental surplus produced just equals the cost of a building (including the external cost imposed on city residents). Hence the optimal building times are independent of each other. In contrast, the equilibrium times [t.sub.1, . . . , t.sub.n] disregard external costs and the surplus produced for tenant firms. Further, they are strongly interdependent. The suboptimality of [t.sub.1], . . . , [t.sub.n], like the suboptimality of n, is the combined result of neglecting externalities and the underlying technological indivisibility.(6)

IV. LUMPY DEVELOPMENT AND

COMMUNITY RIGHTS

Consider now the commercial development process that results when the city holds the rights to commercial development instead of landowners. Assume that landowners retain the rights to residential development in the city, and that demand and technology in the office market are the same as before.

The city's commercial development rights can be protected by either a liability rule or a property rule. If the city's rights are protected by a liability rule, then the city must relinquish those rights to any landowner who wishes to develop commercially and offers to compensate the city for the resulting external damage, in this case D per unit of land developed. In the alternative, where the city's development rights are protected by a property rule, the city may refuse to sell commercial development rights to landowners at any price or may agree to sell these rights only for a price greater than D per unit of land.

For generality, suppose the city's zoning rights policy is to sell commercial development rights to any landowner wishing to build offices for a price of F per unit of land. Depending on various things, including the nature of the city's property rights, F may equal, exceed, or be less than D.

The change in the timing and extent of commercial development from the previous case where landowners held commercial development rights is straightforwardly described. Charging F for rights to develop a unit of land simply raises the developer's cost of building an office building by F. Preemptive competition among developers still assures that buildings are put up in a time sequence that is as early as possible while avoiding loss.

As before, it is conditions of technology and demand in the office market that determine how many buildings are put up. Call the final number of buildings in the city m, where m is the maximum number that can be built without causing the last one to earn negative profit:

[Mathematical Expression Omitted]

The last building is built at [Tau.sub.m], the earliest moment at which a loss can be averted. [Tau.sub.m] solves

[Mathematical Expression Omitted]

Buildings 1, . . . , m -1 are built at times [Tau.sub.1], . . . , [Tau.sub.m -1] which are solved by recursing backward using [Tau.sub.m] and

[Mathematical Expression Omitted]

The main properties of the development process defined by m and [Tau.sub.1], . . . , [Tau.sub.m] are the same as those of the process outlined earlier. Developing land at the times [Tau.sub.1], . . ., [Tau.sub.m] dissipates all the rents from commercial development for each of the m buildings. Further, the development process defined by m and [Tau.sub.1], . . . , [Tau.sub.m] is not surplus maximizing. This is so even when the city's rights are protected by a liability rule such that F must equal D. Equating F to D removes the distortions to commercial development occasioned by externalities, but it does not remove the distortions caused by the indivisibility of office supply. Whether or not F equals D, the number of buildings m can be suboptimal and the development times [Tau.sub.1], . . . ,[Tau.sub.m] can be either too late or too early.

Similarly, but more surprisingly, the development process that results when the city is assigned commercial development rights is not uniformly superior in terms of welfare to the regime where landowners hold commercial development rights. Consider first how m and a compare and how [Tau.sub.1], . . . , [Tau.sub.m] compares to [t.sub.1], . . . , [t.sub.n].

Comparing [4(*)] and [4] indicates that m [is less than or equal to] n. When the city holds commercial development rights and F [is greater than] O, landowners must absorb part or all of the external cost imposed by commercial development. This increases the cost of commercial development and it may reduce (or at office buildings that can be supported by the city's office market.

Further, comparing [5(*)] with [5] indicates that if m = n, then [Tau.sub.m] [is greater than] [t.sub.n]. That is, if the property rights assignment does not affect the number of office buildings that are built, then the process always is prolonged by assigning rights to the city. Alternatively, if m [is less than] n, the process may be either prolonged or hastened by assigning rights to the city.

The effect of development rights assignment on the timing of earlier development projects is much more complicated (than the last project). Nothing general may be claimed about whether assigning rights to the city postpones or hastens development at the various stages. In most instances it postpones some projects and hastens others (as subsequent numerical examples illustrate).

The welfare effect of changing the assignment of development rights is found by comparing the discounted surplus produced by commercial land development in the city under both property rights regimes. The total benefit conferred at t by l units of office space is

[Mathematical Expression Omitted]

The discounted surplus produced when landowners hold commercial development rights is the capitalized value of s at all times net of construction, land, and external costs:

[Mathematical Expression Omitted]

Similarly, the discounted surplus is

[Mathematical Expression Omitted]

when the city holds commercial development rights.(7)

The relationship between w and w(*) is not uniform. In some cases w is larger and in others w(*) is larger. To assess the range of possibilities, and to explore some related issues, I introduce some numerical examples based on a particular class of demand functions.

V. NUMERICAL EXAMPLES

Consider an isoelastic demand function of the form

[Mathematical Expression Omitted]

where b is a positive demand scaling parameter, [eta] is the price elasticity of demand for l, and g is a demand growth parameter. With this specification, demand is increasing but becomes asymptotically stable as t [right arrow] [Symbol Omitted]. Assume that [eta] [is greater than] 1 in keeping with the positive marginal revenue assumption [A3].

For simplicity all the examples reported in this section of the paper share common values of most variables. The assumed value of the interest rate r is .06 and of price elasticity [eta] is 1.2. The fixed cost C of developing one unit of land is 100 units of value and the opportunity cost h of a unit of land at t = O is 30 units of value. The growth parameter g is assumed to be .0825, which means demand grows to exactly half its asymptotic value at t = 10 "years." (8) Three remaining variables distinguish the reported examples. These are the growth parameter b, the external cost D of developing a unit of land commercially, and the price F the city charges for commercial development rights where it owns them.

Table 1 displays some numerical examples that compare timing and welfare in two scenarios: (i) when landowners own commercial development rights, and (ii) when the city owns all commercial development rights where rights are protected by a liability rule (e.g., F = D). The values of parameters that distinguish the examples appear at the bottom of the table. In examples 1 and 2, m = n and [Tau.sub.m] [is greater than] [t.sub.n], which means the assignment of development rights has no effect on the final supply of office space in the city. The main effect of assigning development rights to the city in both of these examples is to postpone both the beginning and the end of the development process. Notice however that the welfare effect of assigning rights to the city differs in the two examples. In example 1 welfare is greater with landowners retaining development rights; in example 2 welfare is greater if the city holds the development rights.

In examples 3 and 4, m [is less than] n, which means the supply of office space in the city [Tabular Data Omitted] is reduced when the city owns commercial development rights. Also in these examples, development starts and ends earlier when the city owns development rights. In example 3 welfare is greater with landowners retaining ownership of development rights; in example 4 welfare is greater with the city owning the rights.

Taken together examples 1-4 illustrate that development is not uniformly slower or faster when cities own development rights. Similarly they show that neither property rights regime is uniformly superior to the other. Simple indicators like whether m = n or whether development is postponed or hastened by reassigning development rights are insufficient for predicting whether reassigning rights will improve the performance of the office market.

This is further shown by the examples displayed in Table 2. These examples are distinguished only by the value of the growth parameter b. As demand increases successively from example 5 to example 6 and example 7, one sees that the identity of the superior property rights regime alternates. In example 5 welfare is greater with landowner development rights. In example 6, with slightly greater demand, welfare is greater when the city owns development rights. This is because the increase in demand is sufficient to induce a fifth development project under this regime as under the other. In example 7, with another small increase in demand, a sixth project is supported under the regime with landowners retaining rights and welfare emerges greater once again with this regime. Small changes in demand often are sufficient by themselves to change which regime achieves the best performance.

TABLE 3
i   [t.sub.i]   [Tau.sub.i]   [t.sub.i]   [tau.sub.i]
1   2.50        0.76          2.50        0.00
2   2.50        5.42          2.50        0.00
3   2.50        6.31          2.50         -
    w           [w.sub.*]     w           [w.sub.*]
    1,805       1,839         1,779       1,758
b            61                        43
D            10                        20
F            10                        20


TABLE 4
i   [t.sub.i]   [Tau.sub.i]   [t.sub.i]   [Tau.sub.i]
1   0.13        0.74          4.00        1.63
2   0.13        3.92          4.00         -
3   0.13        4.83           -           -
4   0.13        4.83           -           -
    w           [w.sub.*]     w           [w.sub.*]
b            90                        39
D            15                        100
F            20                        90


As mentioned above, the performance of commercial development timing in the city is subjected to two distortions when landowners own commercial development rights. These are the ability of landowners to escape the external cost their decisions impose on city residents and the distortions created by the indivisibility of office supply. When the city owns development rights the first of these distortions is removed because landowners must compensate the city for external costs imposed by development. Thus the comparative advantage of a regime where the city owns development rights is in removing the externality distortion. It might appear that with this comparative advantage city ownership of rights is more likely to produce superior performance the greater are the external costs of development D. Often this is true, but not universally. Table 3 displays two examples that illustrate this. In example 8 the regime that assigns development rights to the city is superior. But in example 9, which differs from example 8 only in the doubling of the variables D and F, the superior regime is the one where landowners retain development rights. In this instance, increasing external costs actually favors the regime that assigns rights to landowners who will neglect external effects.

All the examples presented thus far assume that the city's commercial development rights are protected by a liability rule such that F = D. The examples in Table 4 demonstrate that market performance sometimes is superior when commercial development rights are sold for a price other than D. For the city to sell development rights at a price of F > D, these rights must be protected by a property rule rather than a liability rule.

Example 10 duplicates example 2 in every respect except the value of F. In example 2, F = D = 15. But in example 10, F = 20 with the result that development times change and the discounted surplus from commercial development [w.sup.*] rises. In this instance performs better if the city holds the process performs better if the city holds the development rights and sells them for a price greater than the external cost of commercial development.

Similarly, example 11 duplicates example 3 except for the value of F. In example 3, D = F = 100, while in example 11, F = 90. In this instance the office market's performance improves when F is less than D - when the city sells development rights for a price less than the external costs imposed by development.

Just as neither private nor community ownership of development rights always outperforms the other, the surplus-maximizing fee for the city to charge for development rights may not equal the external cost imposed by development.

VI. CONCLUSION

In summing up, the main claim of this paper is that none of the property rights regimes examined are uniformly superior in terms of land market performance. Under some conditions of technology and demand, the land market performs better when the community holds property rights to the most intensive land uses, as often is the case (Ellickson 1973). This assignment of rights enjoys wide support (e.g., Ellickson 1973; Kmiec 1981; and Wittman 1986, among others). But even here there is no clear rule of thumb as to the optimal impact fee to extract from landowners in exchange for development rights. In general the optimal fee is not equal to damages because of the perversities of development timing with preemptive competition. And in any case, under some conditions the land market performs better when development rights are retained by landowners, as prescribed, for instance, by Siegan (1972).

The model presented in this paper can be extended to analyze other property rights regimes including those where some landowners retain property rights to commercial development while others do not. One speculates that this asymmetry in the distribution of property rights invites some degree of cartelization of the office supply in the community and has additional effects on timing and welfare.

(1) The model of preemptive competition here is similar to those of Gilbert and Harris (1984) and Mills (1989b).

(2) All the results in this section of the paper would go through for any combination of fixed construction costs [gamma] and maintenance costs v such that [gamma] + v/r = c. The same holds for sections III and IV if assumption [A3] is strengthened to bound marginal revenue above v.

(3) Fischel (1985) points out that the unitization of community interests by local governments has been eroded in recent years by the National Environmental Policy Act (1970) and various other state land-use regulations. I will disregard laws and procedures that permit agents other than local government to have a role in determining the pace and character of land development.

(4) This supports Ellickson's (1973) arguments favoring the assignment of most development rights to local governments rather than landowners. He indicates that, in fact, most development rights are held by local governments rather than landowners.

(5) See Mills (1989b) for a demonstration of supply shortfall.

(6) Mills (1989b) shows that the social costs stemming from indivisibilities per se diminish rapidly as the degree of lumpiness declines.

(7) F does not appear in equation [10] because it is only a transfer from landowners to the community at large.

(8) That is, [Mathematical Expression Omitted].

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Department of Economics, University of Virginia, Charlottesville.

The author thanks Jan Brueckner, Bill Oakland, Bill Wheaton, and especially Bill Fischel for helpful comments on an earlier version of this paper presented at the October 1989 TRED confenrence on Growth Management and Land-Use Controls at the Lincoln Insititute of Land Policy in Cambridge, Massachusetts. Research support was provided by the Center of Advanced Studies at the University of Virginia.
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Title Annotation:Land-Use Controls
Author:Mills, David E.
Publication:Land Economics
Date:Aug 1, 1990
Words:6128
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