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This study surveys theoretical analyses at the individual parcel or block level of several land use policies that are employed by local governments. The goals of each of the three models presented are twofold: 1. to gain an understanding of the effects of policies as they operate in the relevant markets, and 2. to formulate reasonably simple methods for cost-benefit analyses of these policies. Numerical examples or empirical results are employed to illustrate the possible use of each model. Zoning ordinances allocate land to uses and regulate the intensity of land use. The first model examines the allocation of a parcel of land to a particular use by land-use zoning. The parcel in question is subject to property taxation, and it is assumed that there is unemployed labor residing in the jurisdiction. The next model continues the examination of zoning by studying the effects of land-use intensity regulations at the individual parcel level. The final model studies land-use zoning at the block level and explicitly introduces external effects into the model.

Introduction

This study surveys theoretical analyses at the individual parcel or block level of several land use policies that are employed by local governments. The goals of each of the three models presented are twofold; to gain an understanding of the effects of policies as they operate in the relevant markets, and to formulate reasonably simple methods for cost-benefit analyses of these policies. Numerical examples or empirical results are employed to illustrate the possible use of each model. Zoning ordinances allocate land to uses and regulate the intensity of land use. The first model examines the allocation of a parcel of land to a particular use by land-use zoning. The parcel in question is subject to property taxation, and it is assumed that there is unemployed labor residing in the jurisdiction. The next model continues the examination of zoning by studying the effects of land-use intensity regulations at the individual parcel level. The final model studies land-use zoning at the block level and explicitly introduces external effects into the model.

The main purpose of the article is to point out that there are three basic types of benefits (on an annual basis) to the local jurisdiction associated with a zoning decision: land rent, local taxes in excess of the required spending on additional public services and employment benefits. Benefits to the local jurisdiction are not necessarily maximized by pursuing the zoning policy that maximizes land rent. For example, choosing to zone a parcel of land for residential use may maximize land rent, but it is likely that the public services associated with residential use exceed the local taxes collected (unless an additional impact fee is assessed), and employment benefits associated with commercial or industrial use are foregone.

Cost-Benefit Analysis of Local Land-Use Allocation Decisions

State and local governments are making extensive use of policies and programs that are intended to stimulate economic activity. Among those programs are land use allocation decisions for the purpose of generating economic activity. For example, the book by Rast (1999) recounts the recent history of the decision by the City of Chicago to attempt to stimulate industrial growth by designating "protected manufacturing districts" in which changes in zoning to permit residential development are prohibited. These districts were created in spite of the fact that the value of the land in residential use was much higher than in industrial use. A suburban example is found in a recent newspaper article by Orr (2000) in which, "Naperville residents seek study of city's last vacant land." Here the issue is whether land that had been designated for a business park should instead be allocated to residential development.

Bartik (1990) and Courant (1994) advocate the use of conventional cost-benefit methods to assess local economic development policies. The purpose of this section is to devise some methods through which the principles of benefit-cost analysis can be applied to land use allocation decisions. The central point is to make the connection between policies and economic outcomes in the urban land and labor markets. The model shows that land use allocation policies have impacts that can be measured in the urban labor and land markets: changes in employment, land values and the intensity of land use. Procedures for the estimation of benefits and opportunity costs are derived. The benefits in this model fall into three categories: employment of previously unemployed or underemployed workers (including possible multiplier effects), increases in local tax revenue in excess of the cost of additional local public goods and services required, and higher value of land. Local economic development policies considered here have no benefits if there is no unemployment, if users of local public goods pay taxes equal to the value of the benefits of those goods (as in Tiebout, 1956 and Hamilton, 1976), and if land is already allocated to its "highest and best" use. In short, the benefits exist in a world with distorted markets. This section follows McDonald (2001).

One crucial assumption is that involuntary unemployment (or underemployment) may exist in the jurisdiction in question. Workers may be available at a reservation wage that is lower than the market wage; the opportunity cost of labor is less than the value of its marginal product. The plan is to proceed through a sequence of models. The first model is devised to study the benefits and costs of land use allocation decisions and other economic development policies for a small, "open" jurisdiction. All input and output prices are exogenous to the jurisdiction, and the economic efficiency of policy is examined from the point of view of that jurisdiction and from the point of view of the larger society. A more complex model, which is presented in McDonald (2001), examines the case in which the jurisdiction is not completely open, but faces demands for its industrial (export) product and for housing that are of finite elasticity. In this model the estimation of benefits and costs is a more complex task than is in the case of the open jurisdiction.

This study does not consider the question of the timing of economic development programs. Mauer and Ott (1999) have considered this issue in the context of a model of firm location (and relocation). In their preliminary discussion of the model, state that, "The benefits may include a reduction in the direct and indirect costs of unemployment, an increase in tax revenue, and the multiplier effect of an increase in economic activity," (p. 425). They take these benefits as given and do not consider them further.

The fundamental points of the section can be made with a simple model of land use and land value. Consider a small, one-unit parcel of land that might be allocated to either housing or industrial use by a local jurisdiction that is open; it is assumed that the opportunity cost of industrial land is its use for housing. All output and input prices (except for land rent) are exogenous to the jurisdiction. This model would usually be applied to the case of a jurisdiction that allocates another unit of land to businesses that produce goods for export outside the jurisdiction. The possibility of externalities (negative or positive) is ignored here. All markets are assumed to be perfectly competitive.

Housing services are produced by combining the services of land and capital. The market price of a unit of housing services is P^sub h^, which is exogenous both to the parcel in question and to the jurisdiction. Capital services have an exogenous opportunity cost r per unit, so the annual benefit of allocating the unit parcel of land to housing is:

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where H is units of housing services produced, K^sub h^ is unit of capital services allocated to housing and R^sub h^ is land rent calculated as a residual. If housing services are produced with constant returns to scale, R^sub h^ is also the value of the marginal product of land in housing. The assumption of constant returns will be made.

Industrial activity involves combining the services of land, labor and capital to produce output (value added). The market price of output p is exogenous both to the parcel and the local jurisdiction in question, as is the opportunity cost of capital services r. The cost of labor to industrial firms is w. However, for purposes of this example it shall be assumed that some labor is involuntarily unemployed at wage rate w. The opportunity cost of labor (reservation wage) is assumed to be w* < w. An increase in land allocated to industrial use will shift the demand for labor to the right, and the resulting increase in employment will have a benefit to the worker and to society of (w - w*) per additional worker employed. As Mishan (1982: 68-71) points out, the benefit to society will also include the worker's unemployment compensation or other forms of income support that are eliminated when the person is hired. In other words, society gains additional output that has a value of w at a cost of w* minus the annualized value U of the unemployment compensation and other income maintenance that the worker received. However, if the costs and benefits are considered from the point of view of the local jurisdiction, only the portion of U that is paid by the local jurisdiction (and denoted C) is counted. In other words, it is necessary to impute to the local jurisdiction its share of the marginal cost of the unemployment compensation and welfare programs of the state. Another benefit of increasing employment in a particular location may be savings in commuting time and expense. The idea would be to estimate these savings for the residents of the jurisdiction who are employed at the site in question (using the value of reductions in commuting time to convert the time savings into money). Another approach would be to estimate the extent to which their reservation wages are lower than the market wage because of the saving in commuting cost. Denote this benefit as TS (for travel savings).

The increase in industrial employment is simply:

dN / dL = N / L,

where N is industrial employment and L is land. In the long run, each parcel of industrial land of standard quality and accessibility will have the same ratio of labor to land, N/L. Therefore, assuming that the unit parcel in question is of standard quality and accessibility, its employment density will be N/L as well. The addition of the parcel in question to industrial use has resulted in a net gain of (N/L) jobs for the jurisdiction. No jobs located on this parcel have "moved" from other locations within the jurisdiction. However, as Bartik (1991) points out, many of the jobs will be taken by workers who are not original residents of the jurisdiction. In Bartik's typical case, original residents take 23% of the increase in employment, and 77% of the jobs are taken by workers who move to the jurisdiction.

The benefit to the local jurisdiction from allocating the parcel in question to industrial use can be found as follows. It is assumed that the parcel is owned by someone in the jurisdiction (or that, by definition, the owner of the parcel is a member of the jurisdiction). The market rent of the unit parcel in industrial use captures the value added by labor and capital, and is:

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where Q is output and K^sub n^ is units of capital services allocated to industry on the parcel. R^sub m^ is only part of the benefit because the increase in employment has generated benefits equal to f(w + C - w*)(N/L), where f is the fraction of jobs taken by original residents or the jurisdiction. The first-round benefits of allocating the unit parcel to industrial use are therefore Rm + f(w + C - w*)(N/L). As Sridhar (1996) points out, benefits to society as a whole include benefits that arise from the movement of workers to the jurisdiction.

Cost-benefit experts such as Mishan (1982) point out that the net addition to income generated by the industrial use (compared to the residential use) may generate a multiplier effect that should be counted as a benefit. The multiplier effect that counts as a net benefit for the local jurisdiction is the extent to which there is any additional employment of heretofore unemployed workers who are original residents of the jurisdiction. Felsenstein and Persky (1999) provide a more detailed analysis of the multiplier effect by using the "chain of jobs" approach. Each added worker values his/her employment at (w - w*), and C is saved in income maintenance payments per worker. Here it is assumed that the multiplier effects are small enough to have no effects on market prices or land use allocation. McGregor, McVittie, Swales and Yin (2000) and Merrifield (1987) discuss local multiplier models.

The annual benefits to the local jurisdiction of allocating the unit parcel to industrial use minus the cost, or net benefits NB, can now be written as:

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where M is the local employment multiplier effect, TS is travel savings and P is the (annualized) cost of the program itself. Net benefits of industrial use are positive if:

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i.e., if the benefits to labor exceed the differential in land rent plus program costs. It is assumed that, because of local zoning and other constraints on land use allocations, R^sub h^ does not necessarily equal R^sub m^ for the site in question. Thus far the reservation wage has been assumed to be a constant unknown w*. Clearly the level of the reservation wage is a critical variable in the model, but there are a few recent empirical studies that can serve as a guide. A survey of older reservation wage studies by Gordon (1973) shows that the average reservation wage varied from 72% to 98% of the previous wage, and the average wage accepted on the new job varied from 59% to 105% of the previous wage. More recent studies by Feldstein and Poterba (1984) and Jones (1989) show that the reservation wage is a function of sex, the cause of unemployment, the length of unemployment and the generosity of unemployment benefits. In the study by Feldstein and Poterba, people who had voluntarily left the previous job and who had been out of work for less than five weeks had a reservation wage that was 112% of the previous wage, but that those who had lost their jobs (and were not on layoff) and had been out of work for at least fifty weeks had a reservation wage that was 91% of the previous wage. The study by Jones has the result that prime aged males (aged 25-54) have a reservation wage that is essentially equal to the previous wage until they have been unemployed for more than twenty-four months, but the reservation wage for the men who have been unemployed for more twenty-four months is 79% of the previous wage. The reservation wage in the Jones study for females was equal to the previous wage regardless of the duration of the unemployment spell. The studies by Kaspar (1969), Stephenson (1976), Kiefer and Neumann (1979) and Fishe (1982) also show that the reservation wage decreases with the length of unemployment. As noted above, Sridhar (1996) found that the reservation wage is negatively related to the local unemployment rate. In short, the benefits of increasing employment may critically depend on local labor market conditions and characteristics of the unemployed workers who are hired as a direct or indirect result of the local economic development program. It is also clear that more empirical studies of reservation wages are needed to facilitate the evaluation of local economic development policies. It will be important to make the distinction between short-term cyclical unemployment and long-term structural unemployment; the latter is the target of local economic development policies. It may also be important to pay close attention to the stream of employment benefits into the future, rather than just the annualized version shown in Equation (4).

Land and capital are subject to real estate taxes and receive benefits in the form of local public goods, so a more realistic version of the model should include the local public sector. Introduction of the real estate tax also provides another variable that can be manipulated by local officials to influence market outcomes. If the real estate tax is a benefits tax as contemplated in the Tiebout (1956) model literature [e.g., by Hamilton (1976) and many others], then the model reduces to Equation (1). In the more general case, the land rent will include the net benefit of local public sector activity. Because capital and households are perfectly mobile with respect to the unit parcel in question and because the demand for output is perfectly elastic, the incidence of the net local real estate tax is entirely on land. In other words, if the local public sector confers benefits in excess of real estate taxes, then that net benefit will be reflected in land rent. For residential use this net benefit will usually be positive, and it represents the value of local public services that are costly to produce. Therefore, this net benefit (net cost) to the residents of the site should be subtracted from (added to) land rent. The benefits to the local jurisdiction of allocating the unit parcel of land to housing are:

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where T^sub h^ is the net contribution (taxes minus value of services) of the parcel to the local public sector. It is likely that T^sub h^ is negative for residential use; value of services exceeds taxes collected. For this reason many local jurisdictions also assess a development impact fee.

The case of industrial use is similar to the residential case. The net benefit of local public goods will be capitalized into land value. In the case of retail use, local taxes include sales taxes as well as real estate taxes. However, given the assumptions of this model, sales taxes are also fully capitalized into land value. Ordinarily the costs of public services attributable to commercial and industrial activity are less than those costs for residences largely because of the cost of public schools (Netzer, 1966), so the taxes will exceed the value of the benefit of local public goods for industrial or commercial use. The net benefit of allocating the unit parcel to industrial or commercial use in the presence of the local public sector can now be written as:

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where T^sub m^ is the net contribution of the parcel in industrial or commercial use to the local public sector. (Note that it is probable that T^sub m^ > 0 and T^sub h^ < 0.) Equation (7) can be used as the basis of a cost-benefit analysis of a local economic development program from the standpoint of the local jurisdiction provided that the assumptions of the model are satisfied; the allocation of the additional parcel of land to employment activity does not subtract from the amount of employment at any other location in the local jurisdiction (because output and input prices are exogenous), and the local multiplier effect increases employment but has no effect on prices or land use allocation.

Assuming that all output and input prices are exogenous, the net benefit of the local economic development program to the larger society includes all of the employment increase (not just fraction f), the national multiplier effect, and all income maintenance costs that are avoided (U). Net benefits to the nation are:

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where M^sub n^ is the national multiplier effect of the program. In this model the rest of the nation benefits from the local economic development program in the amount:

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Assuming w > w*, in this basic model the rest of the nation has an incentive to encourage local jurisdictions to allocate land to industrial use.

A numerical example can serve to illustrate the annualized version of cost-benefit analysis that is proposed. Some of the data used in the example are drawn from a Chicago case study discussed by Rast (1999: 144-5). In 1994, a developer proposed to build 330 townhouses on an eleven-acre largely vacant site that is zoned for manufacturing. The value of the land is $5 per square foot as industrial space and estimated at $15 per square foot as residential space. The issue is whether the city should accept this development plan, or market the property to an industrial user. It is assumed that the townhouse project is the residential use of the highest value (compared to, for example, single-family houses).

Assume that the townhouses have a market value of $250,000 each, so the total value of the residential development would be $82,500,000. Residential property taxes in Chicago are 1.8%10 of market value, which would be $1,485,000 annually. Assume that the development would contain 200 children who attend the public schools. At $5000 per child, the necessary expenditure per year would be $1,000,000. Assume that an additional $1,000,000 will be needed per year to cover the other public services, so the net contribution of the site to the local public fisc is -$515,000. With a land value of $15 per square foot and, assuming a 10% interest rate, annual land rent for eleven acres would be $718,740.

It is assumed that the site is in demand as industrial space at a market price of $5 per square foot. At this price, with an interest rate of 10%, annual land rent is $239,580. Data from McDonald (1985) for Chicago in 1970 indicate an industrial floor-area ratio of 0.59, so there would be 282,700 square feet of industrial space on eleven acres. The data from McDonald (1985) also show 840 square feet per industrial employee, so the projected employment for the site is 337. Assume a salary of $30,000 per year. The reservation wage is estimated to be 84% of that salary, and the local share of welfare and unemployment benefits avoided is negligible. Assume that there are no commuting cost savings. The market value of the industrial facility is estimated to be $33,700,000. If the capitalization rate is 10%, then the annual rent for the facility is $3,370,000 (and the share of labor is 75%). Of this the land rent is $239,580 and the rent for the capital is $3,130,420 ($11.07 per square foot). The property tax rate on industrial property in Chicago averages 5%, but property tax incentives would be used to reduce that rate to 3.5%. Annual property tax collections would therefore be $1,180,000. Recall that costs for public services other than schools are $1,000,000. Following Bartik (1991), assume that f = 0.23 (the share of jobs filled by Chicago residents), and assume that the local employment multiplier is 1.15.

These data permit the terms in Equation (7) to be filled in as follows:

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In this example, the use of the site for industry is indicated on efficiency grounds. The loss of annual land rent in residential use is more than made up by the fact that, in this model, industrial use does not require the provision of public schools and that the wage exceeds the reservation wage. Note that the annual net benefit of residential development is $718,740 - $515,000 = $203,740, while the annual net benefit of industrial development is $847,435.

Performing the cost-benefit analysis presents some difficult empirical issues. The variables needed include land rents, reservation wages, the local employment multiplier, the proportion of jobs created that will be held by local residents, net contributions of each land use to the local fisc, and so on. These are the sorts of problems one faces in any detailed cost-benefit analysis, and a standard method is to perform sensitivity analysis with alternative estimates of the important variables.

Cost-Benefit Analysis of Land-Use Intensity Regulations

This section examines the effects of the direct regulation of the intensity of land use at the level of the individual parcel. It is assumed that land use has been determined. Now the question is the intensity of that use. The model is developed for the housing market, in which (as in the previous section) stocks of land L and capital K produce housing real estate according to a linear-homogeneous production function:

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Here the local property tax is assumed to be a benefits tax that has no effect on the intensity of land use. For example, the current system of zoning in the city of Chicago, which was enacted in 1957, contains a system for the zoning of residential land that controls the intensity of land use directly. The crucial provision in the ordinance controls the "floor-area ratio," which is the ratio of usable floor area to the area of the lot. The allowable floor-area ratio ranges from 0.5 for R-1 zoned land to 10.0 for R-8 zoned land. For example, R-1 zoning permits the construction of a two-story house that covers 25% of the lot, and R-8 zoning allows the construction of a forty-- story building that occupies 25% of the lot. The zoning ordinance also controls minimum lot area per housing unit, minimum front, side, and backyard widths, and minimum parking spaces. What is important from a theoretical standpoint is the limitation on the floor-area ratio. This provision is very nearly a direct control on the ratio of capital to land. Of course, structures of equal floor area can contain different capital inputs by variations in the quality of construction, number of bathrooms, etc. However, the building code places limitations on allowable variations of this kind.

Consider housing production on a unit parcel of land with exogenously fixed accessibility and other amenities. Assume that the land market contains many sites with identical characteristics, so that competition fixes the land rent (and value) of the site in question. The rental price of capital is also exogenous to the site and the producer (or producers) who occupy the site. Only one level of output is consistent with long-run equilibrium. This output can be produced and sold because competition in the output market establishes the exogenously fixed price of housing (given the accessibility and other amenities of the site). The value of the marginal product of land is simply:

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where R^sub h^(a) is the rent on land, p^sub h^(a) is the price of a unit of housing services, a is a vector of site amenities and MPL is the marginal product of land. The usual approach in land-value studies is to make the observation that p^sub h^(a) and K^sub h^(a)/L(a) are both functions of a, p^sub h^(a) and k(a) = K^sub h^(a)IL(a) are perfectly correlated. One thus only needs to examine land rent (or value) as a function of the variables in a, or R^sub h^(a) = g(a).

The introduction of zoning to regulate the floor-area ratio potentially breaks the perfect correlation between R^sub h^(a) and MP^sub L^. If the allowable capital-land ratio Z is less than the market determined capital-land ratio k*, then MP^sub L^ is less than is otherwise would be, but p^sub h^(a) is unaffected. Now land rent can be expressed as:

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where D = 1 if k* /Z is greater than one (and D = 0 if k* /Z is less than or equal to one). In other words, land value is equal to g(a) unless Z is less than k*, in which case land value is less than g(a) by an amount that is a function of the extent to which Z is less than k*. This point can also be expressed in the language of nonlinear programming. For an individual land parcel: phi(Z - k) = 0, where phi is the shadow price of the zoning constraint (which equals zero if Z is greater than k, where k is the actual capital-land ratio).

For purposes of empirical estimation, the zoning variable is relevant only if Z is less than k*. Furthermore, the appropriate variable to use is k*/Z, and not Z. The equation to be estimated is:

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where u^sub 1^ is a normal error term. Failure to include the term Dlnh(k*/Z) will lead to a potentially serious omitted variable bias in the coefficients of the In g(a) function. However, k*/Z cannot be measured directly because k* is not observed if Z is less than k*. Furthermore, as is seen below, there are problems with determining D on the basis of a comparison of actual k and Z. One further point about Equation (11) is of interest. If the production function for housing is assumed to have a constant elasticity of substitution (CES), then the functional form of the equation is simplified to:

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In other words, if the elasticity of substitution equals 1.0, the 75% reduction in the allowable floor-area ratio reduces the land rent by 75%. If sigma > 1 (sigma < 1), this 75% reduction in the allowable floor-area ratio reduces land rent by less than (more than) 75%. There are no other costs in this model because, while the supply of housing is reduced, the demand for housing on the site is of infinite elasticity. If the local property tax is not a benefits tax, but rather the property taxes collected fall short of the cost of additional public services provided to the site, then a reduction in the floor-area ratio will reduce the size of this cost that is being imposed on the local jurisdiction. The reduction in the net tax cost to the local jurisdiction tends to offset the cost as reflected in the decline in land rent.

An empirical study by Jud (1980) found that the imposition of large-lot zoning reduced the per-square-foot value of single-family houses by 8%. The numerical example in the previous section can be adapted to the case of a reduction in the allowable density of development. Suppose that the residential development now consists of 220 townhouses (a 33% reduction), and that residential land values fall to $10 per square foot (also a 33% reduction). The number of school children in the development falls from 200 to 133. Residential land rent per year falls by 33% to $479,160. The value of each house consists of $228,220 of structure and $21,780 in land, for a total of $250,000 per unit as before. Total property tax collections (at 1.8% of value) are $990,000. Local public expenditures are $1,333,333 (two-thirds of the previous total of $2,000,000), so the net contribution to the local fisc is -$343,333. The annual net benefits of industrial use can now be computed as:

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The imposition of the density control on residential use reduced the benefits of residential development from $203,740 to $135,827.

Cost-Benefit Analysis of Externality Zoning at the Block Level

The models developed here thus far have not considered zoning for the purpose of mitigating the effects of external effects. This section contains a simple model of land use, land values and zoning in the presence of externalities that has been estimated empirically. The unit of analysis is the "block," an area that is small enough so that externalities matter, but an area that is larger than the amount of land normally owned by a single owner. The external effects contemplated are localized to the block level and result from the mixing of land uses on the block. In contrast, if the external effects were generated by a large plant, it would be appropriate to represent the harm incurred by distance from a residence to the plant. It is assumed that the externality incurred by residential land users is a function of the proportion of the block that is in nonresidential use.

The model can be formulated as a nonlinear programming problem that extends the model developed by Crone (1983). The presentation here follows McMillen and

McDonald (1993). The problem under consideration is the maximization of land on the block with respect to the proportion of land in residential use. The problem is to maximize:

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Zoning to Increase Land Values

Given this model of land use and land values, what might be accomplished by block-- level zoning? Two types of zoning are considered. Zoning might be an instrument for "fine-tuning" the allocation of land to maximize land values, or it might be a blunt instrument that assigns a block to be residential. The zoning as a fine-tuning ordinance would alter the market allocation of land only when the market fails to be efficient-the case of fragmented ownership and the failure of the Coase theorem. An improvement in the allocation of land might require a boundary solution, but it also might require mixed land use in accordance with the interior optimality condition above.

The first case in which exclusive residential zoning could increase land values is when the competitive market leads to mixed use on the block, in which case V^sub r^ = v^sub c*^ Let kappa^sub r^* be the proportion of land in residential use when v^sub r^ = v^sub c*^ Exclusive residential zoning can increase the value of land if v^sub r^(1) > v^subr^(kappa^sub r^*).

This condition clearly requires that the residential land-value function be upwardsloping over some range, although it need not slope upward at either kappa^sub r^* or kappa^sub r^ = 1 The global maximum in land value may occur at kappa^sub r^ = 1, but it could occur at some other value. Thus, a zoning ordinance that assigned a mixed-use block exclusively to residential use could increase land value, but not necessarily maximize land value.

There is also a case in which the market leads to exclusive nonresidential use on a block, but the value of land would be higher with exclusive residential use. This case must have v^sub c^(0) > v^sub r^(O) so that there is no incentive for a single owner of a small amount of land to convert from nonresidential to residential use. Also, the value of land in exclusive residential use must be higher than existing land value; i.e., v^sub r^(1) > v^sub c^(0).

Again, this condition implies that the residential land value function must have an upward slope over some range. Also, exclusive residential zoning may not maximize land values even if it increases them.

Empirical Evidence

The model discussed in this section implies that a necessary condition for the assignment of a block exclusively to residential use to increase land value is that residential land values rise with the proportion of the block in residential use (over some range). Empirical land value functions were estimated by McMillen and McDonald (1993) for Chicago in 1921, two years before the first zoning ordinance was adopted. This study found that residential land values did not increase with the proportion of land in residential use on the block, so the conclusion was reached that the zoning system that was adopted in 1923 could not have brought about a general increase in land values. However, a subsequent study by McMillen and McDonald (2002) found that land zoned for residential use increased in value more rapidly after 1923 than did land assigned to commercial use. The conclusion that can be reached as a result of these two studies is that residential zoning provided a kind of insurance policy against the invasion of commercial or industrial activity that would create strongly negative external effects, even though such invasion had not generally been the case prior to zoning. Apparently the value of residential zoning was a value attached to a reduction in a form of risk. This finding is consistent with Speyrer's (1989) empirical result that residential zoning increased property values by about 8% (compared to an absence of zoning) and with Jud's (1980) result that residential zoning increased house value per square foot by 11% (compared to non-residential zoning).

However, as the previous analysis in this article emphasizes, additional residential land use on a block can be accompanied by an increase in public services demanded in excess of property taxes collected and by the loss of employment benefits attached to the commercial use. It is not necessarily true that zoning to eliminate the mixing of land uses on a block will result in net benefits for the local jurisdiction even if the value of the land rises. The net tax and employment effects should be included if they are relevant. Following the numerical example from above, suppose that the site could contain a mixed-use development that is two-thirds residential and one-third commercial. Assume that, with this development mix, equilibrium land value is $10 per square foot (in both uses)-while it would be $15 if the site were entirely residential. The residential portion of the development consists of 147 townhouses each with a market value of $250,000 as before ($228,220 in structure and $21,780 in land). Annual land rent in the residential portion is $320,166 (10% of the land value). Property tax collections on the 147 housing units are $661,500, and local public expenditures are $809,909 (44.55% of $2,000,000, including school expenditures for eighty-nine children). Assume that the commercial portion of the development generates one-third of the property tax and employment benefits of the previous industrial development example. The annual benefits of the mixed-use development are:

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Recall that the annual net benefit of 100% residential development is $203,740, so converting the plan for the site from mixed use to entirely residential use would increase land values but result in a reduction in total benefits. (However, commercial development is the use of the site with the greatest benefits in this example.)

Conclusion

This article provides a set of related models of the land market and land-use intensity that can be used to assess the effects of a variety of local zoning on land values, employment, local property tax base and other related variables. The models are applications of conventional microeconomic theory in which urban land is an input into the production of urban goods-housing or commercial or industrial outputs produced on urban land. In each case the goal is to formulate a relevant model that requires only a few parameter values for application to specific situations. Given estimates of parameter values, cost-benefit analyses of particular policy actions at the individual parcel or block level can be undertaken.

The models are: (1) cost-benefit analysis of land-use allocation decisions for individual parcels; (2) cost-benefit analysis of land-use intensity regulations for individual parcels; and (3) cost-benefit analysis of zoning at the block level with externalities.

Additional versions of the models can be developed for other uses. For example, McDonald (1983) explored the effects of variations in the property tax rate applied only to capital or only to land on land value, land-use intensity and employment at an urban site. Omitted from this study are models of zoning and overall spatial patterns in urban areas, such as the models developed by D'Ouville and McDonald (1988) and Frew, Jud and Winkler (1990).

The cost-benefit analysis of land-use allocation decisions leads to the conclusion that the annual benefits of a particular choice of land use fall into three categories: land rents, employment effects and net costs of additional public services. The costs of a particular land-use selection are the benefits of the next-best choice of land use. The basic conclusion is that benefits to the local jurisdiction are not necessarily maximized if the land is allocated to the use with the highest land rent. This conclusion carries over to the other two models. The cost of restricting the intensity of residential land use in terms of a reduction in land rent can be offset by a reduction in the net tax cost associated with the land parcel in question. And the benefit of eliminating mixed land use by zoning the parcel entirely for residential use can be offset by both the increase in net tax cost and the loss of employment benefits associated with the commercial use that has been eliminated. Studies of these effects are needed to obtain a complete picture of the cost and benefits of land use regulations.