Skip Navigation Planning & Markets
Subscribe Submission Requirements Editorial Board Archive Links Search Home



IV. A model of development incentive shifting

The model that follows details the impact that the capitalization process may have on (1) the cost/profit differential generated by tax abatements granted businesses operating within enterprise zones and (2) business use of tax abated production inputs. The price effects arising from competition for an inelastic supply of business sites within an enterprise zone and corresponding tax abatements are analyzed with a conventional profit maximization model (5). Consider a firm that produces output Q using land A and a composite commodity v as production inputs. The input A represents acres of land within a community utilized by the firm in production. The amount of A made available or zoned for business use by the community is restricted to an amount equal to . For ease of analysis, is assumed to encompass one geographical area or zone of the community. The unit price of A is equal to one. Conversely, the input v is variable with a price equal to pv. The firm's production technology, Q = f(v), is decreasing in v. Moreover, the firm does not set prices, but takes its output price and input prices as set by the market.

The firm's profit maximization problem is expressed in Equations 1 and 2.

(1)
(2)

As expressed in Equation 2, profit maximization requires the firm to utilize v = v* so that its marginal revenue product, MRPv, is equal to its marginal cost, pv. The profit maximizing relationship is portrayed graphically in Figure 1.

Figure 1. Economic rent to land in the absence of an enterprise zone.

Figure 1. Economic rent to land in the absence of an enterprise zone.


The firm's profit maximizing outlay on the variable input is equal to pvv* represented by the checked rectangle. At v* the total revenue to the firm is equal to the checked and shaded rectangles. Under competition for the restricted supply of business sites the producer's surplus (denoted by the shaded rectangle) becomes economic rent to land equal to pQf(v*) - pvv*.

Now, consider the same firm, but assume that is an enterprise zone. Consequently, the firm has the opportunity to secure an economic development incentive by establishing its business operations within the enterprise zone. In this instance, the development incentive is a tax abatement. The tax abatement is provided in the form of a unit subsidy to v. The firm is eligible for the subsidy only if it establishes business operations within the enterprise zone. The subsidy is equal to where is a proportion ranging from zero to one. Consequently, the subsidy could be utilized to lower the unit cost of variable inputs like capital and labor employed within the enterprise zone. The proportion is established by the community and cannot be varied by the firm. The firm may vary only by varying its location among jurisdictions and enterprise zones. Consequently, the dollar value of the subsidy to the firm is and is increasing in v. Given the addition of the enterprise zone subsidy, the firm's profit maximization problem is now expressed in Equations 3 and 4.

(3)
(4)

As before, profit maximization requires the firm to add units of v in production until profits cease to be positive. As expressed in Equation 4, however, the tax abatement reduces the marginal cost of the variable input by . Therefore, the firm utilizes v = v** such that MRPv is equal to . The profit maximizing relationship given the enterprise zone subsidy is expressed graphically in Figure 2.

Figure 2. Economic rent to land in the presence of an enterprise zone.

Figure 2. Economic rent to land in the presence of an enterprise zone.


The firm's profit maximizing outlay on the variable input while operating in the enterprise zone is equal to represented by the checked rectangle. At v** the total revenue to the firm is equal to the checked and shaded rectangles. As before, the producer's surplus (denoted by the shaded rectangle) would, under competition for the restricted supply of business sites within the enterprise zone, become rent to land. Therefore, the enterprise zone tax abatement increases the rent to land in the area by an amount equal to .

page 26

IndexContinue

USC Seal


Main Page | Subscribe | Submission Requirements | Editorial Board | Archive | Links

PLANNING & MARKETS
http://www-pam.usc.edu/
ISSN 1548-6036

Copyright 1999-2000
University of Southern California
Los Angeles, California 90089-0626
USA