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It is well recognized in the finance literature that real asset divisibility may be a binding constraint for the capitalization of information into asset prices, unless there exists a corresponding financial market for ownership claims on these assets, or if equity participation can be enhanced through group ownership forms. Otherwise, capital constraints may become barriers to entry, thereby resulting in market segmentation based on differences in asset size. As a result, the equilibrium price in each segment will be determined by its respective demand and supply schedules, so that asset price may vary across asset size. The existence of capital constraints may also result in reduced competition in the higher-priced segment, leading to greater inefficiency in pricing and possibly to abnormal returns. This hypothesis is the opposite of the "small firm effect" observed in financial markets (see Gau, 1987, p. 5, footnote 6.). Empirical estimation of the possible functional relationship between asset price and size has been conducted for industrial land in only two studies, each of which employed a cross-sectional test on a very limited sample of about thirty data points over an extended time period. Given that P sub i = f (A sub i ), where P sub i is the unit price of a parcel of land with size A sub i , if f' > 0 ( Given the conflicting empirical findings in the literature, as well as the other shortcomings mentioned above, the major objective of this paper is to present a theoretical model for the prediction of the functional form relating industrial land price and size. The predicted model will then be tested for 606 industrial land sales in a major industrial park in Montreal, Canada. THE MODEL On the supply side, it is assumed that the input land factor space is totally disconnected in a topological sense, i.e., land units are of fixed, perhaps different, sizes. This may be due to zoning restrictions, including restricted access or a desire by municipal leaders to attract firms of a given size or nature of business activity; inability of landowners to agree to merge existing lots or the infeasibility of assemblage, due to noncontiguous lots; existing road networks, sewage systems, and rights of passage. On the demand size, it is assumed that profit-maximizing firm demands labor and land to produce a single product by means of a technology given by Q = f (L, A), (1) where L = units of labor, A = units of land, and Q = amount of output. The following theorem is proved. Theorem Let s*(A) be the maximum per unit price a firm is willing to pay for A units of land. Then ds*(A)/d A if and only if f (L, A) exhibits decreasing returns to scale. Proof Define the maximum profit as II*(A), where A is a free variable. Then II*(A) = pf (L*(A), A) - wL(A) (2) where L*(A) = max [pf (L, A) - wL] (3) and p, w are the unit output price and wage rate, respectively. Thus L*(A) satisfies the first order condition. pXdf/dL - w = 0 at an interior point where d sup 2 f/dL sup 2 |
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