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IN THIS paper, an attempt is made to find a starting point for a comprehensive theory of urban land utilization and city growth in its broader aspects. The paper treats of the subject in mathematical terms, starting with certain assumptions as to the demands for land at various price levels in a growing city and proceeding to show the general characteristics of city development which result from the play of economic forces. The paper describes, in general terms, the city pattern and the spread of building development which result from the fact that each owner of land will, in most cases, seek to obtain the greatest possible value by the sale or utilization of his land. An increase of population brings about demands for additional land to serve as sites for additional commercial, industrial, residential, and social use buildings. Certain locations and sites are more desirable than others and, further, the intended use is a factor in determining the purchase price. For example, the prospective purchaser of a site for a legitimate theatre in the central business district of a city cannot pay so high a unit price for land as the prospective purchaser of a site for an office building. Starting with a tract of land, or an aggregate of parcels of land, all in the same ownership, and assuming that there is a constant annual demand for this land for many diverse uses and, therefore, at different price levels, it is shown that the owner will realize the maximum value by accepting off ers at all the prices from the highest down to a certain price, called the critical price, and by rejecting all offers at prices lower than this critical price. This means that he will realize a greater value by selling some land each year at each of the various price levels above a certain level than he will by selling it all at any one price, high or low, regardless of how slowly or rapidly he may be able to dispose of it. The critical price depends on the demand rates, the range of offered prices, and the original area involved. Methods are described in this paper for determining the critical price under various sets of conditions. It is also shown that, for a maximum value, the owner will reject, after a certain time, further demands at the critical price, and after a |
