We model the decision to replace durable capital when intensity is variable. Decisions of this type include land-redevelopment decisions where the density of residential or commercial development is a choice variable as well as capital-replacement decisions where capacity is variable. We provide a general yet simple formulation of the problem using an optimal-stopping framework. We characterize the value of the project, the timing of investment, and the intensity of development. We show that intensity interacts in important ways with timing, taxes, and project values. The ability to vary intensity raises hurdle rents and delays development decisions.

STUDIES of the term structure of interest rates have a long tradition in the literature of finance and economics. Two prominent examples are Roll (1970) and Nelson (1971).1 More recently, a parallel literature has evolved on the pricing of commodity contracts, spawned by the work of Dusak (1973) and Black (1976). With the advent of futures trading in Treasury bills on the Chicago Mercantile Exchange (CME) the direct relationship between the theory of the term structure of interest rates and the theory of commodity contract pricing has become apparent. Since arbitrage is possible between the spot and futures markets, appropriately defined returns in both markets should be identical. In this paper we compare the returns in the spot and futures markets over the first 30 months of trading in the CME Treasury bill futures market. Surprisingly, we find that rather large deviations between returns in the two markets have persisted throughout the sample period, i.e., the one price law is violated. For this result to be obtained, arbitrage costs must be large, differential risk must exist, or traders in the two markets must be distinct non-overlapping groups. In the next section an arbitrage condition connecting the two markets is derived. The condition specifies the relationship between returns in the spot and futures markets under the assumption of a perfect capital market. The third section presents the data and demonstrates that the arbitrage condition has not been satisfied. The fourth section offers a possible explanation for the failure of the arbitrage condition. The paper concludes with a summary of the results.

IN A RECENT PAPER D. R. Capozza and R. Van Order (C.V.) [1] claim to show that there exist conditions under which a competitive firm in industry equilibrium in a spatial environment will charge a higher mill price than a spatial monopolist. This conclusion seems contrary to our intuition and consequently the conditions under which it arises should be made very clear. This paper argues that the C.V. result is not necessarily correct. In particular, there is an apparent error in the three sentences following equation (27). The positive roots of equation (27) are both possible candidates for equilibrium price.2 The difficulty is that there are no grounds for choosing between the two roots within the structure of the model. Capozza has argued, in correspondence, that the smaller root is inappropriate because demand is negative. However, demand is only negative at the border of the market area and one could equally well argue that this is a case of natural monopoly, induced by the cost structure. These remarks are made within the assumptions that C.V. makq in their paper. We can, however, shed further light on the matter by introducing some new elements. In particular, (i) we explicitly impose some simple dynamics on the system, and (ii) we use consumer surplus as a measure cf welfare. (i) Let us suppose that firms are price setters and assume a zero conjectural variation. Under these conditions it is not difficult to show that the larger positive root is stable and the smaller is unstable. (ii) The total of consumer surplus at price m and market radius Do is given by

[Research on the spatial firm has shown that spatial results often differ from non-spatial. This paper considers the relationship between the price of a spatial monopoly and the price of a spatially competitive firm. The conditions under which the competitive price will exceed the monopoly price are outlined.]

The authors model the decision to replace durable capital when intensity is variable. Decisions of this type include land-redevelopment decisions where the density of residential or commercial development is a choice variable as well as capital-replacement decisions where capacity is variable. The authors provide a general yet simple formation of the problem using an optimal-stopping framework. They characterize the value of the project, the timing of investment, and the intensity of development. The authors show that intensity interacts in important ways with timing, taxes, and project values. The ability to vary intensity raises hurdle rents and delays development decisions. Copyright 1994 by American Economic Association.