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If r = 0.10, for instance, then t = 25, and the dealer should store the case of wine for 25 years. Note that the higher the rate of interest (rate of discount) is, the shorter the optimum storage period will be.

The first-order condition, 1 /(2/t) = r, admits of an easy economic interpretation. The left-hand expression merely represents the rate of growth of wine value V, because from (10.22)

so that the rate of growth of V is indeed the left-hand expression in the first-order condition:

The right-hand expression r is, in contrast, the rate of interest or the rate of compound-interest growth of the cash fund receivable if the wine is sold right away—an opportunity-cost aspect of storing the wine. Thus, the equating of the two instantaneous rates, as illustrated in Fig. 10.4, is an attempt to hold onto the rate

Figure 10.4

Figure 10.4

wine until the advantage of storage is completely wiped out, i.e., to wait till the moment when the (declining) rate of growth of wine value is just matched by the (constant) interest rate on cash sales receipts.

The next order of business is to check whether the value of t satisfies the second-order condition for maximization of A. The second derivative of A is

But, since the final term drops out when we evaluate it at the equilibrium (optimum) point, where dA /dt = 0, we are left with

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