RATIONAL EXPECTATIONS 323 price expectation with independent disturbances in the supply function then turns out to have the form (4.1) p=1 where the parameter A would be somewhere between zero and one, its value depending on the demand, supply, and inventory demand parameters Speculation with moderately well-informed price expectations reduces the variance of prices by spreading the effect of a market disturbance over several time periods, thereby allowing shocks partially to cancel one another out. Speculation is profitable, although no speculative opportunities remain These propositions might appear obvious. Nevertheless, contrary views have been expressed in the literature. Before introducing inventories into the market conditions briefly examine the nature of speculative demand for a commodity. optimal speculation. We shall assume for the time being that storage interest, and transactions costs are negligible. Anindividual has an opportun ity to purchase at a known price in the tth period for sale in the succeeding period. The future price is, however, unknown. If we let It represent the speculative inventory at the end of the tth period, 7 then the profit to be realized is I(九+1-) Of course, the profit is unknown at the time the commitment is to be made There is, however, the expectation of gain. The individual demand for speculative inventories would presumably be based on reasoning of the following sort. The size of the commitment depends on the expectation of the utility of the profit. For a sufficiently small range of variation in profits, we can approximate the utility function by the first few terms of its Taylor's series expansion about the origin (4.3) 4=p()=0)+(0)x+"(0a+ The expected utility depends on the moments of the probability distribu Em=0)+(0)Em+2"(E2+ 6 See Baumol [5]. His conclusions depend on a nonspeculative demand such that prices would be a pure sine function, which may always be forecast perfectly 7 Speculative inventories may be either positive or negativRATIONAL EXPECTATIONS 323 price expectation with independent disturbances in the supply function then turns out to have the form (4.1) ft'At_i where the parameter A would be somewhere between zero and one, its value depending on the demand, supply, and inventory demand parameters. Speculation with moderately well-informed price expectations reduces the variance of prices by spreading the effect of a market disturbance over several time periods, thereby allowing shocks partially to cancel one another out. Speculation is profitable, although no speculative opportunities remain. These propositions might appear obvious. Nevertheless, contrary views have been expressed in the literature.6 Before introducing inventories into the market conditions, we shall briefly examine the nature of speculative demand for a commodity. Optimal Speculation. We shall assume for the time being that storage, interest, and transactions costs are negligible. An individual has an opportun￾ity to purchase at a known price in the tth period for sale in the succeeding period. The future price is, however, unknown. If we let It represent the speculative inventory at the end of the tth period,7 then the profit to be realized is (4.2) at-It(pt+1-Pt). Of course, the profit is unknown at the time the commitment is to be made. There is, however, the expectation of gain. The individual demand for speculative inventories would presumably be based on reasoning of the following sort. The size of the commitment depends on the expectation of the utility of the profit. For a sufficiently small range of variation in profits, we can approximate the utility function by the first few terms of its Taylor's series expansion about the origin: (4.3) Ut - 0 (t) (O) + ?' (O) at +"2 O)' (t +... The expected utility depends on the moments of the probability distribu￾tion of a: (4.4) Eut - (0) + 0'(O) Ent + 0) Eat 6 See Baumol [5]. His conclusions depend on a nonspeculative demand such that prices would be a pure sine function, which may always be forecast perfectly. 7 Speculative inventories may be either positive or negative