The rational effect of price promotions on sales and consumption

We explore the rational effect of price variation on sales and consumption in markets where consumers are uncertain about the future price of goods. We first derive an optimal ordering policy which expresses the amount a consumer should purchase and consume in a given period as a function of the observed price of the good, the distribution of future prices, and the nature of his or her inventory. This policy extends previous normative models of inventory control, such as those by Golabi 1985 and Kalymon 1970 to the case where the amount to consume in a given period is an explicit decision variable and prices follow a first-order stochastic process. We then use this model to explore how changes in the long-run frequency and temporal correlations of price promotions should normatively affect the contemporaneous relationship between purchase, consumption and price. Among the predictions which follow from the model are that consumption should rationally increase with the size of existing inventories, the short-term sensitivity of sales to prices should be greater than that of consumption to price, and this discrepancy increases with decreases in the temporal correlation of price deals and the long-term relative frequency of price deals.