Because both prices and quantities are always positive, the ratios PD/QY, PH/QY, and PT/QY are also positive. Therefore, the signs of the three cross-price elasticities in this example are determined by the sign of each relevant parameter estimate in the HMS demand function:
HMS service and prescription drugs are complements.
c PH ~ (+10)(Ph/Qy) > 0 HMS service and hospital service are substitutes.
epT = (+0.0001)(PT/Qy) « 0, so long as the ratio PT/QY is not extremely large
The concept of cross-price elasticity serves two main purposes. First, it is important for the firm to be aware of how demand for its products is likely to respond to changes in the prices of other goods. Such information is necessary for formulating the firm's own pricing strategy and for analyzing the risks associated with various products. This is particularly important for firms with a wide variety of products, where meaningful substitute or complementary relations exist within the firm's own product line. Second, cross-price elasticity information allows managers to measure the degree of competition in the marketplace. For example, a firm might appear to dominate a particular market or market segment, especially if it is the only supplier of a particular product. However, if the cross-price elasticity between a firm's output and products produced in related industries is large and positive, the firm is not a monopolist in the true sense and is not immune to the threat of competitor encroachment. In the banking industry, for example, individual banks clearly compete with money market mutual funds, savings and loan associations, credit unions, and commercial finance companies. The extent of competition can be measured only in terms of the cross-price elasticities of demand.
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