Time preferences and the pricing of complementary durables and consumables

There is strong empirical evidence that consumers discount at significantly higher rates than firms. Yet, most research abstracts from the effect of discount rates on marketing decisions such as pricing. We study the effects of a consumers' discount rate that is higher than a firm's discount rate on prices, profits and consumer surplus of complementary products in four competitive settings and an infinite time setting: the firm is a monopolist or competes in the durable market and either ties the consumable to the durable or sells untied products. Our analysis yields five main results: First, a higher time preference of consumers than the firm never increases the optimal durable price and never decreases the optimal consumable price. Second, the optimal consumable price of tied goods is always higher than the optimal consumable price of untied goods, whereas the optimal durable price is always higher when goods are untied. Third, a higher time preference of consumers than the firm never increases profit, always decreases consumer surplus and, as a result, always decreases welfare. Fourth, the ability of the firm to commit to future prices and of consumers to commit to future purchases benefits both consumers and the firm. Fifth, if the firm competes in the durable market, then tying increases consumer surplus when consumers commit to purchasing the consumable. We discuss the implications of our results for firms' pricing strategies.