Warranty pricing with consumer learning

We consider a problem in which a firm dynamically prices a product and its warranty service over time. Consumers can learn about the reliability of products based on warranty prices. A firm's optimal product and warranty pricing policies are characterized. We find that a warranty should be priced lower than the marginal warranty service cost, which implies that warranty sales will not generate profits directly. However, offering a modest warranty still benefits the firm's overall profits. We also show that consumers' beliefs and the firm's warranty policy converge in the long run. In a steady state, either a fraction of consumers will purchase a warranty or no consumer will purchase a warranty. Comparative statics analysis is conducted to show how factors such as a firm's warranty service cost, consumers' learning speed, and the heterogeneity of consumers' handling costs determine consumers' beliefs, the firm's warranty policy and profitability in a steady state. Lastly, we note that a firm benefits from consumer learning by hiding the information about the true product reliability only when the true product failure rate is relatively high.