2. Prices as a signal of quality A rm has either a high quality or a low quality product (the rm cannot choose the quality of its product). The rm faces a continuum of consumers with a total mass one. Each consumer wishes to buy at most one unit. There are 2 types of consumers: 25 of the consumers are of type 1 and their utility is lO-p if they buy a high quality product and S-p if they buy a low quality product; 3.5 of the consumers are of type 2 and their utility is 6 p if they buy a high quality product and 3 p if they buy a low quality product. Both types of consumers obtain a utility of 0 if they do not buy. The per unit cost of production is 2 if the rm has a high quality product and 0 if it has a low quality product. a. Suppose that consumers can tell the quality of the product before they buy. Determine the prices that each type of rm would charge. (Hint: note that if quality is high, the rm can sell only to type 1 consumers if p 3 5 but to all consumers if p E 5; likewise, if quality is low, the rm can sell only to type 1 consumers if p > 3 but to all consumers if p :1 3.) b. Suppose now that consumers cannot tell the quality of the product before they buy and can only infer it from the price that the rm charges. Show that there exists a separating equilibrium in which high- and low-quality rms behave differently and therefore consumers can infer the quality of the product from the price that the rm charges. In this equilibrium, a low-quality rm behaves as in (a). What is the price that the high-quality rm needs to charge in order to separate itself from the low-quality rm? Show that charging this price is protable for the high quality rm. Does the high-quality rm signal its quality by charging a high price or a low price? Provide an intuition. 3. Warranties as a signal of quality Consumers wish to buy a product and get a utility 10 if the product is of high quality and is working, and a utility of 4 if the product is of low quality and is working. If a product does not work, then the utility from having it is 0 irrespective of its quality. Exante, only the rm knows the quality of its product (but cannot choose it). Consumers expect that the product is of highr'low quality with equal probabilities. The likelihood that a high quality will not work is US and the likelihood that a low quality product will not work is 45. The cost for the rm of replacing a product that does not work is c (this cost is independent of the product's quality) a. Suppose the rm does not offer a warranty. What is the price that consumers will pay for the product? b. Suppose that the rm does offer a warranty. What are the conditions on c such that offering a warranty can serve as a signal of high quality? What happens if the conditions you found in (b) are violated? (1. Compare the prots of rms in (b) and in (c). Comment on your ndings. I .0