. Quality of Experience Goods Consider a monopoly supplier of an experience goods, of which the quality cannot be ascertained by consumers at the time of purchase. The quality of the goods supplied is denoted by q, which can take any value in the interval [0, 10]. Each unit of good with quality q requires a production cost of r." (q) = 1 + qg. Consumption of the goods with quality q brings a utility of t! (q) = 2 + 4q. For simplicity, suppose there is one unit of consumers, and each consumer demands at most one unit of the experience goods in each period. In each period, events unfold in the following order. 0 The rm chooses the quality q of its goods, as well as its price. 0 Consumers learn the price, but not the quality chosen, and decide whether to purchase the goods or not. 0 If they purchase the goods, then they consume it, learn the quality q, and derive the corre- sponding utility. The game above is innitely repeated, with all previous qualities become public record. All players share a common discount factor 6 E (0, 1). (a) What is the level of quality that maximizes the total surplus, i.e., 1.!(q) r (q)? Denote this level of quality by q*. (b) Suppose 6 = 0.9. Consider the following trigger strategies for the rm and consumers which give the outcome that quality (j is produced in every period. 0 We say the rm has a good reputation if there is no previous period in which the revealed quality is different from (i; and a bad reputation if in some previous period, the revealed quality is different from q. o The rm produces quality I} and charges price 1' (9?), if it has a good reputation. It produces quality 0 and charges price 15(0), if it has a bad reputation. 0 Consumers only buy the goods at prices no higher than T.-' (q), if the rm has a good reputation They only buy at prices no higher than t.' (0), if the rm has a bad reputation. Can the trigger strategies support a subgame-perfect Nash equilibrium (SPNE) with the outcome that the rm always produces quality (f = q* (the efcient level computed in part (a))'? Explain. (c) Suppose 6 = 0.3. What is the highest level of quality that can be supported as a SPNE outcome by the trigger strategies? What is the rm's per-period prot? (d) Suppose the experience-goods rm develops a new technology of production. The new tech- nology gives rise to the following new cost function (mu. (q) = q + 0.75912. It can be checked (and you do not need to) that e the value of q* computed in part (a) would still maximize the total surplus with this new cost function; and