Answer Happy

3. Suppose a monopolist produces a product with quality q at cost c(g) = 1/2q². There are two types of consumers. Type A has utility given by 5q-t and type B has utility given by 4q-t where q is the quality purchased and t is the price. The monopolist maximizes profit. Type A and B customers make up p and (1-p) of the market respectively. (a) Suppose the monopolist knows whether each customer is A or B and can target options accordingly. Which products at which prices does he offer to each group? 5 points (b) Suppose the monopolist does not know whether a consumer is type A or B, and must offer all available options to every consumer. Which products at which prices does he offer? 10 points Suppose p = 1/2 on aggregate, but that the firm learns that its consumers live in one of two towns, Left Lake or Right Lake. The populations of each town are equal. In Left Lake the proportion of type A is 2/3 vs. 1/3 type B. In Right Lake the proportion of type type A is 1/3 vs. 2/3 type B. Left Lake and Right Lake are miles away and no one has any means of transportation... yet... 3 (e) Which products are offered at which prices in each town? How does the consumer surplus of each consumer type compare across the two towns? Explain why. 15 points Fast forward five years from now and the Model T is invented. 1/4 of type A consumers own Model T cars (independently across towns). None of type B customers have them. The customers who have cars can now travel between the towns and access the products offered there. Suppose first that travel between the towns is free (opp cost and all). (d) Which products are offered at which prices in each town? Which types of con- sumer's do better and which do worse (in terms of consumer surplus in the current market) with the increased mobility. 10 points (e) Fast forward another 5 years and now all type A consumers have Model T cars. Still none of type B consumers have them. Which products are offered at which prices in each town? 10 points (f) Extra Credit: In another 5 years, all type A consumers still have cars, but the price of gasoline has skyrocketed and it now costs $1 to make the round trip journey to the other town and back. Could the firm increase profits compared to 5 years before? If so, describe some way to change the offerings in each town from 5 years ago to increase profits. Would type A consumers ever drive to the other town if the firm were optimizing? 15 points