Suppose a monopolist produoes a product with quality we at cost cfo] = 5 r32 . There are two types of consumers. Type A has utility given by So -t and type B has utllity giyen by 4y r where q is the quality purchased and t is the price. The monopolist maximizes profit. Type A 1 and B customers make up P and i1 - Pl ofthe market respectively. Suppose :1 = E on aggregate, but that the rm learns that Its consumers line in one of two towns, Left Lake or 2 Flight Lake. The populations of each town are equal. In Left Lake the proportion of type A is q l I 2 vs. 3 type B- In Right Lake the proportion oftype type A is E yrs. 5 type B. Left Lake and Right Lake are miles away and no one has any means of transportation yet a. Which products are offered at whlch prlces 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 inyented. E of type A consumers own Model T cars {independently across towns]. None of type El customers have them. The customers who have cars can now trayel between the towns and access the products offered there. Suppose rst that trayel between the towns is free {opp cost and all}. h. Which products are offered at whlch prlces In each town? Which types of consumer's do better and which do worse [in terms of consumer surplus in the current market] with the increased mobility. 1i] points It. Fast fonoard another 5 years and now all type A consumers have Model T cars. Still none of type B consumers haye them. Which products are offered at which prices in each town? in points Two rms engage in simultaneous quantity competition in a market whose demand is given by P {Q}: 24 [131+ c2} . Firm 1 has a sac. Firm 2 has ME that depends on whether it is a good year or a bad year. If it is a good year Firm 2 also has '3 MC. If it is a bad year, then rm 2 has constant ME = 3 for every unit. The probability of a _ 1 good year Is 5' a. Suppose rst that firm 2 does not know whether it is a good year or a bad year. Both firms maximize expected profit. Find the ME quantities for both rms. Hint: you should treatthis the same as iffirm 2 had constant M E = so. 1D points b. Suppose now that rm 2 knows whether it is a good year or not, butfirm 1 does not. This means that rm 2 can condition their quantity on their cost but rm 1 cannot. Find the NE quantities for both firms in a good year and in a bad year. Hint firm 1 best responds to the average quantity of rm 2 across the two conditions.l points c. Now suppose that before observing whether it is a good year or a bad year, rm 2 can commit to disclose this information to firm 1 or not. If they do not disclose we are in the world ofthe previous part. Does firm 2 choose to disclose or not disclose? 11] points d. Provide some economic intuition for your previous answer. i.e. do not appeal to the specific calculations you did. Hint: consider an ext reme version of the question where there is uncertainty about hits but in each state the MC of the firms are vastly different