ANSWER ALL PARTS PLZ.

3. Apple's market research shows that there are two types of consumers for its iMac computer and bMac computer {baby iMac]. The bMac is physically the same as the iMac but has some functions disabled. Both iMac and bMac cost 300 dollars to produce per unit. Both consumer typesJ h and I, get utility or if they have m dollars and no computer: uh[,m] = mufns) = m. High type consumers with m dollars [after paying for a computer} get utility ah (i? m] = 1500 +11\": and ret-3. m) : Sl3l3+$v1j where 2' denotes having one iMac and I] having one bMac. Low types get utility 1:21 {am} = 600 + m and uglm} = 500 + at. Apple knows that there are one million consumers of high type and 2 million consumers of low type. Once Apple announces a price? it must serve all consumers who demand its product at that price. The consumers start with enough money to buy a computer if it raises their utility. They demand at most one computer during the period considered. a. Suppose Apple sells iMacs at 150D}? unit and bMacs at 500 ,r" unit. Find the maximum sales and prots Apple could get. b. Suppose Apple offers only iMacs. Find prot maximising price? sales and prot. c. Suppose Apple offers only bMacs. Find prot maximizing price, sales and prot. d. Suppose Apple offers iMacs at price ph and bMacs at price p;. Show that no prices are such that high types buy bMacs and low types buy iMacs. e. Find prot maximizing prices ph and p; that can induce high types to buy the iMac and low types to buy the bMac. What is the corresponding prot? f. Do part a assuming instead that the number of lD'W types is 1 million. In this case? nd prot maximising prices and compare the resulting prot to what Apple receives if it offers only the iMac at a prot maximizing price. ____ _______ _' __ ____ ___'_ ___D__ _'____'u' ' ___'__1____ ____ ______'_____ __ '_____ ___ ___u" e. Find and interpret all conditions on the exogenous Twariables under which there is a weak perfect Bayesian equilibrium [WPBEI i.e., weak sequential equilibrium} where, for sure.J the worker nishes her degree no matter what her ability is. f. Find and interpret all conditions on the exogenous variables under which there is a weak perfect Bayesian equilibrium [WPBEI i.e., weak sequential equilibrium} where, for sure.J the worker does not nish her degree no matter what her ability is. g. 1What can be said about the eiciency of the outcomes in the equilibria in parts c? d. and e? Dene an appropriate notion of efciency for the economy consisting of the worker and rm. How does your answer depend on the values of A and W? W l, EW 1,2 \"'0 1.0 w 2, 2w 1, 0 13,1] _2r FIGURE 1 4. A worker has to decide whether to nish her degree or not before applying for a job with a particular rm. The rm knows that the worker is of high or low ability and will know if the worker nishes her degree. Finishing the degree costs the worker I if she is of high ability and 2 otherwise. If the worker is of high ability, then she will produce 5 units of revenue for the rm if she nishes her degree and 3 units if she does not. If the worker is of low ability she will produce 2 units of revenue for the rm if she nishes her degree and 1 unit if she does not. The rm pays each of its workers with a degree W [D C W =1: 5} and pays each of its workers without a degree 1. Initially, before the worker decides about her degree, the rm believes with probability A E [I], 1} that she is of high ability and decides whether to hire her or not. The interaction between the worker and rm is represented, as a game of common knowledge, in the tree in Figure 1, below, where the worker is player I, with the rst listed payoff, and the rm is player 2 with the second listed a off. .1 P 3" a. Why might it make sense to model a worker's cost of nishing a degree as depending on her ability even when there is no discrimination among students in pricing of education? b. Label the players' moves in the tree in Figure 1. Refer to your labels in your answers to the remaining parts of this problem. c. Under what {if any] conditions is there a Nash equilibrium (NE) in which the worker nishes her degree for sure if she has low ability and does not if she has high ability? d. Under what [if any} conditions on the exogenous variables A and W is there a NE in which for sure the worker does not nish her degree if she has low ability and for sure she nishes it if she has high ability? Interpret the conditions if there are any. e. Find and interpret all conditions on the exogenous variables under which there is a weak perfect Bayesian equilibrium [WPBE i.e., weak sequential equilibrium] where, for sure, the worker nishes her degree no matter what her ability is. f. Find and interpret all conditions on the exogenous variables under which there is a weak perfect Bayesian equilibrium [WPBE i.e., weak sequential equilibrium] where, for sure, the worker does not nish her degree no matter what her ability is. g. What can be said about the efciency of the outcomes in the equilibria in parts c, 'I H \"I" I" m' I" .'I I'I'I