Evaluate the following questions.

1) Consider the following technology: c(yi) = yi2 +2yi +4.

Many firms have access to this technology, in fact so many that there is not room for all to profitably operate in the industry. The market demand for the product is given by, P = 30-Y , where Y is the market quantity. Assume also that these firms are price takers, and entry / exit is costless.

A) What is the long-run free entry equilibrium per- firm quantity produced by each firrm in the industry? Explain (10 pts)

B)Do you have enough information to determine the number of firms who operate in such a long-run free entry equilibrium? If so, what is the number and justify your solution. If not, explain what other information you would need. (10 pts)

C) Is the price-taking behavioral assumption sensible for this industry? Explain (10 pts)

2) A monopolist has access to an industry with market demand D(p) = 24-2p and its cost function is c(y) = y2.

A)Determine its proft - maximizing output level y* and the market price p(y*). (5 pts)

B)Calculate the monopolist s profit. (5 pts)

C)Compute the point-elasticity of demand at the profit maximizing output level y* . Would the monopolist ever operate at a point elasticity |e(y)|

D)Suppose this monopolist is regulated to produce at that quantity where price equals average cost. Calculate the quantity the monopolist will produce and the price it will charge given this regulatory scenario. (5 pts)

E)Calculate the profit for the monopoly if it is regulated to produce where price equals average cost. Explain. (5 pts)

F)Suppose this monopolist is regulated to produce at that quantity where price equals marginal cost. Calculate the quantity the monopolist will produce and the price it will charge given this regulatory scenario. (5 pts)

G)Calculate the profit for the monopoly if it is regulated to produce where price equals marginal cost. (5 pts)

H)Is this is a natural monopoly? Explain. (5 pts)

3) A monopoly is facing two types of consumers. Type 1 consumer has relatively low demand given by pL(yL) = 8 yL and type 2 consumer has relatively high demand given by pH(yH) = 10 yH. The firm's marginal cost is MC = 0.

A)Suppose the two types are observable and the firm offers two packages using the two-part tarrifs pricing scheme (it charges a fee as well as a per unit price). What quantities and fees maximize the firms profit? Show these outcomes on graphs. (8 pts)

B)Now suppose that the firm is unable to distinguish the types, would the pricing scheme from part (a) work if the firm kept offer the same quantities yL and yH? (6 pts)

C)If the firm is unable to distinguish between the two types, but wants to offer the two different quantities you found in part (a), what fees should it charge to the different types of consumers? (8 pts)

D)Based on the pricing scheme used in part (c), calculate the consumer s surplus (for both types) and the producer s surplus. Do we have DWL in the market? ...

QUESTION 2 Let e denote the level of education. There are three types of potential workers: those (type _) with productivity Of , those (type M) with productivity , and those (type #) with productivity ey , with OH > 0w > 0, > 0. For each type i c (L, M, H; the fraction of type i in the population is } . Each potential worker knows her own type, while the potential employer cannot tell the type of any potential worker, although he knows the distribution of types in the population. The employer observes the education level of each potential worker (but not her type) and offers a wage which depends on the applicant's level of education. For every type ic {L, M, /} the cost of acquiring e units of education is . Each worker's utility is given by the difference between the wage she is paid and the cost of education. (a) [Note: for this part do not assume that each worker must be paid a wage equal to her productivity.] Is there an incentive-compatible situation where (1) the employer offers two wages, depending on the education level: wage w to those whose education level is e and wage wy # w to those whose education level is ey # e and refuses to hire anybody with education ec (e , ey ), (2) both types 0, and ey choose education level e', while type , choose education ey ? [Note that you should make no assumptions about whether ey, ey and similarly for wy and w .] If there is such an incentive-compatible situation, please describe it in detail. If your claim is that it does not exist, please prove it. For parts (b) and (c) assume that the employer pays each worker a wage equal to the worker's expected productivity (as computed by the employer, who is risk neutral). (b) Define and describe in detail a pooling equilibrium, that is, a signaling equilibrium where all three types make the same choice of education level, call it a. [Assume that the employer believes that anybody who shows up with education level ex e must be of type L.] (c) Find all the pooling equilibria when 0, = 1, 0M =2, ey =6. Now let us change the situation as follows. There are only two types of potential workers: those with productivity &, and those with productivity Oy, with Oy > 0, >0. The fraction of type Or in the population is equal to the fraction of type Oy . Assume that the cost of education is the same for both types and is given by c(e) = e. Suppose that the utility of worker of type de (0 , , } who is paid wage w and chooses education level e is U(w,e, 0) =0w-e. Assume also that ee [a,b] with 0