Needed ASAP!

32. Let the buyer and seller for the bilateral monopoly discussed in Sec 8.5 have the production

functions q1 = 270q2 - 2 and x = 0.25 respectively. Assume that the price of q1 is 3 and

the price of x is 6. (a) Determine the values of q2, p2 and the profits of the buyer and seller for

the monopoly, monopsony, and quasi-competitive solutions. (b) Determine the bargaining

limits for p2 under the assumption that the buyer can do no worse than the monopoly solution

and the seller can do no worse than the monopsony solution.

33. Consider a two-person two-commodity, pure-exchange economy with paper money. The

utility functions are U1 = .and U2 = .. Consumer I has initial endowments of 30

units of Q1, 5 units of Q2, and 43 units of money; II has respective endowments of 20, 10, and

2. Each of the consumers desires to hold a money stock equal to one-fifth of the value of her

initial commodity endowment. Determine equilibrium money prices for Q1 and Q2. Show that

the equilibrium prices would triple if the initial money stocks of I and II were increased to129

and 6 respectively.

34. Find equilibrium prices for the three-commodity system given by

E2 = 2

+ +

+ =

E3 = p2 - 2p3 + 2 = 0

35. An economy satisfies all the conditions for Pareto optimality except for one producer who is

a monopolist in the market for her output and a monopolist in the market for the single input

that she uses to produce her output. Her production function is q = 0.5x, the demand function

for her output is p = 100 - 4q, and the supply function for her input is r = 2 + 2x. Find the

values of q, x, p, and r that maximize the producer's profit. Find the values for these variables

that would prevail if she satisfied the appropriate Pareto conditions.

36. Consider an economy with two consumers, two public goods, one ordinary good, one implicit

production function, and a fixed supply of one primary factor that does not enter the

consumer's utility functions. Determine the first-order conditions for a Pareto-optimal

allocation. In particular, what combination of RCSs must equal the RPT for the two public

goods?

37. Assume that the cost functions of two firms producing the same commodity are

C1 = 2

+ C2 = 3

+

Determine the output levels of the firms on the assumption that each equates its private MC

to a fixed market price of 240. Determine their output levels on the assumption that each

equates its social MC to the market price.

38. Determine taxes and subsidies that will lead the firms described in Exercise 36 to their Paretooptimal output levels but leave their profits unchanged. What is the size of the social dividend

secured by this change in allocation?

39. Assume that there are two consumers and two commodities. Let the utility functions be U1 =

q11q12 and U2 = q21q22 with q11 + q21 =q1 and q12 + q22 = q2. Show that Scitovsky contours are

given by q1q2 = ( + )

40. A consumer's consumption-utility function for a two-period horizon is U =

.; his income stream is y1 = 1000, y2 = 648; and the market rate of interest is 0.08. Determine values for c1 and c2 that maximize his utility. Is he a borrower or lender?