all relevant information is provided please attempt

21. The long-run cost functions for each firm that supplies Q is C = ?

? jQuery2240738072256793288_1620135363113

? + ??. Firms will

enter the industry if profits are positive and leave the industry if profits are negative. Describe

the industry's long-run supply function. Assume that the corresponding demand function is

D = 2000 - 100p. Determine equilibrium price, aggregate quantity, and number of firms.

ANS: Firms will have a profit maximum of zero if p = MC = AC, which occurs at the minimum

22. Construct an effective supply curve for an industry which has two sources of supply: (1)

domestic production with the supply curve S = 20 + 8p, and (2) an unlimited supply of imports

at a fixed price of 20.

23. Assume fifty years supply commodity Q at location I and fifty at location II. The cost of

producing output qi for the ith firm (in either location) is 0.5??

?

. The cost of transporting the

commodity to the market from location I is 6 dollars per unit and from location II, 10 dollars

per unit. Determine the aggregate supply function.

24. Consider the following markets which are characterized by lagged supply response:

(a) Dt = 40 - 10pt ; St = 2 + 9pt-1.

(b) Dt = 30 - 5pt ; St = 20 - pt-1.

Determine equilibrium price and quantity for each market. Assume an initial price 20 percent

below the equilibrium price for each market, and determine the number of periods necessary

for each price to adjust to within 1 percent of equilibrium

25. A monopolist uses one input X, which she purchases at the fixed price r = 5 to produce her

output, Q. Her demand and production functions are p = 85 -3q and q = 2? respectively.

Determine the values of p, q, and x at which the monopolist maximizes her profit.

26. Let the demand and cost functions of a multiplant monopolist be p = a - b(q1 + q2), C1 =

???? + ????

?

, and C2 = ???? + ????

? where all parameters are positive. Assume that an

autonomous increase of demand increases the value of a, leaving the other parameters

unchanged. Show that output will increase in both plants with a greater increase for the plant

in which marginal cost is increasing less fast.

27. Let the demand and cost functions of a monopolist be p = 100 - 3q + 4? and C = 4q2 + 10q

+ A where A is the level of her advertising expenditure. Find the values of A, q, and p that

maximize profit.

28. Consider a market characterized by monopolistic competition. There are 101 firms with

identical demand and cost functions:

29. Let duopolist I, producing a differentiated product, face an inverse demand function given

by p1 = 100 - 2q1 - q2 and have the cost function C1 = 2.5??

?

. Assume that duopolist II wishes

to maintain a market share of ?

?

. Find the optimal price, output, and profit for duopolist I.

Find the output of duopolist II.

30. Let two duopsonists have production functions ?? = ???? ?. ???

?

and ?? = ???? ?. ???

?

where x1, x2 are the input levels employed by the duopsonists. Assume that the input supply

function is r = 2 + 0.1(x1 + x2) where r is the supply price of the input, and that q1 and q2 are

sold in competitive markets for prices p1 = 2 and p2 = 3. (a) Find the input reaction functions.

(b) Determine the Cournot equilibrium values for x1, x2, and q1, q2, ??,??.