20.Assume fifty years supply commodity Q at location I and fifty at location II. The cost of producing output q_i for the i^th 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.

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

(a) D_t = 40 - 10p_t ; S_t = 2 + 9p_t-1. (b) D_t = 30 - 5p_t ; S_t = 20 - p_t-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

22.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 + 4and 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: p_k = 150 - q_k - 0.02 ₌

C_k = 0.5 + k = 1, ......, 101

Determine the maximum profit and the corresponding price and quantity for a representative firm. Assume that the number of firms in the industry does not change.

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, , .