Hello, I need help.

1. 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, ,.
2. 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.
3. 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.
4. 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
5. 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.
6. 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.
7. 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.
8. Consider a market characterized by monopolistic competition. There are 101 firms with identical demand and cost functions: pk = 150 - qk - 0.02 = Ck = 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.
9. 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.
10. What are the Administrative Problems of State Enterprises?