Help me to solv.e these questions in the attachment.

Problem 2: Production economy There two firms, X and Y, and two factors of production: labor L and capital K. Firm X produces the output good X using a technology described by the following continuous, differentiable and strictly concave production function: fx (lx, kx) = Vix + Vkx where (x 2 0 is the quantity of labor employed and kx 2 0 is the quantity of capital employed by firm X. Firm Y produces the output good Y using a technology described by the following continuous and differentiable production function: fy (ly , ky) = ly + ky where ly 2 0 is the quantity of labor employed and ky 2 0 is the quantity of capital employed by firm Y. The economy has a strictly positive endowment of labor L and capital K, where L > K. The output price for good X is px > 0, and the output price for good Y is py > 0. The output prices are determined on international markets, and are parameters in this model economy. (1) Find the set of production efficient factor allocations in this econ- omy, and illustrate them in a Bowley box diagram. (2) Find the set of production efficient output allocations in this econ- omy, and illustrate the production possibility frontier in a diagram. What is the marginal rate of transformation? (3) For all possible values of the parameters (px and py) find the com- petitive equilibrium factor prices (w and r) and the competitive equilibrium allocations. What are the equilibrium profits of each of the firms?Question 1 (40 pts) Consider the following model of a vertical market. In a market for a good, there exists a monop- olist manufacturer with a marginal cost of 5 who charges a wholesale price of Pm to a monopolist retailer. The retailer's only marginal cost if the manufacturer price; however, the retailer must pay a fixed cost F in order to sell the manufacturer's goods. (For example, he must remodel parts of his store.) The retailer charges a price to consumers of pr. Demand is linear with p, = 15 - Q. a. Write down the retailer's profit function. b. What is the price the retailer charges as a function of P.? c. Write down the manufacturer's profit function as a function of p.. What is the optimal pm set by the wholesaler? d. Given p., what is the retailer's profit? At what level of F will the retailer no longer be willing to purchase from the manufacturer? e. Consider the vertically integrated monopolist. At what level of F will the vertically inte- grated monopolist no longer be willing to stock the good in his retail division? At what values of F will the manufacturer carry the good if and only if it is vertically integrated with the retailer? Question 2 (35 pts) Suppose that two types of people exist, high (H) and low (L) productivity. Education is worthless other than to potential employers. Those workers that receive an education are identified as H- type and get a wage of wy = $9,000 while those that do not are identified as L-type and receive WL = $7,500. H-types can obtain an education at a cost of CH = $1,000, and L-types receive an education at a cost of GL = $3,000. Denote A as the probability that an individual is high productivity, A = P(H). a. Show a separating equilibrium exists. b. Does a pooling equilibrium exist at A = !?Find the absolute maximum and absolute minimum values of the function, if they exist, on the indicated interval. 1) ((x ) = x3+ 2 (3 + 1x2 - 4x + 2; [-9, 0] Find the absolute maximum and absolute minimum values of the function, if they exist, over the indicated interval. When no interval is specified, use the real line ( , *). 2) f(x) = - -x3 + 4x - 1; (-,0) Use a graphing calculator or computer graphing software to solve the problem (correct to one decimal place). 3) Find the absolute maximum value for the function f(x) = x(x - 8)2/3 over the interval [- 1, 7] 4) Maximize Q = xy, where x and y are positive numbers, such that ~x- + y = 9. 5) Find the maximum profit given the following revenue and cost functions: R(x) = 118x - x2 C(x) = -x3- 9x2+ 82x + 34 where x is in thousands of units and R(x) and C(x) are in thousands of dollars