Kwami and Adzqa quit their jobs and decided to start a piggery joint venture business. The company processes and packs pork for sale. The output from this firm is described by the Cobb-Douglas production function, q= K¹/2 A1/2 Where q is the number of pigs processed in a quarter, K is the number of hours invested by Kwami in a quarter, and A is the number of hours invested by Adzoa in a quarter. Kwami and Adzoa value 1 hour of their time at $12 and $3 respectively based on what each was earning before quitting their jobs. a) Obtain the number of hours that Adzoa needs to invest (as a function of q and K) for 150 pigs to be processed in a quarter b) How many hours should Adzoa invest for 150 pigs to be processed in a quarter if it is known that Kwami invested 750 hours? c) The cost function for this company may be written as, C=vK + WA where v and w are unit costs for Kwami and Adzoa. wwwwwwwmm wwww Substituting for v and w gives C= 12K + 3A Express this cost of production function as a function of K and g What is the marginal cost of the 150th pig produced if Kwami invested 750 hours.

The following table shows the capital and labor requirements for 10 different levels of production. Assuming that the price of labor (PL) is $8 per unit and the price of capital (PK) is $6 per unit, compute and graph total cost, marginal cost, and average cost for the firm. To do this, fill in the total cost for each output level in the table below. (Enter your responses as whole numbers.) 9 0 1 2 3 4 5 6 7 8 9 10 K 0 20 20 20 20 20 20 20 20 20 20 L 0 3 7 10 13 17 23 31 41 53 67 TC 0 Cost per unit ($) 0 1 2 3 4 5 6 7 8 9 10 11 12 Units of output Q ✔

There are three companies - Ceramic, Pottery and Tile - producing mugs. The production function of mugs for Ceramic is given by Qc = 10K0.5 10.5, where K is hours of machine time and L is hours of labour employed. Pottery's production function of mugs is Qp = 10K0.6L0.4 and Tile's production function of mugs is QT 20K 0.6L0.5. a) Using a graph show how, ceteris paribus, an improvement in technology would affect Ceramic's production function. b) If all companies use the same amount of capital and labour, which will generate more output? Explain. c) Find the marginal product of capital and the marginal product of labour for each company. d) Assume that K = L = 2,000. Which company will benefit the most from increasing its labour? Which company will benefit the most from increasing its capital? Why? e) What type of returns to scale is each company exhibiting? Explain. =

Suppose the production of Scooby Snacks at x units of labor and y units of capital is given by the Cobb-Douglas production function P(x, y) = kx"y" where m, n, k are known positive constants and m+ n = 1. The company can spend only p dollars for the production of Scooby Snacks. The cost of one unit of labor is b dollars, while the cost of one unit of capital is c dollars. Using Lagrange multipliers, find an expression for x and y where maximum production will occur?

Consider a firm with production function in the Cobb-Douglas form q = K^.5L^.5 Suppose that one unit of capital costs r=12.5, whereas one unit of labor costs w=8. Determine the optimal input mix that leads to an output of q = 2. Determine the firm’s cost function, that is, the minimum cost required to produce output q.

Suppose that Flamerock Tires must decide where to produce one million tires: the US, where wages are 30 and the cost of capital is 5; or China, where wages are 5 and the cost of capital is 25. Production in each location follows the same technology (production function) given by: Q = f(L, K) = L^0.25 K^0.75 Computationally solve the cost - minimizing input levels in each location to produce the goal of 1 million tires

Does the production function y=0.8x_1x_2 exhibit constant returns to scale, increasing returns to scale, decreasing returns to scale, or homothetic returns to scale

A software firm has only two inputs to production: domestic programmers based in the firm's U.K. office and international programmers working from home in low-cost countries. The two types of programmers are perfect substitutes but domestic programmers are more productive due to better communication in the office. The production function is: S=2D + I Where S is the amount of software written, D is the number of domestic programmers and I is the number of international programmers. Programmers can work part-time, so hiring 0.3 of a programmer would be possible. (a) The firm must produce 10 pieces of software this year. Show the firm's isoquant in a suitably labelled graph. Put "domestic programmers" on the vertical axis and "international programmers" on the horizontal axis. Label each axis from 0 to 10. (b) A domestic programmer can be hired for £100,000 per year. An international programmer can be hired for £60,000 per year. On the same graph, show the different combinations of…

please only solve part d, e, f

Consider a production function of three inputs, labor, capital, and materials, given by Q = LKM. The marginal products associated with this production function are as follows: MPL = KM, MPK = LM, and MPM = LK. Let w = 5, r = 1, and m = 2, where m is the price per unit of materials.a) Suppose that the firm is required to produce Q units of output. Show how the cost - minimizing quantity of labor depends on the quantity Q. Show how the cost- minimizing quantity of capital depends on the quantity Q. Show how the cost - minimizing quantity of materials depends on the quantity Q. b) Find the equation of the firms long-run total cost curve.c) Find the equation of the firms long-run average cost curve.d) Suppose that the firm is required to produce Q units of output, but that its capital is fixed at a quantity of 50 units (ie., K 50). Show how the cost- minimizing quantity of labor depends on the quantity Q. Show how the cost- minimizing quantity of materials depends on the quantity Q. e)…