Question

A firm has a production function Y 2 K05L05. Use w to denote the wage rate and r to denote the capital rental price Let us first consider the short run situation, where the firm has K = 25 and In order to produce 10 units of output, how many units of labour does the firm need to hire? What is the average cost of the firm? Let us first consider the short run situation, where the firm has K-25. In the factor market, r 2 and w 3. Write out the cost function of the firm. What is its marginal cost? Let us first consider the short run situation, where the firm has K-25. The firm operates in a perfectly competitive market and the price of its product is p-1 Derive its demand for labour. (Hint: in a perfectly competitive market, a firm should operate as P-MC.) Draw the labour demand curve in a graph with w on y-axis and amount of labour on x-axis. In the long run, the firm will be able to choose both K and L, according to MRTS -w/r. (Please check your 203 notes if you cannot remember this part.) Derive the function of relative demand in the factor markets (this asks for L/K as a function of w/r). In a graph, draw out the relative demand of labour to capital by the firm (the graph should have w/r on the y-axis and L/K by the x-axis). a. 2. b. C. d.

Answer 1

Y = 2 squareroot KL, w_1 r_1 a) k^bar = 25, r = 2, q = 10, so q = 2 middot squareroot 25 squareroot L = > 10 = 2 times 5 middot squareroot L = > thus L* = 1. So total cost of prodn, C = WL* + rK = w + 25 times 2 = 50 + w a) Now Ac = c/q = 50 + w/10 (b) k^bar = 25, r = 2, w = 3, Now cost funcn C = WL + rK^bar = 50 + 3L*_c Now Y = 2 squareroot K middot L = > Y = 10 squareroot L = > (Y/10)^2 = L_c* L_c* = Y^2/100 rightarrow conditional labor dd funcn, Now C = 50 + 3Y^2/100, MC = dc/dy = 6y/100 = 3Y/50 (c) price of o/p = 1, perfect compt, Now at eqn v middot Mp_L = wage VMP_L = P times MP_L = > MP_L = partial differential y/partial differential L = 2/2 squareroot