Question

1. Consider the production function y = f(L,K) for a firm in a competitive market setting. The price of the output good is p > 0. The prices of the inputs Labour and Capital are w> 0 and r>0 respectively. The firm chooses L and K in order to maximize profits, (L.K). (a) How does the short-run production function differ from the long-run production function? (b) Write out the profit function for the firm, (L,K). (c) Derive the first order conditions for profit maximization. (d) Explain what the first order conditions tell us about the way in which each factor is used by the firm in a competitive market. How would this change for a firm operating in a monopoly market? (e) Suppose the production function exhibits Constant Returns to Scale (CRS). Given CRS, by Euler's Theorem: fiL + fKK = f(L,K) where f, denotes the partial derivative of the production function with respect to factor i. Show that Euler's Theorem along with the first order conditions from (c) imply that the total payment to all factors of production will equal the total value of output produced.

Answer 1

a) in the short rum capital is fixed a the amount of Labor to be used for production depends on the amount of goods to be produced 4 the the fixed copital.& In Long on every factor input is variable 4 input use depends on factor prices 4 the output to be produced b) Profit function: IT (2,6)= py_fortrk (Reverna cost S T spg (hk)-(W2 trk) c) OL First order conditions are: dla Pfe-w zo lie Pf Law o dll a Pf xar=orie Pf xar- OD 4 are first onder conditions the first order condition tells that the each factor should be used till marginal revenue from using it is equal to marginal Cost- do

of the firm is operating in monopoly market. P will be function of the Ceutput) to T = plyn-y-loltok) - TI = Plys . f (2,42 - (oltrk) The first order conditions are : om - Port + flow wzo pptype=wC es pot feln, K) dhe mrze 4 are the first order condition der londinom