Re: ISI 2015 PEA Answer Key

Posted by onionknight on May 03, 2015; 2:59pm
URL: http://discussion-forum.276.s1.nabble.com/ISI-2015-PEA-Answer-Key-tp7596538p7596559.html

Q1.) In the short run, K is fixed as K* so the only decision the firm needs to make is how much labour to employ. Whatever labour the firm employs, the production function is Y= L^0.25 * K^0.25 and since capital is fixed as K*, L^0.25 = Y/K^0.25 which means L= Y^4/K. Now cost in the short run is wage rate times labour which is 10*Y^4/K.

In the long run, to maximize profits, set marginal derivative of profit with respect to labour=0, which gives
0.25*p*L^-0.25*K^0.25 = 10
Similarly, set marginal derivative of profit with respect to capital =0
0.25*p*K^-0.25*L^0.25 = 10
Divide the two equations to get K=L
Now K^0.25 * L^0.25 = Y, L and K are equal so L=K= Y^2
cost= w*L+r*K = 20*Y^2