Re: MSQE 2006 MICRO

Posted by Amit Goyal on Apr 08, 2010; 4:26am
URL: http://discussion-forum.276.s1.nabble.com/jnu-tp2844632p4869130.html

Hi Priyanka,

Short-run Objective of the firm can be written as:
Max (with respect to L) pf(L, K) -  wL - rK
where f(L, K) is the production function, L and K are variable and fixed inputs, respectively.
First order condition can be used to solve the problem (provided production function exhibits decreasing marginal returns to variable input L)
FOC is p(∂f/∂L) = w, we can solve this for optimal L.
Notice that when p and w doubles the FOC is still the same:
FOC is 2p(∂f/∂L) = 2w is equivalent to p(∂f/∂L) = w and hence the optimal L is same as above.
Now K is unchanged and from our analysis we figured out that L is also unchanged, hence optimal output will remain the same. Let Q* be the optimal output and L* be the equilibrium employment. Then Short run profit (gross of fixed cost) = pQ* - wL* for the former case and 2pQ* - 2wL* for the latter.
Hence, Optimal short-run profit (gross of fixed cost) will double.
Short-run profit (net of fixed cost) will more than double:
2pQ* - 2wL* - rK > 2pQ* - 2wL* - 2rK = 2(pQ* - wL* - rK)