A ï¬rm has the following long run production function x =a(K^1/2)(L^1/2)(P^1/4), where a > 0 is a constant and K, L , Pare inputs of the three factors. The prices of K, L , P are Rs. 1 ,Rs. 9 and Rs. 8 respectively.
a) Derive the ï¬rm’s long run total cost function , long runaverage cost function and long run marginal cost function. Show theworkings in detail
b) In the short run P is ï¬xed and K and L are variable. Derivethe ï¬rms short run a) Total Cost Function b) Variable Cost Functionc) Average Variable Cost Function d) Marginal Cost Function.
c) Obtain an equation of the form P = f(x) showing the optimumquantity of the ï¬xed factor P for the ï¬rm to acquire as a functionof the intended output x.
