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A firm has the following long run production function x = a(K^1/2)(L^1/2)(P^1/4), where a > 0...

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Economics

A firm 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 firm’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 fixed and K and L are variable. Derivethe firms 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 fixed factor P for the firm to acquire as a functionof the intended output x.

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