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

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 , P are 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 run average cost function and long run marginal cost function. Show the workings in detail

b) In the short run P is ﬁxed and K and L are variable. Derive the ﬁrms short run a) Total Cost Function b) Variable Cost Function c) Average Variable Cost Function d) Marginal Cost Function.

c) Obtain an equation of the form P = f(x) showing the optimum quantity of the ﬁxed factor P for the ﬁrm to acquire as a function of the intended output x.

Expert Solution

Rahul Sunny answered 7 months ago

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