Suppose, the production function for X company is given by ? = 5(??) 0.5 where, Q is the amount of output produced, K is the amount of capital employed in production and L is the amount of labor employed in production. The prices of capital and labor are given by ?? = $48 and ?? = $75.
a)Express the total cost in terms of K and Q.
b)Derive the expression of marginal cost of capital.
c)Derive the long-run cost function in terms of Q.
We are given
Squaring both sides
Total Cost, TC is given as
In this case, price of capital is constant. So,
Marginal Cost of capital=PK=$48
Marginal cost of output keeping K constant is given as
MC of product=dTC/dQ=6Q
In long run
Set K=(25/16)*L in production function
Long run cost is given as
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