# Fixed proportion production function Q = min(5K, 10L)

Suppose that a firm's fixed proportion production function is given by Q = min(5k,10L)

The firm's Total Cost (TC) function is given by TC = vK + wL,

where v is the cost of K and w is the cost of L.

v = 1

w = 3

TC = K + 3L

a) Calculate the firm's long-run total, average and marginal functions.

b) Suppose that K is fixed at 10 in the short run. Calculate the firm's short-run total, average and marginal cost functions, and state the domain of the functions.

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#### Solution Preview

a) Calculate the firm's long-run total, average and marginal cost functions.

To make one unit of q requires (1/5 =) 0.2 units of K and (1/10 =) 0.1 units of L

The cost of K is v and the cost of L is w, so:

LRAC = 0.2v + ...

#### Solution Summary

Given a firm's fixed production function:

Q = min(5k,10L)

And its total cost function:

TC = vK + wL

where v = 1 and w = 3

This solution shows how to calculate the firm's long-run total, average and marginal functions, and, if K is fixed at 10 in the short run, the firm's short-run total, average and marginal cost functions. All calculations are given in detail.