ECON7030 Microeconomic Analysis

Tutorial Exercise 8 (Week 9)

Question 1

Consider the following production function:

y = F (L, K) = 4L1/3 K 1/3

where L and K are the amount of labour and capital used in the production process, and

y is the output. Throughout this question, the output price p is 3 and the rental rate of

capital r is 1.

We will first consider a firm in the short run, where the amount of capital is fixed at

K = 64. The fixed cost is therefore 64.

(a) Is there diminishing returns to labour? Explain.

(b) Suppose the wage w is 1. Find the profit-maximising choice of L. Then calculate

the profit-maximising output level and the maximised profit.

(c) Now suppose the wage w increases to. Find the profit-maximising choice of L.

Then calculate the profit-maximising output level and the maximised profit. You

can leave your answer in square roots.

(d) What is the change in L when w increases from 1 to 2 in the short run? You can

leave your answer in square roots.

Now consider a firm in the long run, where K is variable and can be

chosen by the firm.

(e) Does the production function exhibit increasing, decreasing, or constant returns to

scale?

(f) Suppose the wage rate w is 1. Find the profit maximising choice of L and K.

Calculate the profit-maximising output level and the maximised profit. How does

the profit in the long run compare to the profit in the short run (from part b)?

Why?

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(g) Now suppose the wage rate w increases to 2. Find the profit maximising choice of

L and K. Calculate the profit-maximising output level and the maximised profit.

How does the profit in the long run compare to the profit in the short run (from

part c)? Why?

(h) What is the change in L when w increases from 1 to 2 in the long run? Is the change

in L bigger or smaller in the long run when compared to the short run (from part

d)? Give intuition for your comparisons.

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