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Question: The firm faces a long-run production function (for output per week)
X = 10L1/2K1/2
and input prices of £100 per week for labour and £200 per week for capital rental.
(a) What are the firm's cost-minimising levels of employment and capital stock if it produces 200 units of output?
(b) What if it produces 400 units of output? What are long-run average and marginal costs in each case (i.e. if output = 200 and 400)?
(c) Suppose that the firm becomes more efficient technically, so that the production function becomes
X = 11L1/2K1/2
What happens to total, average and marginal costs if output equals 200? If output equals 400?
(d) What happens to the capital-labour ratio if output equals 200 and the wage rate increases by 10 per cent? What happens to total and marginal costs?
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