What are the firms cost-minimising levels of employment and

Question

Question: The firm faces a long-run production function (for output per week)

X = 10L^1/2K^1/2

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 = 11L^1/2K^1/2

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?