Question

9. A firm faces the following production function: Q = (41/3)K^(2/3)L^(2/3) where Q is output, K is capital, and L is labour. Labour and capital can be purchased in competitive markets at a unit cost of Â£1 and Â£8 respectively. In what ratio would the firm wish to employ capital and labour to ensure production at minimum cost in the long run? Solve for the long-run cost function LRC = f(Q). [10 marks] (b) Assume the amount of capital in the short run is fixed at K = 8. Solve for the short-run cost function. Explain why long-run costs are smaller than short-run costs almost everywhere, and why they are equal for some values of Q. [5 marks] (c) Show that long-run variable costs feature increasing returns to scale, and short-run variable costs feature decreasing returns to scale.

          9. A firm faces the following production function:
Q = (41/3)K^(2/3)L^(2/3)

where Q is output, K is capital, and L is labour. Labour and capital can be purchased in competitive markets at a unit cost of Â£1 and Â£8 respectively.

In what ratio would the firm wish to employ capital and labour to ensure production at minimum cost in the long run? Solve for the long-run cost function LRC = f(Q).

[10 marks]

(b) Assume the amount of capital in the short run is fixed at K = 8. Solve for the short-run cost function. Explain why long-run costs are smaller than short-run costs almost everywhere, and why they are equal for some values of Q.

[5 marks]

(c) Show that long-run variable costs feature increasing returns to scale, and short-run variable costs feature decreasing returns to scale.

9 a firm faces the following production function q 413k23 l23 where q is output k is capital and l is labour labour and capital can be purchased in competitive markets at a unit cost of 1 an 51447

Added by Dana C.

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