In the short-run, a firm cannot vary its capital, Kequals 4, but can vary its labor, L. It produces output q. Explain why the firm will or will not experience diminishing marginal returns to labor in the short-run if its production function is A) q=10L + K and B) q = L^0.5 K^0.5

Question

Paul Cooke

Business

29 August, 16:30

In the short-run, a firm cannot vary its capital, Kequals 4, but can vary its labor, L. It produces output q. Explain why the firm will or will not experience diminishing marginal returns to labor in the short-run if its production function is A) q=10L + K and B) q = L^0.5 K^0.5

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Frank Sampson · Answer 1

a) given that the capital is fixed at k=2 and the production function is shown as

q = 10L + K

Then the firm will not experience any diminishing returns to labour this is because when the firm varies the labour input, keeping capital fixed at K=2, the marginal product of labour (MPL) is constant at 10.

b) with the production function, q = L^0.5 K^0.5, with the increase in labour input the firm will experience diminishing marginal returns to labour in the short run.

q = L^0.5 K^0.5 = L^0.5 (2) ∧0.5

=1.41L∧0.5

Thus MPl = 0.705L∧-0.5

That is the increase in L, the MPl diminishes