In the short-run, a firm cannot vary its capital, Kequals4, 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

Explanation:

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

you have to put the parentheses like this:

in fact, you have to perform the operation inside parentheses first, and then proceed in order:

answer; the nav calculated at the market close at 4: 00 pm new york time;