A firm produces an output y using labor and capital, whose quantities are denote

Question

A firm produces an output y using labor and capital, whose quantities are denoted respectively by xLand xK. Suppose this firm's production function is given by

Answer the following questions.

a. Derive the marginal product of labor and the marginal product of capital.

b. Is the marginal product of labor diminishing everywhere? Does it ever take negative values?

c. Does the production process of this firm exhibit increasing, constant, or decreasing returns to scale?

A firm produces an output y using labor and capital, whose quantities are denoted respectively by xL and xK. Suppose this firm's production function is given by f ( L, K ) = sqrt KL +K+L Answer the following questions. a. Derive the marginal product of labor and the marginal product of capital. b. Is the marginal product of labor diminishing everywhere? Does it ever take negative values? c. Does the production process of this firm exhibit increasing, constant, or decreasing returns to scale?

Explanation / Answer

a) MPL  = ?f/?L = (1/2.5)*(K/L).5 + 1

MPK = ?f/?K = (1/2.5)*(L/K).5 + 1

b) it never takes negative values, it is always decreasing..(diminishing every where)

c) it exibit constant return to scale

because,

f(K,L) = (2*K*2*L).5+2*K+2*L

f(K,L) = 2[(K*L).5+K+L]

IT MEANS WHEN WE DOUBLE THE INPUT TOTAL OUTPUT ALSO GET DOUBLED

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