A firm as the following production function5LK05 2L2KL3k Wha

A firm as the following production function:5LK^0.5 +2L^2K-L^3k What is the short- run production function if capital is fixed at k = 9? What are the firm\'s marginal product of labour and average product of labour in the short run ?

Solution

(Q1)

(a) K = 9

Q = 5L x (9)^0.5 + 2L² x 9 - L³ x 9

= 15L + 18L² - 9L³ .......(1) [Short run production function]

(b) From (1),

MPL = dQ / dL = 15 + 36L - 27L²

APL = Q / L = 15 + 18L - 9L²

(c)

Elasticity of output = [(dQ / dL)] / [(Q / L)]

= MPL / APL [Since MPL = dQ / dL & APL = Q / L]

From part (b),

Elasticity of output = (15 + 36L - 27L²) / (15 + 18L - 9L²)

NOTE: Out of 3 questions, the first question is answered in full.