Answer to Question #290260 in Accounting for Anonymous

Question

Firm ABC has the following production function 𝑄 = 6𝐾 3 + 4𝐾𝐿 − 𝐿 3 i. Determine the average products of capital (K) and labour (L). [4 Marks] ii. Find the marginal products of capital and labour (MPK and MPL)

Answer 1

Solution:

i.). Average Product of Capital (AP_K) = $\frac{Q}{K}$ = 6K³ + 4KL – L³ $\div$ K = 6K² + 4L – $\frac{L^{3} }{K}$

Average Product of Labor (AP_L) = $\frac{Q}{L}$ = 6K³ + 4KL – L³ $\div$ L = $\frac{6K^{3} }{L}$ + 4K – L²

 

ii.). Marginal Product of Capital (MP_K) = $\frac{\partial Q} {\partial K}$ = 18K² + 4L

Marginal Product of Labor (MP_L) = $\frac{\partial Q} {\partial L}$ = 4K – 3L²