Question

SHOW WORK

8) Suppose the economy's production function is Y = AK"3 No.7. Suppose K = 200, N and A 1. Calculate the marginal product of capital. A) 1.0 B) 1.5 C) 2.0 D) 2.5 2000

Answer 1

Production function is as follows -

Y = A K^0.3 N^0.7

Calculate the marginal product of capital (MPK)

$MPK = \frac{\mathrm{d} Y}{\mathrm{d} K}$

$MPK = \frac{\mathrm{d} \left ( AK^{0.3}N^{0.7} \right )}{\mathrm{d} K}$

$MPK = \frac{0.3AN^{0.7}}{K^{0.7}}$

Putting the value of A, N, and K in MPK

$MPK = \frac{0.3\times 1\times 2000^{0.7}}{200^{0.7}}$

$MPK = \frac{0.3\times 1\times 204.51}{40.80}$

$MPK = \frac{61.35}{40.80}$

MPK = 1.5

Thus,

The marginal product of capital is 1.5

Hence, the correct answer is the option (B).