Answer to Question #195635 in Macroeconomics for Emmanuella

Question

Q1. A firm’s production function is , where L denotes the size of the workforce. Find the value of MPL in the case when: 

(a) L=1, (b) L=10, (c) L=100, (d) L=1000

Does the law of diminishing marginal productivity apply to this particular function?

Q2. Show that the price elasticity of demand is constant for demand functions of the form

where A and n are positive constants.

Answer 1

Q1.

Given information: 

$Q = 50L - 0.01L^2$

The formula for MPL $= \frac{\delta Q}{\delta L}$

$=50 - 0.02L^{2-1}$

$=50 - 0.02L$

When L = 1 

MP_L = 50 - 0.02

    = 49.98units

When L = 10

MP_L = 50 - 0.02(10)

    = 50 - 0.2

    = 49.8 units

When L = 100

MP_L = 50 - 0.02(100)

    = 48 units 

When L = 1000

MP_L = 50 - 0.02(1000)

    = 30 units

$fLL =\frac{\delta MPL}{\delta L} = -0.02$

f_LL < 0

When L rises the MP_L decreases from 49.98 to 30units.

The law of diminishing marginal productivity is applied in this function.

Q2.

If the form of the demand function is $Q=AP^{-n}$ where A and n

 are positive constants, the elasticity of demand is 𝑐

Therefore the elasticity of demand is constant.