Question

Given the aggregate consumption function C = 0.9Y + 100(where C is aggregate consumption

and Y is aggregate income)

(a) Find the marginal propensity to consume (MPC) and average propensity to consume (APC)

(b) Find the elasticity of consumption with respect to income, and show that it equals MPC/APC

Answer 1

Solution:

a.). Marginal propensity to consume (MPC) and average propensity to consume (APC):

MPC = $\frac{\triangle C}{\triangle Y}$ = 0.9

APC is the ratio of consumption expenditures (C) to disposable income (DI):

APC = $\frac{C}{DI}, or \;\frac{C}{Y}$

Y = C + I + G

Y = 0.9Y + 100

Y – 0.9Y = 100

0.1Y = 100

Y = $\frac{100}{0.1}$ = 1000

Y = 1000

Y = C + I + G

1000 = C

C = 1000

APC = $\frac{C}{Y} = \frac{1000}{1000} = 1$

APC = 1

 

b.). The elasticity of consumption with respect to income:

Elasticity measures the responsiveness of an economic variable in response to a change in another economic variable.

Elasticity = %ΔC / %ΔY

Elasticity of consumption with respect to income =$\frac{900}{1000} = 0.9$

$\frac{MPC}{APC} = \frac{0.9}{1} = 0.9$ MPC / APC = 0.9 / 1 = 0.9

Therefore:

The elasticity of consumption with respect to income = $\frac{MPC}{APC}$