Question

Consider the Keynesian consumption function $C=\alpha+\beta Y$, where $C$ is aggregate consumption, $Y$ is aggregate income, $\alpha>0$ is a constant, and $\beta$ is the marginal propensity to consume $(0<\beta<1)$. Then, the average propensity to consume is

• A. $\alpha$
• B. $\dfrac{\alpha}{Y}+\beta$
• C. $\alpha Y+\beta Y^{2}$
• D. $\alpha+\dfrac{\beta}{Y}$

Hint:

Average measures divide the level by $Y$; marginal measures are derivatives. For linear $C=\alpha+\beta Y$, APC $=C/Y=\alpha/Y+\beta$ while MPC $=\beta$.

Answer 1

The Correct Option is B

Average Propensity to Consume (APC) is defined as consumption per unit of income:
\[ \text{APC}=\frac{C}{Y}=\frac{\alpha+\beta Y}{Y}=\frac{\alpha}{Y}+\beta. \] Hence the APC equals $\dfrac{\alpha}{Y}+\beta$ \Rightarrow option \fbox{(B)}.
(Observe that as $Y$ rises, $\alpha/Y \downarrow$ so APC approaches $\beta$.)