Question

Establish the relationship between Marginal Propensity to Consume and Average Propensity to Consume with the help of an example and diagram.

Hint:

Linear case: $APC=\dfrac{a}{Y}+MPC$; as $Y$ rises, $APC \downarrow$ and approaches $MPC$.

Answer 1

Definitions: Consumption function $C=a+bY$, where $a$ is autonomous consumption and $b$ is MPC ($0<b<1$). APC is $C/Y$.
Relationships: (1) $MPC=\dfrac{\Delta C}{\Delta Y}=b$ (constant in the linear case). (2) $APC=\dfrac{C}{Y}=\dfrac{a}{Y}+b$. Since $\dfrac{a}{Y}$ falls as income rises, APC decreases with income, approaching MPC from above: $\lim_{Y\to\infty} APC = b = MPC$. (3) At very low $Y$, $APC$ can exceed 1 (because $a$ is positive), while $MPC$ remains between 0 and 1.
Example: Let $C=50+0.8Y$. At $Y=200$, $C=210$, so $APC=210/200=1.05$ and $MPC=0.8$. At $Y=500$, $C=450$, so $APC=0.90$; still above $0.8$, but closer. At $Y=1000$, $C=850$, so $APC=0.85$. Thus as $Y$ rises, APC $\downarrow$ toward MPC.
Diagram (verbal): Plot $C$ on vertical axis, $Y$ on horizontal. The $45^\circ$ line is $C=Y$. The consumption line with intercept $a$ and slope $b$ lies below/above the $45^\circ$ line depending on $Y$. The slope of the consumption line equals MPC. The ray from origin to any point on the consumption line has slope equal to APC. As you move rightward, this ray's slope falls toward the constant slope of the line—visually showing $APC \to MPC$.
Macro significance: Declining APC with income implies rising saving ratio, affecting multiplier size and growth dynamics.