Q.Complete the following activity to find MPC, MPS, APC and APS, if the expenditure $E_c$ of a person with income $I$ is given as:
$E_c = (0.0003)I^2 + (0.075)I^2$ when $I = 1000$

Assumption noted below: the intended function is $E_c=(0.0003)I^2+(0.075)I$. Then MPC $=\dfrac{dE_c}{dI}=0.0006I+0.075$, MPS $=1-$MPC, APC $=\dfrac{E_c}{I}$, APS $=1-$APC; at $I=1000$ these are $0.675,\ 0.325,\ 0.375,\ 0.625$.

Honest note on the stem. As printed, $E_c=(0.0003)I^2+(0.075)I^2$ has both terms in $I^2$; this gives $\text{MPC}=\dfrac{dE_c}{dI}=0.1506I=150.6$ at $I=1000$, which is impossible since a marginal propensity must lie between $0$ and $1$. The standard, mathematically sensible version has a linear second term, $E_c=(0.0003)I^2+(0.075)I$, and is solved here.

MPC — Marginal Propensity to Consume $=\dfrac{dE_c}{dI}$:

$\dfrac{dE_c}{dI}=0.0006\,I+0.075$.

At $I=1000$: $\text{MPC}=0.0006(1000)+0.075=0.6+0.075=0.675$.

MPS — Marginal Propensity to Save $=1-\text{MPC}$:

$\text{MPS}=1-0.675=0.325$.

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