Which of the following represents the consumption function when
$M P C = 0.4 + \frac { 0.1 } { \sqrt { Y } }$, and $C = 50$ when $Y = 100$ ?
A) $0.4 Y + 0.2 \sqrt { Y } + 8$
B) $0.4 Y + 0.2 \sqrt { Y } + 50$
C) $0.4 Y + 0.05 \sqrt { Y } + 50$
D) $0.4 Y - 0.2 \sqrt { Y } + 50$
E) $0.4 Y - 0.05 \sqrt { Y } + 5$

Question

Quizplus · Accepted Answer

Given $MPC = 0.4 + \frac{0.1}{\sqrt{Y}}$, the consumption function can be derived by integrating the MPC with respect to income (Y), since the marginal propensity to consume (MPC) is the derivative of the consumption function with respect to income. Given $C = 50$ when $Y = 100$, we can solve for the constant of integration. The correct formula that fits the given conditions is $0.4Y + 0.2\sqrt{Y} + 8$.

Which of the Following Represents the Consumption Function When MPC=0.4+0.1YM P C = 0.4 + \frac { 0.1 } { \sqrt { Y } }MPC=0.4+Y​0.1​

Which of the Following Represents the Consumption Function When $M P C = 0.4 + \frac { 0.1 } { \sqrt { Y } }$