Question

\[ \begin{array}{|c|c|c|c|} \hline \textbf{Income (Y)} & \textbf{Savings (S)} & \textbf{(APC)} & \textbf{(MPS)} \\ \hline 0 & -50 & -- & -- \\ \hline 100 & 0 & 1 & 0.5 \\ \hline 200 & 50 & \frac{3}{4} & 0.5 \\ \hline 300 & 100 & \frac{2}{3} & 0.5 \\ \hline \end{array} \]

Hint:

Use \( C = Y - S \) to calculate consumption and derive \( APC \) and \( MPS \) using their respective formulas: \( APC = \frac{C}{Y} \), \( MPS = \frac{\Delta S}{\Delta Y} \).

Answer 1

Consumption Function: \( C = Y - S \) At \( Y = 0 \): \( C = -50 \) (Autonomous Consumption). Marginal Propensity to Consume (\(MPC\)) = \( 1 - MPS = 1 - 0.5 = 0.5 \). 
Values: At \( Y = 100 \): \( S = 0 \), so \( C = 100 - 0 = 100 \). \( APC = \frac{C}{Y} = 1 \). At \( Y = 200 \): \( S = 50 \), so \( C = 200 - 50 = 150 \). \( APC = \frac{C}{Y} = \frac{150}{200} = 0.75 \). At \( Y = 300 \): \( S = 100 \), so \( C = 300 - 100 = 200 \). \( APC = \frac{C}{Y} = \frac{200}{300} = 0.67 \).