Question

Find MPC, MPS, APC and APS, if the expenditure \(E_c\) of a person with income I is given as \( E_c = (0.0003)I^2 + (0.075)I \); when \( I=1000 \).

Hint:

Remember the key relationships: `APC + APS = 1` and `MPC + MPS = 1`. 'Average' refers to the overall ratio (C/I), while 'Marginal' refers to the instantaneous rate of change (dC/dI).

Answer 1

Given the consumption function \( C = E_c = 0.0003I^2 + 0.075I \) and \( I=1000 \).
Step 1: Calculate Consumption (C) and Savings (S). \[ C = 0.0003(1000)^2 + 0.075(1000) = 0.0003(1000000) + 75 = 300 + 75 = 375 \] \[ S = \text{Income} - \text{Consumption} = I - C = 1000 - 375 = 625 \] Step 2: Calculate Average Propensities (APC and APS). \[ \text{APC} = \frac{C}{I} = \frac{375}{1000} = 0.375 \] \[ \text{APS} = \frac{S}{I} = \frac{625}{1000} = 0.625 \] Step 3: Calculate Marginal Propensities (MPC and MPS). First, find the derivative of the consumption function with respect to income. \[ \text{MPC} = \frac{dC}{dI} = \frac{d}{dI}(0.0003I^2 + 0.075I) = 0.0006I + 0.075 \] Now, evaluate MPC at \( I=1000 \). \[ \text{MPC} = 0.0006(1000) + 0.075 = 0.6 + 0.075 = 0.675 \] \[ \text{MPS} = 1 - \text{MPC} = 1 - 0.675 = 0.325 \] Final Answer: APC = 0.375, APS = 0.625, MPC = 0.675, MPS = 0.325.