Question

What is the new equilibrium income when the investment rises from 10 to 20 at a given consumption function:
\(C = 40 + 0.8Y\)

• A. 300
• B. 250
• C. 320
• D. 50

Hint:

Multiplier approach: \(k = \frac{1}{1 - 0.8} = 5\).
Initial \(Y = 5 \times (40 + 10) = 250\).
\(\Delta Y = k \times \Delta I = 5 \times 10 = 50\).
New \(Y = 250 + 50 = 300\).

Answer 1

The Correct Option is A

Concept:
In a two-sector Keynesian macroeconomic model without government and foreign sectors, equilibrium national income is determined where aggregate output equals aggregate expenditure: \[ Y = C + I \]

Step 1: Identifying Given Parameters:
The consumption function is given as: \[ C = 40 + 0.8Y \] The autonomous investment expenditure increases from \(I_1 = 10\) to a new value of: \[ I_{\text{new}} = 20 \]

Step 2: Solving for New Equilibrium Income:
Substitute the consumption function and the new investment level into the equilibrium condition: \[ Y = 40 + 0.8Y + 20 \] Combine the autonomous terms: \[ Y = 60 + 0.8Y \] Subtract \(0.8Y\) from both sides: \[ Y - 0.8Y = 60 \] \[ 0.2Y = 60 \] Solve for \(Y\): \[ Y = \frac{60}{0.2} = \frac{600}{2} = 300 \] Final Answer:
The new equilibrium level of national income is 300. Thus, option (A) is the correct answer.