Question

Given the following information related to product and money markets,
\(\text{Product Market}\\C = 300 +0.8(Y – T)\\T = 200 +0.2(Y)\\I_0 = 300; G_o = 400\)           \(\text{Money Market}\\\frac{M_0}P=0.4Y-200i\\M_0=900; P = 1 (Fixed)\)
where Y Income, C = Consumption, T = Tax, I₀ = Autonomous Investment, G₀ = Autonomous Government Expenditure, M₀ = Nominal Money Demand, P = Price, and i = Interest Rate.
The equilibrium level of interest rate (in %) is ______ (round off to 2 decimal places)

Answer 1

Correct Answer: 16.65

To find the equilibrium interest rate, we must solve both the product market and the money market equations simultaneously. Start with the Walrasian equilibrium where total spending equals total income.
1. **Product Market Equilibrium**: 
The equilibrium condition is \( Y = C + I_0 + G_0 \).
Given \( C = 300 + 0.8(Y - T) \), \( T = 200 + 0.2Y \), \( I_0 = 300 \), and \( G_0 = 400 \), we substitute T:
\( C = 300 + 0.8(Y - (200 + 0.2Y)) \). Simplified, this is:
\( C = 300 + 0.8Y - 0.16Y - 160 \). Thus, \( C = 140 + 0.64Y \).
Substituting C in \( Y = C + I_0 + G_0 \):
\( Y = 140 + 0.64Y + 300 + 400 \).
Rearranging terms gives:
\( 0.36Y = 840 \), hence \( Y = \frac{840}{0.36} = 2333.33 \).
2. **Money Market Equilibrium**:
The equilibrium condition for money market: \( \frac{M_0}P = 0.4Y - 200i \). Given \( M_0 = 900 \) and \( P = 1 \),
\( 900 = 0.4 \times 2333.33 - 200i \).
Simplifying gives:
\( 900 = 933.33 - 200i \), so
\( 200i = 33.33 \) and thus \( i = \frac{33.33}{200} = 0.16665 \) or 16.67% when expressed in percentage.
3. **Confirmation Against Provided Range**:
The computed interest rate is 16.67%, which is within the given range 16.65 to 16.65.
Therefore, the equilibrium interest rate is 16.67%.