i. Find the equilibrium income

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Here are the solutions to Question 3: i. Find the equilibrium income The equilibrium condition is Y = AE, where Y is the national income and AE is the aggregate expenditure. Given: Consumption function: C = 200 + 0.8Y; Investment: I = 50; Government Spending: G = 60; Aggregate Expenditure: AE = C + I + G (assuming (X−M)=0 as no information is provided for net exports) Step 1: Substitute the given values into the aggregate expenditure equation. AE = (200 + 0.8Y) + 50 + 60; AE = 310 + 0.8Y; Step 2: Set Y = AE to find the equilibrium income. Y = 310 + 0.8Y Step 3: Solve for Y. Y − 0.8Y = 310; 0.2Y = 310; Y = 310/0.2; Y = 1550 The equilibrium income is 1550. ii. Derive the government spending multiplier and explain its economic implications Step 1: Identify the marginal propensity to consume (MPC). From the consumption function C = 200 + 0.8Y, the MPC is the coefficient of Y, which is 0.8. Step 2: Calculate the government spending multiplier (k_G). The formula for the government spending multiplier is: k_G = 11 − MPC; k_G = (1)/(1 − 0.8); k_G = 1/0.2; k_G = 5 The government spending multiplier is $

I. Find the equilibrium income

Answer

Step-by-step solution

Part i· 3 steps

Substitute the given values into the aggregate expenditure equation.

Set $Y = AE$ to find the equilibrium income.

Solve for $Y$ .

Part ii· 2 steps

Identify the marginal propensity to consume (MPC).

Calculate the government spending multiplier ( $k_G$ ).

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