This economics question tests your understanding of economic models and analysis. The step-by-step answer below applies the relevant framework and explains the reasoning.
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Morning LA — let's get this done. a) The statistics include consumption, investment, government spending, and income tax, but no mention of exports or imports initially. This implies a closed economy with a government sector. b) To calculate the equilibrium level of national income, we use the aggregate expenditure formula Y = C + I + G. Step 1: Express disposable income (Y^d) in terms of national income (Y). Y^d = Y - T Given T = 0.5Y: Y^d = Y - 0.5Y = 0.5Y Step 2: Substitute Y^d into the consumption function (C). C = 60 + 0.8Y^d C = 60 + 0.8(0.5Y) C = 60 + 0.4Y Step 3: Substitute the expressions for C, I, and G into the equilibrium equation. Y = C + I + G Y = (60 + 0.4Y) + 200 + 400 Y = 660 + 0.4Y Step 4: Solve for Y. Y - 0.4Y = 660 0.6Y = 660 Y = (660)/(0.6) Y = 1100 The equilibrium level of national income is 1100 million francs CFA. c) When exports and imports are introduced, the new equilibrium condition is Y = C + I + G + (X - M). Step 1: Identify the new components. Exports (X) = 300 Imports (M) = 0.2Y From part b, C = 60 + 0.4Y, I = 200, G = 400. Step 2: Substitute all components into the new equilibrium equation. Y = (60 + 0.4Y) + 200 + 400 + (300 - 0.2Y) Y = 60 + 0.4Y + 200 + 400 + 300 - 0.2Y Step 3: Combine constant terms and terms with Y. Y = (60 + 200 + 400 + 300) + (0.4Y - 0.2Y) Y = 960 + 0.2Y Step 4: Solve for Y. Y - 0.2Y = 960 0.8Y = 960 Y = (960)/(0.8) Y = 1200 The new equilibrium level of national income is 1200 million francs CFA. d) The value of the multiplier in (c) can be found from the equilibrium equation Y = Autonomous Expenditure + Induced Expenditure. In part (c), we had Y = 960 + 0.2Y, which simplifies to 0.8Y = 960. The multiplier is (1)/(1 - marginal propensity to spend). Step 1: Identify the components affecting the multiplier. Marginal Propensity to Consume (MPC) = 0.8 (from C = 60 + 0.8Y^d) Marginal Tax Rate (t) = 0.5 (from T = 0.5Y) Marginal Propensity to Import (MPM) = 0.2 (from M = 0.2Y) Step 2: Apply the multiplier formula for an open economy with government and proportional tax. k = (1)/(1 - MPC(1-t) + MPM) k = (1)/(1 - 0.8(1-0.5) + 0.2) k = (1)/(1 - 0.8(0.5) + 0.2) k = (1)/(1 - 0.4 + 0.2) k = (1)/(0.6 + 0.2) k = (1)/(0.8) k = 1.25 The value of the multiplier is 1.25. e) To determine the country's balance of payment and budget situation, we use the equilibrium income from part (c), which is Y = 1200. (i) Balance of payment situation Step 1: Calculate Exports (X) and Imports (M) at equilibrium. X = 300 M = 0.2Y = 0.2 × 1200 = 240 Step 2: Calculate Net Exports (X - M). X - M = 300 - 240 = 60 Since X > M, the country has a balance of payments surplus of 60 million francs CFA. (ii) Budget situation Step 1: Calculate Government Spending (G) and Tax Revenue (T) at equilibrium. G = 400 T = 0.5Y = 0.5 × 1200 = 600 Step 2: Calculate the Budget Balance (T - G). T - G = 600 - 400 = 200 Since T > G, the country has a budget surplus of 200 million francs CFA. What's next? Send 'em!