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Given the following information for a closed economy: Consumption function C = 60 + 0.8Yd, Investment I = 200, Government spending G = 400, Income tax T = 0.5Y. Calculate the equilibrium level of nati

Economics

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2 parts
b

1100 million francs CFA\text{1100 million francs CFA}

c

1200 million francs CFA\text{1200 million francs CFA}

1.25

Step-by-step solution

14 steps

Part 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

Part b

1100 million francs CFA\text{1100 million francs CFA}

To calculate the equilibrium level of national income, we use the aggregate expenditure formula Y=C+I+GY = C + I + G.

  1. Express disposable income (YdY^d) in terms of national income (YY).

    Yd=Y−TY^d = Y - T

    Given T=0.5YT = 0.5Y:

    Yd=Y−0.5Y=0.5YY^d = Y - 0.5Y = 0.5Y
  2. Substitute YdY^d into the consumption function (CC).

    C=60+0.8YdC = 60 + 0.8Y^d C=60+0.8(0.5Y)C = 60 + 0.8(0.5Y) C=60+0.4YC = 60 + 0.4Y
  3. Substitute the expressions for CC, II, and GG into the equilibrium equation.

    Y=C+I+GY = C + I + G Y=(60+0.4Y)+200+400Y = (60 + 0.4Y) + 200 + 400 Y=660+0.4YY = 660 + 0.4Y
  4. Solve for YY.

    Y−0.4Y=660Y - 0.4Y = 660 0.6Y=6600.6Y = 660 Y=6600.6Y = \frac{660}{0.6} Y=1100Y = 1100

    The equilibrium level of national income is 1100 million francs CFA\boxed{\text{1100 million francs CFA}}.

Part c

1200 million francs CFA\text{1200 million francs CFA}

When exports and imports are introduced, the new equilibrium condition is Y=C+I+G+(X−M)Y = C + I + G + (X - M).

  1. Identify the new components.

    Exports (XX) = 300
    Imports (MM) = 0.2Y0.2Y
    From part b, C=60+0.4YC = 60 + 0.4Y, I=200I = 200, G=400G = 400.

  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) Y=60+0.4Y+200+400+300−0.2YY = 60 + 0.4Y + 200 + 400 + 300 - 0.2Y
  3. Combine constant terms and terms with YY.

    Y=(60+200+400+300)+(0.4Y−0.2Y)Y = (60 + 200 + 400 + 300) + (0.4Y - 0.2Y) Y=960+0.2YY = 960 + 0.2Y
  4. Solve for YY.

    Y−0.2Y=960Y - 0.2Y = 960 0.8Y=9600.8Y = 960 Y=9600.8Y = \frac{960}{0.8} Y=1200Y = 1200

    The new equilibrium level of national income is 1200 million francs CFA\boxed{\text{1200 million francs CFA}}.

    d) The value of the multiplier in (c) can be found from the equilibrium equation Y=Autonomous Expenditure+Induced ExpenditureY = \text{Autonomous Expenditure} + \text{Induced Expenditure}. In part (c), we had Y=960+0.2YY = 960 + 0.2Y, which simplifies to 0.8Y=9600.8Y = 960. The multiplier is 11−marginal propensity to spend\frac{1}{1 - \text{marginal propensity to spend}}.

  5. Identify the components affecting the multiplier.

    Marginal Propensity to Consume (MPC) = 0.8 (from C=60+0.8YdC = 60 + 0.8Y^d)
    Marginal Tax Rate (tt) = 0.5 (from T=0.5YT = 0.5Y)
    Marginal Propensity to Import (MPM) = 0.2 (from M=0.2YM = 0.2Y)

  6. Apply the multiplier formula for an open economy with government and proportional tax.

    k=11−MPC(1−t)+MPMk = \frac{1}{1 - MPC(1-t) + MPM} k=11−0.8(1−0.5)+0.2k = \frac{1}{1 - 0.8(1-0.5) + 0.2} k=11−0.8(0.5)+0.2k = \frac{1}{1 - 0.8(0.5) + 0.2} k=11−0.4+0.2k = \frac{1}{1 - 0.4 + 0.2} k=10.6+0.2k = \frac{1}{0.6 + 0.2} k=10.8k = \frac{1}{0.8} k=1.25k = 1.25

    The value of the multiplier is 1.25\boxed{1.25}.

Part e(i)· 2 steps

Balance of payment situation

To determine the country's balance of payment and budget situation, we use the equilibrium income from part (c), which is Y=1200Y = 1200.

  1. Calculate Exports (XX) and Imports (MM) at equilibrium.

    X=300X = 300 M=0.2Y=0.2×1200=240M = 0.2Y = 0.2 \times 1200 = 240
  2. Calculate Net Exports (X−MX - M).

    X−M=300−240=60X - M = 300 - 240 = 60

    Since X>MX > M, the country has a balance of payments surplus of 60 million francs CFA.

Part e(ii)· 2 steps

Budget situation

  1. Calculate Government Spending (GG) and Tax Revenue (TT) at equilibrium.

    G=400G = 400 T=0.5Y=0.5×1200=600T = 0.5Y = 0.5 \times 1200 = 600
  2. Calculate the Budget Balance (T−GT - G).

    T−G=600−400=200T - G = 600 - 400 = 200

    Since T>GT > G, the country has a budget surplus of 200 million francs CFA.

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