Consider The Following Model: Y, C, I, G, X, M, C 300

Consider The Following Model1 Y C I G X M2 C 300 0

Consider the following model: (1) Y = C + I + G + X – M (2) C = 300 + 0.5Y (3) I = ? G = ? X = ? M = 150 + 0.25 Y Please answer the following questions: a. How much is equilibrium income or output (Y)? b. What is the equation for the saving function in this economy? c. What are the values of MPC, MPS and MPM? d. What is the value of spending multiplier for this economy? e. At equilibrium income, is the trade balance in deficit or surplus? By how much? f. In an effort to reduce the trade deficit, government decides to cut its spending by 100. What will be the impact on the trade balance? g. Another way to improve the position of the trade balance is to encourage exports. Suppose government provides subsidies to exporters that result in an increase in exports by 100. What will happen to the trade balance and by how much?

Paper For Above instruction

This economic analysis focuses on determining the equilibrium income, savings function, marginal propensities, and trade balance impacts within a closed economy with open trade features. The model comprises key macroeconomic components including consumption (C), investment (I), government spending (G), exports (X), and imports (M), with specific functional forms provided for the household and trade sectors. The primary objectives are to compute the equilibrium income level, analyze marginal propensities to consume, save, and import, calculate the fiscal multiplier, and evaluate the implications of policy measures such as fiscal contraction and export subsidies on the trade balance.

Determination of Equilibrium Income (Y):

Given the consumption function C = 300 + 0.5Y, and the import function M = 150 + 0.25Y, along with fixed levels of investment (I = 200), government spending (G = 200), and exports (X = 200), the equilibrium condition is derived from the aggregate demand identity:

Y = C + I + G + X – M

Substituting the given functions and values:

Y = (300 + 0.5Y) + 200 + 200 + 200 – (150 + 0.25Y)

Combining like terms:

Y = 300 + 0.5Y + 200 + 200 + 200 – 150 – 0.25Y

Simplifying:

Y = (300 + 200 + 200 + 200 – 150) + (0.5Y – 0.25Y) = 750 + 0.25Y

Rearranged to solve for Y:

Y – 0.25Y = 750

0.75Y = 750

Y = 750 / 0.75 = 1000

Thus, the equilibrium output is Y = 1000.

Verification of Equilibrium:

Calculating individual components at Y = 1000:

  • Consumption C = 300 + 0.5(1000) = 300 + 500 = 800
  • Investment I = 200 (given)
  • Government G = 200 (given)
  • Exports X = 200 (fixed)
  • Imports M = 150 + 0.25(1000) = 150 + 250 = 400

Sum of components:

C + I + G + X – M = 800 + 200 + 200 + 200 – 400 = 1000, which confirms the consistency of the model.

Savings Function:

Savings (S) is the portion of income not consumed:

S = Y – C

Substituting C = 300 + 0.5Y:

S = Y – (300 + 0.5Y) = Y – 300 – 0.5Y = 0.5Y – 300

Hence, the savings function is:

S = 0.5Y – 300

Marginal Propensity Calculations:

- Marginal Propensity to Consume (MPC): the slope of the consumption function, 0.5.

- Marginal Propensity to Save (MPS):

MPS = 1 – MPC = 1 – 0.5 = 0.5.

- Marginal Propensity to Import (MPM): the slope of the import function 0.25.

Spending Multiplier:

The multiplier effect in an open economy considering imports is calculated as:

Multiplier = 1 / (1 – MPC + MPM) = 1 / (1 – 0.5 + 0.25) = 1 / 0.75 = 1.33

Trade Balance at Equilibrium:

Trade balance (X – M) at Y = 1000:

  • Exports X = 200 (fixed)
  • Imports M = 150 + 0.25(1000) = 400

Trade deficit = X – M = 200 – 400 = –200. Therefore, the economy experiences a trade deficit of 200 units at equilibrium income.

Impact of Government Spending Cut on Trade Balance:

A decrease in G by 100 reduces G to 100. To analyze the effect on the trade deficit, we look at the change in income (ΔY). The change in Y following a G change, knowing the multiplier, is:

ΔY = Multiplier × ΔG = 1.33 × (–100) ≈ –133

Change in imports (ΔM):

ΔM = 0.25 × ΔY = 0.25 × (–133) ≈ –33.3

Since exports remain constant (X = 200), the new trade balance:

New trade balance = 200 – (400 + ΔM) = 200 – (400 – 33.3) = 200 – 366.7 = –166.7

This indicates an improvement in the trade deficit by approximately 33.3 units, moving from –200 to –166.7.

Effect of Export Subsidies on Trade Balance:

An increase in exports (ΔX) by 100, with X = 200, makes new exports X' = 300. The effect on income (ΔY):

ΔY = Multiplier × ΔX = 1.33 × 100 = 133

Corresponding increase in imports:

ΔM = 0.25 × ΔY = 0.25 × 133 ≈ 33.3

The net change in trade balance:

Δ(TB) = ΔX – ΔM = 100 – 33.3 = approximately 66.7

Therefore, the trade surplus increases by approximately 66.7 units, significantly improving the trade balance.

References

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