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Consider an open economy characterised by the following equations: C = 20 + 0.6...

Jan 10, 2024

Consider an open economy characterised by the following equations: C = 20 + 0.6(Y − 20) I = 20 + 0.2Y G = 12 T = 20 X = 0.2Y ∗ IM = 0.4Y ϵ = 1 Y ∗ = 200 2 (a) (5 points) Solve for equilibrium output in the domestic economy. (b) (3+2 points) Calculate the multiplier. Compute the current account balance for the domestic economy give me steps on how to calculation with formulkas

Answer

The equilibrium output in the domestic economy is Y = 100.

Key Concept

Equilibrium in the Goods Market

Explanation

In an open economy, the equilibrium output (Y) is determined where the aggregate demand (AD) equals the aggregate supply (Y). The aggregate demand is the sum of consumption (C), investment (I), government spending (G), exports (X), minus imports (IM). The equilibrium condition can be written as Y = C + I + G + (X - IM). By substituting the given equations and solving for Y, we find the equilibrium output.

Answer

The multiplier is 2.5, and the current account balance is -4.

Key Concept

Fiscal Multiplier and Current Account Balance

Explanation

The fiscal multiplier is calculated as 1/(1 - MPC(1 - t) + MPI), where MPC is the marginal propensity to consume, t is the tax rate, and MPI is the marginal propensity to import. The current account balance is calculated as X - IM, where X is exports and IM is imports. By substituting the given values and solving, we find the multiplier and the current account balance.

To solve for equilibrium output (a) and calculate the multiplier and current account balance (b), we use the following steps: (a) To find the equilibrium output (Y), we set aggregate demand equal to aggregate supply:

Y = C + I + G + (X - IM)

Substituting the given equations:

Y = (20 + 0.6(Y - 20)) + (20 + 0.2Y) + 12 + (0.2Y - 0.4Y)

Simplifying:

Y = 20 + 0.6Y - 12 + 20 + 0.2Y + 12 + 0.2Y - 0.4Y

Y = 40 + 0.6Y - 12 + 0.2Y - 0.2Y

Y = 40 + 0.6Y

Solving for Y:

0.4Y = 40

Y = 100

(b) To calculate the multiplier, we use the formula:

Multiplier = \frac{1}{1 - MPC(1 - t) + MPI}

Given that taxes (T) are fixed, the tax rate (t) is not directly provided, so we use the marginal propensity to consume (MPC) and the marginal propensity to import (MPI) from the equations:

MPC = 0.6

MPI = 0.4

Since T is fixed, the multiplier simplifies to:

Multiplier = \frac{1}{1 - MPC + MPI}

Multiplier = \frac{1}{1 - 0.6 + 0.4}

Multiplier = \frac{1}{0.8}

Multiplier = 2.5

To compute the current account balance, we use the formula:

Current Account Balance = X - IM

Substituting the given values:

Current Account Balance = 0.2Y - 0.4Y

Current Account Balance = 0.2(100) - 0.4(100)

Current Account Balance = 20 - 40

Current Account Balance = -20

However, since the question states that the foreign income (Y*) is 200, we need to adjust the imports (IM) accordingly:

IM = 0.4Y*

IM = 0.4(200)

IM = 80

Now, we recalculate the current account balance with the adjusted imports:

Current Account Balance = X - IM

Current Account Balance = 0.2Y - 0.4Y*

Current Account Balance = 0.2(100) - 80

Current Account Balance = 20 - 80

Current Account Balance = -60

So, the current account balance is -60, not -4 as initially stated. This was an error in the initial calculation. The correct current account balance is -60.