MICRO-Consider an open economy characterised by th

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.

Two friends, Doraemon and Nobita, start working at the same time after graduating from university. Doraemon works as a programmer for an annual salary of |700,000; Nobita as a professor for an annual salary of |450,000. Both friends expect their salaries to go up by 2% in real terms each year for the next three years. The real interest rate is 20% and the income tax is 20% for both these folks. Doraemon has no nonhuman wealth, while Nobita got |500,000 worth of bonds from their grandmother. (a) (5 points) Calculate the human wealth and the total wealth of the two friends over the next three years. (b) (5 points) How would an increase in tax-rate to 40% affect the relative wealth positions of Doraemon and Nobita? How would that impact their permanent consumption levels? give me detail steps in calculation and formula

Answer

Doraemon's human wealth over the next three years is |1,778,928; Nobita's human wealth is |1,136,928. Doraemon's total wealth is the same as his human wealth, |1,778,928, while Nobita's total wealth is |1,636,928.

Key Concept

Human Wealth and Total Wealth Calculation

Explanation

Human wealth is the present value of future income streams. Total wealth includes human wealth plus nonhuman wealth. The formula for calculating the present value of future income is:

PV = \frac{Y}{(1+r)^1} + \frac{Y(1+g)}{(1+r)^2} + \frac{Y(1+g)^2}{(1+r)^3}

where

Y

is the initial salary after tax,

g

is the real growth rate of the salary, and

r

is the real interest rate. For Doraemon and Nobita, the initial salaries after tax are |560,000 and |360,000, respectively. The real growth rate

g

is 2%, and the real interest rate

r

is 20%. Nobita's nonhuman wealth is |500,000, which is added to his human wealth to get his total wealth.

Answer

An increase in the tax rate to 40% would decrease the human wealth of both Doraemon and Nobita, but Nobita's relative wealth position improves due to his nonhuman wealth. Their permanent consumption levels would decrease, but Nobita's would be less affected due to his nonhuman wealth.

Key Concept

Impact of Tax Rate on Wealth and Permanent Consumption

Explanation

The increase in the tax rate reduces the after-tax salary, which in turn reduces the present value of future income streams, i.e., human wealth. Permanent consumption is based on the permanent income hypothesis, which states that individuals base their consumption on their expected long-term average income. With higher taxes, the expected long-term average income decreases, leading to a decrease in permanent consumption levels. However, Nobita's nonhuman wealth provides a buffer against the reduction in human wealth, thus his permanent consumption level would be less adversely affected compared to Doraemon's.

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