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 detail stes for calulation

Answer

Equilibrium output in the domestic economy is Y = 200.

Key Concept

Equilibrium in the Goods Market

Explanation

In an open economy, equilibrium output (Y) occurs where the demand for goods (Z) equals the supply of goods. The demand for goods is the sum of consumption (C), investment (I), government spending (G), and net exports (NX), which is exports (X) minus imports (IM). The equilibrium condition can be written as Y = C + I + G + NX.

Answer

The multiplier is 2.5, and the current account balance is 0.

Key Concept

Fiscal Multiplier and Current Account Balance

Explanation

The fiscal multiplier is calculated as 1/(1 - marginal propensity to consume + marginal propensity to import). The current account balance is the difference between exports and imports, which at equilibrium is zero when Y = Y*.

To solve for equilibrium output in the domestic economy, we set the supply of goods equal to the demand for goods:

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 + 0.2Y - 0.4Y

Y - 0.6Y - 0.2Y + 0.4Y = 40

0.6Y = 40

Y = \frac{40}{0.6}

Y = 200

For the multiplier, we use the formula:

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

Where MPC is the marginal propensity to consume (0.6) and MPM is the marginal propensity to import (0.4):

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

Multiplier = \frac{1}{0.8}

Multiplier = 2.5

For the current account balance, we calculate net exports (NX) at equilibrium:

NX = X - IM

NX = 0.2Y - 0.4Y

NX = 0.2(200) - 0.4(200)

NX = 40 - 80

NX = 0

At equilibrium output (Y = 200), the current account balance is zero.

Policy coordination and the world economy. Consider an open economy in which the real exchange rate is fixed and equal to one. Consumption, investment, government spending, and taxes are given by C = 10 + 0.8(Y − T), I = 10, G = 10 and T = 10 Imports and exports are given by IM = 0.3Y and X = 0.3Y ∗ (a) Solve for equilibrium output in the domestic economy, given Y ∗ . What is the multiplier in this economy? If we were to close the economy – so exports and imports were identically equal to zero – what would the multiplier be? Why would the multiplier be different in a closed economy? (b) Assume that the foreign economy is characterised by the same equations as the domestic economy (with asterisks reversed). Use the two sets of equations to solve for the equilibrium output of each country. [Hint: use the equations for the foreign economy to solve for Y ∗ as a function of Y and substitute this solution for Y ∗ in part (a).] What is the multiplier for each country now? Why is it different from the open economy multiplier in part (a)? (c) Assume that the domestic government, G, has a target level of output of 125. Assuming that the foreign government does not change G∗ , what is the increase in G necessary to achieve the target output in the domestic economy? Solve for net exports and the budget deficit in each country. (d) Suppose each government has a target level of output of 125 and that each government increases government spending by the same amount. What is the common increase in G and G∗ necessary to achieve the target output in both countries? Solve for net exports and the budget deficit in each country. (e) Why is fiscal coordination, such as the common increase in G and G∗ in part (d), difficult to achieve in practice? give deatilail steps to calculation

Answer

Equilibrium output in the domestic economy is

Y = 100

and the multiplier is

1.25

. If the economy were closed, the multiplier would be

5

.

Key Concept

Equilibrium Output and Multiplier in an Open Economy

Explanation

To find the equilibrium output

Y

, we set aggregate demand equal to aggregate supply. Aggregate demand is

C + I + G + (X - IM)

. Substituting the given equations, we get

10 + 0.8(Y - 10) + 10 + 10 + (0.3Y* - 0.3Y)

. Simplifying and solving for

Y

, we get

Y = 100

given

Y*

. The multiplier is the change in equilibrium output divided by the change in autonomous spending, which is

1/(1 - 0.8 + 0.3) = 1.25

. In a closed economy, exports and imports are zero, so the multiplier would be

1/(1 - 0.8) = 5

. The multiplier is different in a closed economy because there are no leakages due to imports.

Answer

Equilibrium output for each country is

Y = Y* = 100

and the multiplier for each country is

1.1111

.

Key Concept

Equilibrium Output and Multiplier in Interdependent Economies

Explanation

Using the foreign economy equations, we solve for

Y*

as a function of

Y

and substitute it into the domestic economy's equation. We get two equations with two unknowns,

Y

and

Y*

, and solve them simultaneously to find

Y = Y* = 100

. The multiplier for each country is now

1/(1 - 0.8 + 0.3 - 0.09) = 1.1111

, which is different from the open economy multiplier due to the interdependence of the economies.

Answer

The increase in

G

necessary to achieve the target output in the domestic economy is

20

, net exports in the domestic economy are

-5

, and the budget deficit in each country is

20

.

Key Concept

Fiscal Policy to Achieve Target Output

Explanation

To achieve a target output of

125

in the domestic economy, we calculate the required increase in

G

by using the multiplier and the gap between current and target output. The increase in

G

is

(125 - 100) / 1.25 = 20

. Net exports

(X - IM)

and the budget deficit

(G - T)

can then be calculated using the new level of

G

.

Answer

The common increase in

G

and

G*

necessary to achieve the target output in both countries is

11.11

, net exports in each country are

0

, and the budget deficit in each country is

11.11

.

Key Concept

Symmetric Fiscal Expansion in Interdependent Economies

Explanation

To achieve a target output of

125

in both countries, we use the multiplier for the interdependent economies and solve for the common increase in

G

and

G*

. The common increase is

(125 - 100) / 1.1111 = 11.11

. Net exports remain balanced at

0

because both countries increase spending by the same amount, and the budget deficit in each country is the increase in

G

or

G*

.

Answer

Fiscal coordination is difficult to achieve in practice due to differences in national objectives, economic conditions, political constraints, and potential for free-riding.

Key Concept

Challenges of Fiscal Coordination

Explanation

Fiscal coordination requires countries to align their fiscal policies, which is challenging because each country has its own economic goals, political situations, and constraints. Additionally, there is a risk of free-riding, where one country benefits from the fiscal expansion of another without reciprocating, leading to imbalances and potential conflict.

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