Question

1. Consider an economy in which autonomous consumption is 800, the marginal propensity to consume is 0.8, investment is 400, government spending is 500, taxation is 400, and net exports are 100.

A. What is the equilibrium GDP in this economy? Show your work.

B. What is the savings at this level of GDP? Show your work.

C. What are the spending and tax multipliers? Show your work.

D. If government spending increases by 200, what is the new equilibrium GDP and what is the increase over the original equilibrium GDP? Show your work.

E. If the government increases both spending and taxation by 200, what is the new equilibrium GDP and what is the increase over the original equilibrium GDP? Show your work.

Answer 1

The equilibrium GDP in this economy is 3200. The savings at this level of GDP is 760. The spending multiplier and tax multiplier are both 6.6667. If government spending increases by 200, the new equilibrium GDP is 3400, with an increase of 200. If both government spending and taxation increase by 200, the new equilibrium GDP is 3000, with a decrease of 200.

Step-by-step explanation:

To find the equilibrium GDP in this economy, we can use the equation Y = C + I + G + X - M, where Y represents the GDP, C is consumption, I is investment, G is government spending, X is exports, and M is imports. Given the information provided:

C = 400 + 0.85(Y - T) = 400 + 0.85(Y - 0.25Y) = 400 + 0.85(0.75Y) = 400 + 0.6375Y
I = 300
G = 200
X = 500
M = 0.1(Y - T) = 0.1(0.75Y) = 0.075Y
Substituting these expressions into the equilibrium GDP equation:

Y = 400 + 0.6375Y + 300 + 200 + 500 - 0.075Y
Simplifying the equation:

Y - 0.5625Y = 1400
0.4375Y = 1400
Y = 3200

Therefore, the equilibrium GDP in this economy is 3200.

To find the savings at this level of GDP, we can use the equation S = Y - C. Substituting the values:

S = 3200 - (400 + 0.85(3200 - 0.25(3200)) = 3200 - (400 + 0.85(3200 - 800)) = 3200 - (400 + 0.85(2400)) = 3200 - (400 + 2040) = 3200 - 2440 = 760

Therefore, the savings at this level of GDP is 760.

The spending multiplier can be found by taking the inverse of the savings rate. The savings rate is the marginal propensity to save, which is 1 - the marginal propensity to consume. In this case, the marginal propensity to consume is given as 0.85. Therefore, the savings rate is 1 - 0.85 = 0.15. Taking the inverse, the spending multiplier is 1/0.15 = 6.6667.

The tax multiplier can be found by taking the inverse of the marginal propensity to save. In this case, the marginal propensity to save is 0.15. Therefore, the tax multiplier is 1/0.15 = 6.6667.

If government spending increases by 200, the new equilibrium GDP can be found by adding the increase in government spending to the original equilibrium GDP. Therefore, the new equilibrium GDP is 3200 + 200 = 3400. The increase over the original equilibrium GDP is 3400 - 3200 = 200.

If the government increases both spending and taxation by 200, the new equilibrium GDP can be found by subtracting the increase in taxation from the original equilibrium GDP. Therefore, the new equilibrium GDP is 3200 - 200 = 3000. The increase over the original equilibrium GDP is 3000 - 3200 = -200.