Q: Suppose the government increases its purchases (G) by $$100, with a marginal propensity to spend on domestic output z=0.5$. What is the resulting change in equilibrium national income ($$\Delta Y$)?

$$\Delta Y = \frac{1}{1-0.5} \times 100 = 2 \times 100 = 200$$

Q: Suppose the marginal propensity to consume (MPC) is 0.7, the net tax rate $$t is 0.1$$, and the marginal propensity to import $$m is 0.2. $$What is the marginal propensity to spend on domestic output ($$z$$)?

$$z = 0.7 \times (1-0.1) - 0.2 = 0.43$$

Q: If autonomous exports ($$X) $$increase by $$20$$ and the marginal propensity to spend on domestic output is $$z=0.6$$, what is the change in equilibrium income ($$\Delta Y$$)?

$$\Delta Y = \frac{1}{1-0.6} \times 20 = 2.5 \times 20 = 50$$

Q: Suppose the government reduces transfer payments by $$50$$, with a net tax rate $$t = 0.2$$ and MPC $$= 0.8. $$What is the immediate effect on disposable income ($$Y_d) if $$national income $$Y = 1,000$$?

$$Y_d = Y - T = 1,000 - (0.2 \times 1,000 - 50) = 1,000 - 150 = 850$$

Question 1

Suppose the government increases its purchases (G) by $$100, with a marginal propensity to spend on domestic output z=0.5$. What is the resulting change in equilibrium national income ($$\Delta Y$)?

Accepted Answer

$$\Delta Y = \frac{1}{1-0.5} 	imes 100 = 2 	imes 100 = 200$$

Question 2

If the net tax rate $$t is 20$$% and government purchases $$G$$ are $$400$$, what level of national income $$Y$$ will result in a balanced budget?

Accepted Answer

$$Y = 2,000$$

Question 3

Which of the following best describes how government purchases (G) and net taxes (T) enter the aggregate expenditure (AE) model?

Accepted Answer

G enters AE directly, while T enters indirectly by affecting disposable income in the consumption function.

Question 4

Given the net exports function $$NX = X - mY$$, with $$X = 80$$ and $$m = 0.2$$, at what level of income $$Y do $$net exports become zero?

Accepted Answer

$$Y = 400$$

Question 5

If the marginal propensity to import $$m$$ increases, what is the effect on the multiplier in the open economy AE model?

Accepted Answer

The multiplier decreases because more income leaks out as imports.

Question 6

Suppose the marginal propensity to consume (MPC) is 0.7, the net tax rate $$t is 0.1$$, and the marginal propensity to import $$m is 0.2. $$What is the marginal propensity to spend on domestic output ($$z$$)?

Accepted Answer

$$z = 0.7 	imes (1-0.1) - 0.2 = 0.43$$

Question 7

If autonomous exports ($$X) $$increase by $$20$$ and the marginal propensity to spend on domestic output is $$z=0.6$$, what is the change in equilibrium income ($$\Delta Y$$)?

Accepted Answer

$$\Delta Y = \frac{1}{1-0.6} 	imes 20 = 2.5 	imes 20 = 50$$

Question 8

Which of the following statements about the AE model with government and foreign trade is correct?

Accepted Answer

Taxes and imports both act as leakages, reducing the size of the multiplier.

Question 9

If the AE function is $$AE = 600 + 0.5Y$$, what is the equilibrium level of income $$Y$$?

Accepted Answer

$$Y = 1,200$$

Question 10

Suppose the government reduces transfer payments by $$50$$, with a net tax rate $$t = 0.2$$ and MPC $$= 0.8. $$What is the immediate effect on disposable income ($$Y_d) if $$national income $$Y = 1,000$$?

Accepted Answer

$$Y_d = Y - T = 1,000 - (0.2 	imes 1,000 - 50) = 1,000 - 150 = 850$$

Question 11

If Canadian prices rise relative to foreign prices, what is the likely effect on net exports ($$NX$$)?

Accepted Answer

Net exports decrease because imports rise and exports fall.

Question 12

Which of the following best explains why the multiplier is smaller in an open economy with taxes than in a closed economy without taxes?

Accepted Answer

Because both taxes and imports reduce the portion of income spent on domestic goods, causing more leakages.

Question 13

If the marginal propensity to spend on domestic output is $$z=0.4$$, what is the value of the multiplier?

Accepted Answer

$$Multiplier = \frac{1}{1-0.4} = 1.67$$

Question 14

Suppose the AE function is $$AE = 900 + 0.7Y. If $$autonomous spending falls by $$200$$, what is the resulting change in equilibrium income?

Accepted Answer

$$\Delta Y = \frac{1}{1-0.7} 	imes (-200) = 3.33 	imes (-200) = -666.67$$

Question 15

Which of the following is NOT included in government purchases (G) in the AE model?

Accepted Answer

Transfer payments such as unemployment benefits

Question 16

If the marginal propensity to import $$m is 0.25 $$and exports $$X$$ are 50, what is the slope and vertical intercept of the net exports function $$NX = X - mY$$?

Accepted Answer

Slope = $$-0.25$$, intercept = $$50$$

Question 17

In the AE model with a constant price level, what determines equilibrium national income?

Accepted Answer

Aggregate expenditure (AE) determines equilibrium national income because firms supply whatever is demanded at the fixed price.

Question 18

If the net tax rate $$t is 0.15$$, the marginal propensity to consume (MPC) is 0.8, and the marginal propensity to import $$m is 0.1$$, what is the value of $$z$$ and the multiplier?

Accepted Answer

$$z = 0.8 	imes (1-0.15) - 0.1 = 0.58$$, $$Multiplier = \frac{1}{1-0.58} = 2.38$$

Question 19

If the government wants to achieve a balanced budget and the net tax rate is 10%, what should government purchases (G) be if equilibrium income is $$5,000$$?

Accepted Answer

$$G = 0.10 	imes 5,000 = 500$$

Chapter 7: Adding Government and Trade to the Simple Macro Model — Study Notes

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