4. Calculate autonomous expenditure and the marginal propensity to consume.

Autonomous expenditure is $2 billion. Autonomous expenditure is expenditure that does not depend on real GDP. Autonomous expenditure equals the value of aggregate planned expenditure when real GDP is zero.

The marginal propensity to consume is 0.6. When the country has no imports or exports and no income taxes, the slope of the AE curve equals the marginal propensity to consume. When income increases from zero to $6 billion, aggregate planned expenditure increases from $2 billion to $5.6 billion. That is, when real GDP increases by $6 billion, aggregate planned expenditure increases by $3.6 billion. The marginal propensity to consume is $3.6 billion ÷ $6 billion, which is 0.6.

5. a. What is aggregate planned expenditure when real GDP is $6 billion?

Figure 11.1 shows that aggregate planned expenditure is $5.6 billion when real GDP is $6 billion.

b. If real GDP is $4 billion, what is happening to inventories?

Firms’ inventories are decreasing. When real GDP is $4 billion, aggregate planned expenditure exceeds real GDP, so firms sell all that they produce and more. As a result, inventories decrease.

c. If real GDP is $6 billion, what is happening to inventories?

Firms are accumulating inventories. That is, unplanned inventory investment is positive. When real GDP is $6 billion, aggregate planned expenditure is less than real GDP. Firms cannot sell all that they produce and inventories pile up.

6. Explain the difference between induced consumption expenditure and autonomous consumption expenditure. Why isn’t all consumption expenditure induced expenditure?

Induced consumption expenditure is consumption expenditure that changes when disposable income changes. Autonomous consumption expenditure is consumption expenditure that would occur in the short run even if disposable income was zero. Not all consumption expenditure is induced consumption expenditure because, in the short run, even if someone has no income they still will have some (autonomous) consumption expenditure, if for nothing else, for food.

7. Recovery?

In the second quarter, businesses increased spending on equipment and software by 21.9%, while a category that includes home building grew amid a rush by consumers to take advantage of tax credits for homes.

Source: The Wall Street Journal, July 31, 2010

Explain how an increase in business investment at a constant price level changes equilibrium expenditure.

Investment is a component of autonomous aggregate expenditure. An increase in investment increases aggregate expenditure so the AE curve shifts upward. Equilibrium expenditure increases.

Use the following data to work Problems 8 and 9.

An economy has a fixed price level, no imports, and no income taxes. MPC is 0.80, and real GDP is $150 billion. Businesses increase investment by $5 billion.

8. Calculate the multiplier and the change in real GDP.

With no imports and no income taxes, the multiplier equals 1/(1  MPC). So the multiplier is 1/(1  0.8), which is 5.0 Then the $5 billion increase in investment increases real GDP by 5.0 × $5 billion, which is $25 billion.

9. Calculate the new real GDP and explain why real GDP increases by more than $5 billion.

Real GDP was initially $150 billion. The increase in investment increased real GDP by $25 billion, so real GDP increases to $175 billion. Real GDP increases by more than the initial increase in investment because the increase in investment increases disposable income which induces additional increases in consumption expenditure. So real GDP increases both because investment increases and also because of induced increases in consumption expenditure.

Use the following data to work Problems 10 and 11.

An economy has a fixed price level, no imports, and no income taxes. An increase in autonomous expenditure of $2 trillion increases equilibrium expenditure by $8 trillion.

10. Calculate the multiplier and the marginal propensity to consume.

The multiplier is defined as the change in equilibrium expenditure divided by the change in autonomous expenditure. In this problem the multiplier equals $8 trillion ÷ $2 trillion which is 4.0. If there are no imports and no taxes, the multiplier can be calculated from the formula that the multiplier equals 1/(1  MPC). The multiplier equals 4.0, so 4.0 = 1/(1  MPC). Solving this formula for the MPC shows that the MPC equals 0.75.

11. What happens to the multiplier if an income tax is introduced?

If an income tax is introduced, the multiplier decreases in value.

Use the following data to work Problems 12 to 16.

Suppose that the economy is at full employment, the price level is 100, and the multiplier is 2. Investment increases by $100 billion.

12. What is the change in equilibrium expenditure if the price level remains at 100?

The initial change in equilibrium expenditure is $200. The initial effect of the increase in investment increases equilibrium expenditure by the change in investment times the multiplier. The multiplier is 2 and the change in investment is $100 billion, so the initial change in equilibrium expenditure is $200 billion.

13. a. What is the immediate change in the quantity of real GDP demanded?

The quantity of real GDP demanded increases by $200 billion. The increase in investment shifts the aggregate demand curve rightward by the change in investment times the multiplier. The multiplier is 2 and the change in investment is $100 billion, so the aggregate demand curve shifts rightward by $200 billion.

b. In the short run, does real GDP increase by more than, less than, or the same amount as the immediate change in the quantity of real GDP demanded?

In the short-run, real GDP increases by less than $200 billion. Real GDP is determined at the intersection of the AD curve and the SAS curve. In the short run, the price level will rise and real GDP will increase but by an amount less than the shift of the AD curve.

14. In the short run, does the price level remain at 100? Explain why or why not.

In the short run, the price level rises. Real GDP is determined at the intersection of the AD curve and the SAS curve. In the short run, the increase in aggregate demand means that the price level will rise as the economy moves along its upward-sloping SAS curve.

15. a. In the long run, does real GDP increase by more than, less than, or the same amount as the immediate increase in the quantity of real GDP demanded?

In the long run, real GDP equals potential GDP, so real GDP does not increase. Real GDP is determined at the intersection of the AD curve and the SAS curve. After the initial increase in investment, money wages increase, the SAS curve shifts leftward, and in the long run, real GDP moves back to potential GDP.

b. Explain how the price level changes in the long run.

Real GDP is determined at the intersection of the AD curve and the SAS curve. In the long run, money wages increase so the SAS curve shifts leftward, raising the price level by more than it rose in the short run.

16. Are the values of the multipliers in the short run and the long run larger or smaller than 2?

The multiplier in the short run is less than the multiplier of 2 because the short-run increase in real GDP is less than $200 billion. The long-run multiplier is even smaller. It equals zero.

Use the following news clip to work Problems 17 and 18.