Question

Consider a hypothetical economy in which households spend $0.75 of each additional dollar they earn and save the remaining $0.25. The following graph shows the economy's initial aggregate-demand curve (AD1${\mathit{AD}}_1$).

Suppose the government increases its purchases by $3.75 billion.

Use the green line (triangle symbol) on the following graph to show the aggregate-demand curve (AD2${\mathit{AD}}_2$) after the multiplier effect takes place.

Hint: Be sure the new aggregate-demand curve (AD2${\mathit{AD}}_2$) is parallel to AD1${\mathit{AD}}_1$. You can see the slope of AD1${\mathit{AD}}_1$ by selecting it on the following graph.

The following graph shows the money market in equilibrium at an interest rate of 7.5% and a quantity of money equal to $60 billion.

Show the impact of the increase in government purchases on the interest rate by shifting one or both of the curves on the following graph.

Suppose that for each one-percentage-point increase in the interest rate, the level of investment spending declines by $0.5 billion. The change in the interest rate (according to the change you made to the money market in the previous scenario) therefore causes the level of investment spending to   (fall/rise) by    .(2.5 billions/ 1.25 bil/ 0.62 bil)

After the multiplier effect is accounted for, the change in investment spending will cause the quantity of output demanded to   (decrease/increase) by   (5 bil/1.2 bil/2bil)at each price level. The impact of an increase in government purchases on the interest rate and the level of investment spending is known as the   ( multiplier/liquidty preference/ automatic stabilizer/ crowding out) effect.

Use the purple line (diamond symbol) on the graph at the beginning of this problem to show the aggregate-demand curve (AD3${\mathit{AD}}_3$) after accounting for the impact of the increase in government purchases on the interest rate and the level of investment spending.

Hint: Be sure your final aggregate-demand curve (AD3${\mathit{AD}}_3$) is parallel to AD1${\mathit{AD}}_1$ and AD2${\mathit{AD}}_2$. You can see the slopes of AD1${\mathit{AD}}_1$ and AD2${\mathit{AD}}_2$ by selecting them on the graph.

Answer 1

It is given that the economy has the marginal propensity to consume has \(\$ 0.75\) and marginal propensity to save is \(\$ 0.25\)

Further, the government increases its purchase by \(\$ 3.75\) billion.

Government Multiplier \(=1 / 1-\mathrm{MPC}\) \(\mathrm{MPC}=0.75\)

Therefore, government multiplier \(=1 / 1-0.75=4\)

Increase in output can be calculated using the following formula:

\(\Delta \mathrm{Y}=\) Government Multiplier \(\times\) Increase in government spending \(\Delta \mathrm{Y}=4 \times 3.75\)

\(\Delta \mathrm{Y}=\$ 15\) billion

Hence, the increase in output is \(\$ 15\) billion.

The increase in government spending will have a positive effect on the aggregate demand curve. The demand curve will shift rightwards from \(\mathrm{AD}_{1}\) to \(\mathrm{AD}_{2}\).

In the money market, the equilibrium rate of interest is \(7.5 \%\), and the equilibrium quantity of money is \(\$ 60\) billion. An increase in government spending leads to an increase in output. At a higher level of output, the income level increase with further increases the demand for money. The demand for money will shift rightwards. The money supply curve will remain unaffected.

The demand for money increases from MD to MD'. The new equilibrium rate of interest also increases.

For each point, it is given that for each point increase in the interest rate and leads to a decline in investment spending by \(\$ 0.5\) Billion. The change in interest rate will cause the level of investment spending to fall by \(\$ 1.25\) billion.

After the multiplier effected is taken into consideration, the change in investment spending will cause the quantity of output demanded to decrease by 5 billion at each price level.

$$ \Delta \mathrm{Y}=\left(\frac{1}{1-c}\right) \times \Delta \mathrm{I} $$

\(\Delta \mathrm{Y}=\left(\frac{1}{1-0.75}\right) \times \Delta \mathrm{I}\)

\(\Delta \mathrm{Y}=4 \times 1.25\)

\(\Delta \mathrm{Y}=\$ 5\) billion

The impact of an increase in government purchases on the interest rate and investment spending is known as a crowding-out effect.

The aggregate demand curve, \(\mathrm{AD}_{3}\) is the final demand curve that accounts for the impact of government spending on the interest rate and the level of spending.

Answer 2

Multiplier = 1/(1-MPC)= 1/(1-0.75)=4

Increase in Government purchases= $3.75 billion

Change in AD= Multiplier * Change in Government purchases

AD increase = 4*$3.75 billion =$15 billion

AD 1 shift to AD 2. Output increases from 130 to 145.

AD PRICE LEVEL AD3 AD2 100 100 105 110 115 120 125 130 OUTPUT (Billions of dollars) 135 140 145

Suppose that for each one-percentage-point increase in the interest rate, the level of investment spending declines by $0.5 billion. The change in the interest rate (according to the change you made to the money market in the previous scenario) therefore causes the level of investment spending to __ fall___ by __$1.25 billion___ .

After the multiplier effect is accounted for, the change in investment spending will cause the quantity of output demanded to __decrease__ by __$5 billion__ at each price level. The impact of an increase in government purchases on the interest rate and the level of investment spending is known as the crowding-out effect.

Reason- one percentage point increase in interest rate leads to $0.5 billion decrease. When interest rate rises by 2.5% from 7.5% to 10%. As Money demand curve shifts upwards.

2.5*$.5 billion= $1.25 billion fall in investment

Investment decreases by $1.25 billion

AD fall= multiplier* change in investment= 4*$1.25 billion= $5 billion

AD2 shift to AD 3. Output decreases from 145 to 140.

When increase in government Purchases still leads to fall in output level it is known as crowding out.

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