chapter ten

The Aggregate Expenditures model

ANSWERS TO END-OF-CHAPTER QUESTIONS

10-1           What is an investment schedule and how does it differ from an investment demand curve? 

            An investment schedule shows the level of investment spending for a given level of GDP.  An investment demand curve shows how expected rates of profit and real interest rates determine the level of investment spending.  In the simple AE model, investment spending is assumed to be independent of the level of real GDP.

10-2      (Key Question)  Assuming the level of investment is $16 billion and independent of the level of total output, complete the following table and determine the equilibrium levels of output and employment in this private closed economy.  What are the sizes of the MPC and MPS?

 

 

 

 

Possible levels

of employment

(millions)

Real domestic

output (GDP = DI)

(billions)

 

Consumption

(billions)

 

Saving

(billions)

 

 

 

 

 

 

 

 

 

 

 

 

40

45

50

55

60

65

70

75

80

$240

260

280

300

320

340

360

380

400

 

$244

260

276

292

308

324

340

356

372

 

$ _____

$ _____

$ _____

$ _____

$ _____

$ _____

$ _____

$ _____

$ _____

 

 

 

 

 

 

 

10-3      Using the consumption and saving data in question 2 and assuming investment is $16 billion, what are saving and planned investment at the $380 billion level of domestic output?  What are saving and actual investment at that level?  What are saving and planned investment at the $300 billion level of domestic output?  What are the levels of saving and actual investment?  Use the concept of unplanned investment to explain adjustments toward equilibrium from both the $380 and $300 billion levels of domestic output.

            At the $380 billion level of GDP, saving = $24 billion; planned investment = $16 billion (from the question).  This deficiency of $8 billion of planned investment causes an unplanned $8 billion increase in inventories.  Actual investment is $24 billion (= $16 billion of planned investment plus $8 billion of unplanned inventory investment), matching the $24 billion of actual saving.

            At the $300 billion level of GDP, saving = $8 billion; planned investment = $16 billion (from the question).  This excess of $8 billion of planned investment causes an unplanned $8 billion decline in inventories.  Actual investment is $8 billion (= $16 billion of planned investment minus $8 billion of unplanned inventory disinvestment) matching the actual of $8 billion.

            When unplanned investments in inventories occur, as at the $380 billion level of GDP, businesses revise their production plans downward and GDP falls. When unplanned disinvestments in inventories occur, as at the $300 billion level of GDP; businesses revise their production plans upward and GDP rises.  Equilibrium GDP—in this case, $340 billion—occurs where planned investment equals saving.

10-4      Why is saving called a leakage?  Why is planned investment called an injection?  Why must saving equal planned investment at equilibrium GDP in the private closed economy?  Are unplanned changes in inventories rising, falling, or constant at equilibrium GDP?  Explain.

Saving is like a leakage from the flow of aggregate consumption expenditures because saving represents income not spent.  Planned investment is an injection because it is spending on capital goods that businesses plan to make regardless of their current level of income.  If the two are unequal, there will be a discrepancy between spending and production that will result in unplanned inventory changes.  Firms, not wanting inventory levels to change, will change production, implying that equilibrium can only occur when the saving leakage equals the injection of investment spending in a private closed economy.

At equilibrium GDP there will be no changes in unplanned inventories because expenditures will exactly equal planned output levels which include consumer goods and services and planned investment.  Thus there is no unplanned investment including no unplanned inventory changes.

10-5      What effect will each of the changes designated in question 3 at the end of Chapter 9 have on the equilibrium level of GDP?  Explain your answers.

a.       A large increase in the value of real estate, including private houses.

b.       A decline in the real interest rate.

c.       A sharp, sustained decline in stock prices.

d.       An increase in the rate of population growth.

e.       The development of a cheaper method of manufacturing computer chips.

f.        A sizable increase in the retirement age for collecting Social Security benefits.

g.       The expectation that mild inflation will persist in the next decade.

h.       An increase in the Federal personal income tax.

 

(a)  If this means that people have become wealthier, then their consumption schedule will shift up and GDP will rise by a multiple of the increase in consumption. 

(b)  This will increase interest‑sensitive consumer purchases and investment, causing GDP to increase.

(c)  By reducing consumption (because households will feel—or be—less wealthy, or because they fear a recession) and by decreasing investment, the AE schedule will shift downward, causing the GDP to decline.

(d)  This will increase AE, causing GDP to increase.

(e)  Investment will increase both because of increased profitability and because of increased innovations, causing GDP to increase.

(f)  The announcement will lead to an upward shift of the current saving schedule (downward shift of the consumption schedule), causing GDP to decline.

(g)  An increase in the personal income tax will decrease the level of disposable income, and decrease consumer spending, which could mean a decline in aggregate expenditures.  But if the government increases its purchases to the extent of the tax increase, then aggregate expenditures will actually increase, since consumer expenditures fall only by a fraction of the decline in income and government spending is more than offsetting this decline.  If this happens, the equilibrium level of GDP should rise.  On the other hand, if government spending does not rise, then the equilibrium level of GDP may fall as private spending falls.

10-6      By how much will GDP change if firms increase their investment by $8 billion and the          MPC is .80?  If the MPC is .67?

            GDP will increase $40 billion if the MPC is .80.  An MPC of .80 will produce a multiplier of 5.  The multiplier times the $8 billion change in spending will change GDP by $40 billion.

            Change in GDP = Change in Investment x (1/(1 - MPC))     $40 billion = $8 billion x (1/(1 - .8))

            GDP will increase by approximately $24 billion when the MPC is .67

            $24 billion = $8 billion x (1/(1 - .67))  Note: The multiplier for an MPC of .67 is actually 3.03.

10-7      Depict graphically the aggregate expenditures model for a private closed economy.  Now show a decrease in the aggregate expenditures schedule and explain why the decrease in real GDP in your diagram is greater than the initial decline in aggregate expenditures.  What would be the ratio of a decline in real GDP to the initial drop in aggregate expenditures if the slope of your aggregate expenditures schedule were .75?

            If the slope of the aggregate expenditures schedule were .8, then the MPC = .8 and the MPS = .2.  Therefore, the multiplier would be 1/(.2) = 5.  The ratio of decline in real GDP to the initial drop of expenditures would be a ratio of 5:1.  That is, if expenditures declined by $4 billion, GDP should decline by $20 billion.  On the graph it can be seen that a one-unit decline in (C + I) leads to a five-unit decline in real GDP.

                             

10-8      Suppose that a certain country has an MPC of .9 and real GDP of $400 billion.  If its investment spending decreases by $4 billion, what will be its new level of real GDP? 

            The multiplier is 10 or 1/(1-.9) so 10 x -$4 billion = -$40 billion.  The new GDP is $400 billion - $40 billion = $360 billion.

10-9      (Key Question)  The data in columns 1 and 2 of the table below are for a private closed economy.

 

 

 

 

 

 

(1)

Real

domestic

output

(GDP = DI)

billions

(2)

Aggregate

expenditures

private closed

economy,

billions

(3)

 

 

 

Exports,

billions

(4)

 

 

 

Imports,

billions

(5)

 

Net

exports,

private

economy

(6)

 

Aggregate

expenditures,

open,

billions

 

 

 

 

 

 

 

 

 

 

 

 

$200

$250

$300

$350

$400

$450

$500

$550

$240

$280

$320

$360

$400

$440

$480

$520

$20

$20

$20

$20

$20

$20

$20

$20

$30

$30

$30

$30

$30

$30

$30

$30

$ _____

$ _____

$ _____

$ _____

$ _____

$ _____

$ _____

$ _____

$ _____

$ _____

$ _____

$ _____

$ _____

$ _____

$ _____

$ _____

 

 

 

 

 

 


a.   Use columns 1 and 2 to determine the equilibrium GDP for this hypothetical economy.

b.   Now open up this economy to international trade by including the export and import figures of columns 3 and 4.  Fill in columns 5 and 6 to determine the equilibrium GDP for the open economy.  Explain why this equilibrium GDP differs from that of the closed economy.

c.   Given the original $20 billion level of exports, what would be the equilibrium GDP if imports were $10 billion greater at each level of GDP? 

d.   What is the multiplier in this example?

10-10    Assume that, without taxes, the consumption schedule of an economy is as shown below:

 

 

GDP,

billions

Consumption,

Billions

 

 

 

 

 

 

 

 

$100

200

300

400

500

600

700

 

$120

200

280

360

440

520

600

 

 

 

 

 


a.   Graph this consumption schedule and determine the MPC.

b.   Assume now that a lump-sum tax system is imposed such that the government collects $10 billion in taxes at all levels of GDP.  Graph the resulting consumption schedule, and compare the MPC and the multiplier with that of the pretax consumption schedule.

Refer to Figures 9-2 and 9-4 for the graphs for (a) and (b), respectively.

(a)  The size of the MPC is 80/100 or .8 because consumption changes by 80 when GDP changes by 100.

(b)  The resulting consumption schedule will be exactly $8 billion below the original at all levels of GDP (or income).  After-tax income will fall by $10 billion.  Given the MPC of .8, consumption therefore will fall by $8 billion at each level of GDP.  The multiplier is 5 because the MPS is .2.  The MPC and multiplier don’t change from of a lump-sum tax.

10-11    Explain graphically the determination of equilibrium GDP for a private economy through the          aggregate expenditures model.  Now add government spending (any amount that you choose) to       your graph, showing its impact on equilibrium GDP.  Finally, add taxation (any amount of lump-       sum tax that you choose) to your graph and show its effect on equilibrium GDP.  Looking at your    graph, determine whether equilibrium GDP has increased, decreased, or stayed the same in view of the sizes of the government spending and taxes that you selected.

Figures 10-5 and 10-6 show how to do this.  Graphs and answers will differ depending on magnitude of changes.

10-12    (Key Question) Refer to columns 1 and 6 of the tabular data for question 9.  Incorporate government into the table by assuming that it plans to tax and spend $20 billion at each possible level of GDP.  Also assume that all taxes are personal taxes and that government spending does not induce a shift in the private aggregate expenditures schedule.  Compute and explain the changes in equilibrium GDP caused by the addition of government.

 

10-13    (Key Question)  Refer to the table below in answering the questions that follow:

 

 

 

 

 

(1)

Possible levels

of employment,

millions

(2)

Real domestic

output,

billions

(3)

Aggregate Expenditures

(Ca+Ig+Xn+G),

billions

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

90

100

110

120

130

 

$500

550

600

650

700

 

$520

560

600

640

680

 

 

 

 

 

 

 

 

a.   If full employment in this economy is 130 million, will there be an inflationary gap or a recessionary gap?  What will be the consequence of this gap?  By how much would aggregate expenditures in column 3 have to change at each level of GDP to eliminate the inflationary or recessionary gap?  Explain.  What is the multiplier in this example?

b.   Will there be an inflationary or recessionary gap if the full-employment level of output is $500 billion?  Explain the consequences.  By how much would aggregate expenditures in column 3 have to change at each level of GDP to eliminate the gap?  Explain.  What is the multiplier in this example?

c.   Assuming that investment, net exports, and government expenditures do not change with changes in real GDP, what are the sizes of the MPC, the MPS, and the multiplier?

(a)  A recessionary gap.  Equilibrium GDP is $600 billion, while full employment GDP is $700 billion.  Employment will be 20 million less than at full employment.  Aggregate expenditures would have to increase by $20 billion (= $700 billion -$680 billion) at each level of GDP to eliminate the recessionary gap.  The MPC is .8, so the multiplier is 5.

(b)  An inflationary gap.  Aggregate expenditures will be excessive, causing demand-pull inflation.  Aggregate expenditures would have to fall by $20 billion (= $520 billion -$500 billion) at each level of GDP to eliminate the inflationary gap.  The multiplier is still 5 – the level of full employment GDP does not affect the multiplier.

(c)  MPC = .8 (= $40 billion/$50 billion); MPS = .2 (= 1 -.8); multiplier = 5 (= 1/.2).

10-14    (Advanced analysis)  Assume the consumption schedule for a private open economy is such that
C = 50 + 0.8Y.  Assume further that planned investment and net exports are independent of the level of income and constant at Ig = 30 and Xn = 10.  Recall also that, in equilibrium, the real output produced (Y) is equal to the aggregate expenditures:  Y = C + Ig + Xn.

a    Calculate the equilibrium level of income or real GDP for this economy. 

b    What happens to equilibrium Y if Ig changes to 10?  What does this tell you about the size of the multiplier?

(a) 

       

 

 

 

 

 

 

 

Real domestic

output

(GDP = YI)

 

 

C

 

 

Ig

 

 

Xn

Aggregate

expenditures,

open economy

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

$    0

50

100

150

200

250

300

350

400

450

500

 

$  50

90

130

170

210

250

290

330

370

410

450

 

$30

30

30

30

30

30

30

30

30

30

30

 

$10

10

10

10

10

10

10

10

10

10

10

 

$90

130

170

210

250

290

330

370

410

450

490

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(b)  If Ig decreases from $30 to $10, the new equilibrium GDP will be at GDP of $350, for with Ig now $10 this is where AE also equals $350.  This indicates that the multiplier equals 5, for a decline in AE of $20 has led to a decline in equilibrium GDP of $100.  The size of the multiplier could also have been calculated directly from the MPC of 0.8.

10-15    Answer the following questions, which relate to the aggregate expenditures model.

            a.   If Ca is $100, Ig is $50, Xn is -$10, and G is $30, what is the economy’s equilibrium GDP?

            b.   If real GDP in an economy is currently $200, Ca is $100, Ig is $50, Xn is -$10, and G is $30,      will the economy’s real GDP rise, fall, or stay the same?

            c.   Suppose that full-employment (and full-capacity) output in an economy is $200.  If Ca is          $150, Ig is $50, Xn is -$10, and G is $30, what will be the macroeconomic result?

            (a)  Assuming that there is no unplanned inventory investment at these expenditure levels,             equilibrium GDP is $170. (= Ca+Ig+Xn+G)

            (b)  If real GDP is $200, aggregate expenditures of $170 will result in positive unplanned   inventory investment.  GDP will fall as firms respond to the inventory build-up by reducing      output.

            (c)  Assuming that the economy is in equilibrium at these expenditure levels, real GDP is $170,      below the full employment level of output.  There is a recessionary gap, and employment           levels are lower than they would be at full employment.

10-16    (Last Word) What is Say’s law? How does it relate to the view held by classical economists that the economy generally will operate at a position on its production possibilities curve (Chapter 2).  Use production possibilities to demonstrate Keynes’s view on this matter.

  Say’s law states “supply creates its own demand.”   People work in order to earn income and       plan to spend the income on output – why else would they work?  Basically, the classical      economists would say that the economy will operate at full employment or on the production    possibilities curve because income earned will be recycled or spent on output.  Thus the spending     flow is continuously recycled in production and earning income.  If consumers don’t spend all    their income, it would be redirected via saving to investment spending on capital goods.

           The Keynesian perspective, on the other hand, suggests that society’s savings will not necessarily all be channeled into investment spending.  If this occurs, we have a situation in which aggregate demand is less than potential production.  Because producers cannot sell all of the output produced at a full employment level, they will reduce output and employment to meet the aggregate demand (consumption plus investment) and the equilibrium output will be at a point inside the production possibilities curve at less than full employment.