1. Income and Expenditure
SECOND CANADIAN EDITION
MACROECONOMICS Paul Krugman | Robin Wells
Iris Au | Jack Parkinson
Chapter 11
Income and Expenditure
© 2014 Worth Publishers

2. WHAT YOU WILL LEARN IN THIS CHAPTER
The “multiplier”, which shows how initial changes in spending lead to further changes.
The meaning of the aggregate consumption function, which shows how current disposable income affects consumer spending
How expected future income and aggregate wealth affect consumer spending
The determinants of investment spending, and the distinction between planned investment spending and unplanned inventory investment
How the inventory adjustment process moves the economy to a new equilibrium after a change in demand
Why investment spending is considered a leading indicator of the future state of the economy
WHAT YOU
WILL LEARN
IN THIS CHAPTER

3. The Multiplier: A First Look
(D - denotes change)
The marginal propensity to consume, or MPC, is the increase in consumer spending when disposable income rises by $1.
e.g. MPC=0.6 then $0.60 of each extra $1 of income is spent on consumer goods.
(disposable income? Income plus transfers minus taxes)

4. The Multiplier: a first look
Autonomous spending: spending on goods and services that does not depend on income.
The multiplier is concerned with how much output and income ultimately rise due to an increase in autonomous spending.
The ultimate rise is likely larger than the autonomous spending increase that set it off. Why?
The extra autonomous spending becomes someone’s income.
The increase in autonomous spending causes businesses to produce more, hire more workers, make more profits etc. So income increases.
This Extra income leads to additional increases in spending and income. - Businesses produce still more, incomes rise further, more spending etc.
This is the multiplier process.
Process builds on the relationship between output, income and spending (Ch.7)

5. The Multiplier Effect: an example
Say autonomous investment spending increases by $10 billion
First-round spending and incomes rise by $10 billion
+ Second-round increase in consumer spending =
MPC × $10 billion (income rose $10b in first round, MPC is share spent)
+ Third-round increase in consumer spending =
MPC2 × $10 billion (income rose by MPCx$10b in 2nd round so multiply by MPC)
+ Fourth-round increase in consumer spending =
MPC3 × $10 billion (income rose by MPC2x$10b in 3rd round so multiply by MPC)
etc. (process continues)
Total increase in real GDP = (1 + MPC + MPC2 + MPC )× $10 billion
i.e. sum of the rise in spending at each round.

6. The Multiplier: An example
So the $10 billion increase in investment spending sets off a chain reaction in the economy. The net result of this chain reaction is that a $10 billion increase in investment spending leads to a change in real GDP that is a multiple of the size of that initial change in spending.
How large is this multiple? Use result for a geometric series:
(1 + MPC + MPC2 + MPC ) = 1/(1-MPC) (if 0<MPC<1)
So: the Total Increase in real GDP from a $10 billion rise in investment:
$10 billion x 1 1−𝑀𝑃𝐶

7. Geometric Series (for those who want to know!)
Sum of a to exponent i: Sai = 1 + a +a2 + a3 + …+ aN Multiply by ‘a’ to get: aSai = a +a2 + a3 + …+ aN+1 Subtract the second expression from the first to get: (1-a)Sai = 1 - aN+1 Divide by (1-a): Sai = (1 - aN+1)/(1-a) If 0<a<1 (like our MPC) and N goes to infinity then aN+1→0 Then: Sai = 1 /(1-a) (this is the result we used with a=MPC)

8. The Multiplier: Numerical Example
Rounds of Increases of Real GDP when MPC = 0.6
Multiplier = 1/(1-MPC) = 1/(1-.6) = 2.5

9. The Multiplier: Numerical Example
In the end, real GDP rises by $25 billion as a consequence of the initial $10 billion rise in investment spending:
1/(1 − 0.6) × $10 billion = 2.5 × $110 billion = $25 billion
Multiplier = 1 1−𝑀𝑃𝐶 = 1 1−.6 = 2.5

10. The Multiplier
DAE0 is an autonomous change in aggregate spending. i.e. an initial change in the desired level of spending by firms, households, or government at a given level of real GDP.
DY = 1 1−𝑀𝑃𝐶 x DAE0
The multiplier is the ratio of the total change in real GDP caused by an autonomous change in aggregate spending (DY) to the size of that autonomous change (DAE0).
Multiplier = DY DAE0 = 1 1−𝑀𝑃𝐶

11. The Simple Multiplier: Underlying Assumptions
Assumptions underlying the version of the process above:
Producers are willing to supply extra output at a fixed price should demand increase.
Interest rate is assumed constant (unaffected by the change in income and output that is part of the process)
No government: no taxes, transfers or spending.
No imports or exports.
More complicated multiplier processes relax these assumptions but still build on the interdependence between spending, output and income.
(relaxing these assumptions will decrease the multiplier)

12. ECONOMICS IN ACTION The Multiplier and the Great Depression
The concept of the multiplier was originally devised by economists trying to understand the Great Depression.
Most economists believe that the slump from 1929 to 1933 was driven by a collapse in investment spending.
i.e. fall in investment spending was the autonomous spending change (about -$3.7 billion ).
But as the economy shrank, consumer spending also fell sharply, multiplying the effect on real GDP.
- Real GDP fell by -$5.1 billion suggesting a multiplier of about ($5.1 billion/$3.7 billion = DY/DAE0 )

13. Consumer Spending
The individual consumption function is an equation showing how an individual household’s consumer spending (c) varies with the household’s current disposable income (yd).
c= ac + MPC∙ yd
Where: ac=autonomous consumption spending.
MPC = marginal propensity to consume (as before)

14. The Consumption Function
Figure Caption: Figure 11(26)-2: The Individual Consumption Function
The consumption function relates a household’s current disposable income to its consumer spending. The vertical intercept, ac, is individual household autonomous spending: the amount of a household’s consumer spending if its current disposable income is zero. The slope of the consumption function line, cf, is the marginal propensity to consume, or MPC; that is, for every additional $1 of current disposable income, MPC × $1 is spent.

15. The Consumption Function
Deriving the slope of the consumption function

16. Disposable Income and Consumer Spending in 2010
Figure Caption: Figure 11(26)-1: Current Disposable Income and Consumer Spending for Canadian Households in 2010
For each income groups of households, average current disposable income in 2010 is plotted versus average consumer spending in For example, the middle income group is represented by point A, indicating a household average current disposable income of $ and average household consumer spending of $ The data clearly show a positive relationship between current disposable income and consumer spending: families with higher current disposable income have higher consumer spending.
Source: Statistics Canada. 16

17. A Consumption Function fitted to the data
Figure Caption: Figure 11(26)-3: A Consumption Function Fitted to Data
The data from Figure 11(26)-1 are reproduced here, along with a line drawn to fit the date as closely as possible. For Canadian households in 2010, the best estimate of the average household’s autonomous consumer spending, ac, is $ and the best estimate of the marginal propensity to consumer, or MPC, is about 0.50.
Source: Statistics Canada. 17

18. Aggregate Consumption Function
The aggregate consumption function is the relationship for the economy as a whole between aggregate current disposable income and aggregate consumer spending.
Aggregate: sums over individuals.
Text assumes it is linear (doesn’t have to be):
C = ac + MPC ∙yd
C = total or aggregate consumer spending
ac = autonomous consumer spending (aggregate)
yd = total disposable income (across all individuals)
MPC = marginal propensity to consume (between 0 and 1)

19. Shifts in the Aggregate Consumption Function
The aggregate consumption function shifts up or down as autonomous consumption spending changes.
What might cause autonomous C to change?
Changes in expected future disposable income
say it rises: might save less now or borrow against extra future income -- so current C rises!
say it falls: might save more now (or borrow less) in order to have more funds in the future – so current C falls!
Changes in aggregate wealth
Value of assets (houses, financial assets). More wealth, more financial resources to fund C.
Changes in interest rates: affects incentive to save rather than consume. e.g. higher interest rate, save more, consume less.

20. Consumption Function Shift e. g due to a rise in wealth, a fall in
Consumption Function Shift e.g due to a rise in wealth, a fall in interest rates, or a rise in expected future income
Figure Caption: Figure 11(26)-4 (a): An Upwards Shift of the Aggregate Consumption Function
Panel (a) illustrates the effect of an increase in expected aggregate future disposable income. Consumers will spend more at every given level of aggregate current disposable income, YD. As a result, the initial aggregate consumption function CF1, with aggregate autonomous spending AC1, shifts up to a new position at CF2 and aggregate autonomous spending AC2. An increase in aggregate wealth will also shift the aggregate consumption function up.

21. Aggregate Consumption Function
Figure Caption: Figure 11(26)-4 (b): An Downward Shift of the Aggregate Consumption Function
Panel (b) illustrates the effect of a reduction in expected aggregate future disposable income. Consumers will spend less at every given level of aggregate current disposable income, YD. Consequently, the initial aggregate consumption function CF1, with aggregate autonomous spending AC1, shifts down to a new position at CF2 and aggregate autonomous spending AC2. A reduction in aggregate wealth will have the same effect.

22. Aggregate Consumption Function

23. Investment Spending (I)
Planned investment spending is the investment spending that businesses plan to undertake during a given period.
What determines I?
interest rates: negative effect on Investment spending
Cost of borrowing to finance investment spending;
Opportunity cost of a business using its own profits for investment spending.
expected future real GDP: positive effect on I.
Higher future GDP means more demand for goods and services, businesses expand to meet this demand. (this and perceived future business opportunities in Ch. 10)
current production capacity: negative effect on I.
If lots of extra capacity to produce output, less likely to need to expand to meet future demand.
demand for Loanable funds (Ch. 10) suggested government policy
tax incentives aimed at investment.

24. Investment Spending
According to the accelerator principle, a higher rate of growth in real GDP leads to higher planned investment spending to meet the extra demand for goods.
According to the accelerator principle, a lower growth rate of real GDP leads to lower planned investment spending (less capacity is needed)
Investment spending is more volatile than consumption spending.
Plays an important role in recessions, recoveries and booms.
Is it volatile because it depends on expectations?
Investment spending is autonomous in this model (doesn’t depend on current GDP).

25. Investment Spending in recessions
Figure Caption: Figure 11(26)-6: Fluctuations in Real GDP, Investment Spending, and Consumer Spending
These bars illustrate annual percent change in real GDP, investment spending, and consumer spending during three recessions. As the lengths of the bars show, swings in investment spending were much larger in percentage terms than those in consumer spending and real GDP. This pattern has led economists to believe that recessions typically originate as a slump in investment spending.
Source: Statistics Canada.

26. Inventories and Unplanned Investment Spending
Inventories are stocks of goods held to satisfy future sales.
Inventory investment is the value of the change in total inventories held in the economy during a given period.
Unplanned inventory investment occurs when actual sales are more or less than businesses expected, leading to unplanned changes in inventories.

27. Inventories and Unplanned Investment Spending
Actual investment spending is the sum of planned investment spending and unplanned inventory investment.

28. ECONOMICS IN ACTION Interest Rates and the Canadian Housing Market
In the early 2000s, the Bank of Canada reduced interest rates to deal with various causes of economic uncertainty in the marketplace, such as the events of 9/11 and an information technology stock price bubble.
The low interest rates led to a large increase in residential investment spending, reflected in a surge of housing starts.
Unfortunately, the housing boom eventually turned into too much of a good thing.

29. ECONOMICS IN ACTION Interest Rates and the Canadian Housing Market
Between late 2008 and early 2009, interest rates fell and housing starts also fell. Why? Interest rates aren’t the only variable determining investment!
These were the years of the Great Recession, when many had lost their jobs. The Bank of Canada deliberately kept interest rates low to stimulate the sluggish economy, but people were still hesitant to buy homes.

30. ECONOMICS IN ACTION Interest Rates and the Canadian Housing Market
Figure Caption: Figure 11(26)-7: Mortgage Interest Rates Compared to Housing Starts in Canada
When interest rates decrease, housing starts tend to rise, except in extraordinary circumstances, such as a depression or a recession.
Source: Statistics Canada.

31. Income-Expenditure Model
Assumptions underlying the multiplier process:
Changes in overall spending lead to changes in aggregate output. The aggregate price level is fixed.
The interest rate is fixed.
Taxes, transfers, and government purchases are all zero.
Exports and imports are both zero. There is no foreign trade.

32. Planned Aggregate Spending and GDP
Planned aggregate spending is the total amount of planned spending in the economy.
AEPlanned = C + Iplanned
So: AEplanned= AC + MPC ∙ YD + Iplanned
Example: C= YD , Iplanned=500
so: AEplanned= ∙ YD = ∙GDP
GDP = C + I (G=X=IM=0)
YD = GDP (no taxes or transfer)
C = AC + MPC ∙ YD (consumption)

33. Planned Aggregate Spending and GDP
Figure Caption: Figure 11(26)-8: The Aggregate Consumption Function and Planned Aggregate Spending
The slope, or steepness of the line depends on the value of MPC. The greater MPC is, the steeper the line will. AE0 is the intercept on the vertical axis. The lower line, CF, is the aggregate consumption function constructed from the data in Table The upper line, AEPlanned, is the planned aggregated expenditure line, also constructed from the data in Table It is equivalent to the aggregate consumption function shifted up by $500 billion, the amount of planned investment spending, IPlanned. 33

34. Income–Expenditure Equilibrium
The economy is in income–expenditure equilibrium when aggregate output, measured by real GDP, is equal to planned aggregate spending.
Income–expenditure equilibrium GDP is the level of real GDP at which real GDP equals planned aggregate spending.

35. Income–Expenditure Equilibrium
Call Y* the equilibrium level of real GDP (where AEplanned=Y)
Diagram: occurs where AE intersects the 45-degree line.
Planned spending equals output, no unplanned changes in inventory, production stays at its current level.
When planned aggregate spending is larger than Y*, unplanned inventory investment is negative; there is an unanticipated reduction in inventories and firms increase production to rebuild inventories.
So when: AEplanned>Y then Iunplanned<0
When planned aggregate spending is less than Y*, unplanned inventory investment is positive; there is an unanticipated increase in inventories and firms reduce production to limit inventory build-up.
So when: AEplanned<Y then Iunplanned>0

36. Income–Expenditure Equilibrium
Figure Caption: Figure 11(26)-9: Income-Expenditure Equilibrium
Income–expenditure equilibrium occurs at E, the point where the planned aggregate spending line, AEPlanned , crosses the 45-degree line. At E, the economy produces real GDP of $2,000 billion per year, the only point at which real GDP equals planned aggregate spending, AEPlanned , and unplanned inventory investment, IUnplanned , is zero. This is the level of income-expenditure equilibrium GDP, Y*. At any level of GDP less than Y*, AEPlanned exceeds real GDP. As a result, unplanned inventory spending, IUnplanned , is negative and firms respond by increasing reduction. At any level of real GDP greater than Y*, GDP exceeds AEPlanned. Unplanned inventory investment, IUnplanned , is positive and firms respond by reducing production. 36

37. Algebra behind the previous diagram
AEplanned= A + MPC ∙YD (A = autonomous C and I) = ∙GDP (with no taxes or transfers YD=GDP) Equilibrium: AEplanned= GDP ∙GDP = GDP solve for GDP: GDP = 800/(1-.6) =2000 (=Y* in diagram) Notice: equilibrium GDP = autonomous spending x multiplier Multiplier = 1/(1-MPC) =1/(1-.6) =2.5

38. Effect of a Change in Autonomous spending
Say autonomous C rises or planned I rises by DA.
Now: AEplanned = A + MPC∙ GDP + DA
Diagram? AE shifts up by DA (DA =400 in diagram)
AEplanned >Y* (old equilibrium GDP)
inventories fall below planned levels, firms produce more, GDP is rising, incomes are higher, multiplier process underway!

39. Effect of a change in autonomous spending
Finding new equilibrium after rise in A?
Set AEplanned = GDP then solve for GDP:
A + MPC∙ GDP + DA = GDP
solving: GDP =(A+ DA) /(1-MPC)
= (A+ DA) x Multiplier
Effect? GDP is higher by: DA x Multiplier
Example: DA =400 and multiplier=2.5 so GDP is higher by 1000 (see diagram below: Y* rises by 1000)

40. The Multiplier Figure Caption: Figure 11(26)-10: The Multiplier
This figure illustrates the change in Y* caused by an autonomous increase in planned aggregate expenditure. The economy is initially at equilibrium point E1 with an income-expenditure equilibrium GDP, 𝑌 1 ∗ , equal to An autonomous increase in AEPlanned of 400 shifts the planned aggregate expenditure line upward by 400. The economy is no longer in income-expenditure equilibrium: real GDP is equal to 2000 but AEPlanned is now 2400, represented by point X. The vertical distance between the two planned aggregate expenditure lines, equal to 400, represents IUnplanned = -400–the negative inventory investment that the economy now experiences. Firms respond by increasing production, and the economy eventually reaches a new income-expenditure equilibrium at E2 with a higher level of income-expenditure equilibrium GDP, 𝑌 2 ∗ , equal to 3000. 40

41. The Multiplier Process and Inventory Adjustment

42. The Paradox of Thrift
In the paradox of thrift, households and producers cut their spending in anticipation of future tough economic times.
Like a fall in autonomous spending.
GDP falls immediately and still more via the multiplier effect.
These actions depress the economy, leaving households and producers worse off than if they hadn’t acted virtuously to prepare for tough times.
It is called a paradox because what’s usually “good” (saving to provide for your family in hard times) is “bad” (because it can make everyone worse off).

43. ECONOMICS IN ACTION Inventories and the End of a Recession
Figure Caption: Figure 11(26)-11: Inventories and the End of a Recession
This figure shows quarterly changes in real GDP, real consumer spending, and real inventories from the fourth quarter of 2008 to the third quarter of In the last quarter of 2008, the fall in inventories exceeded the drop in real GDP (the driving force behind the recession). Consumer spending began to increase om the second quarter of 2009, but it was not until the first quarter of 2010 that GDP began to rise. It took two quarters of positive change in consumer spending before firms became willing to ramp up production. 43

44. Summary
An autonomous change in aggregate spending leads to a chain reaction in which the total change in real GDP is equal to the multiplier times the initial change in aggregate spending. The size of the multiplier, 1/(1 − MPC), depends on the marginal propensity to consume, MPC, the fraction of an additional dollar of disposable income spent on consumption.
The individual consumption function shows how an individual household’s consumer spending is determined by its current disposable income. The aggregate consumption function shows the relationship for the entire economy.

45. Summary
Planned investment spending depends negatively on the interest rate and on existing production capacity; it depends positively on expected future real GDP. The accelerator principle says that investment spending is greatly influenced by the expected growth rate of real GDP.

46. Summary
Firms hold inventories of goods so that they can satisfy consumer demand quickly. Inventory investment is positive when firms add to their inventories, negative when they reduce them. Often, however, changes in inventories are not a deliberate decision but the result of mistakes in forecasts about sales. The result is unplanned inventory investment, which can be either positive or negative. Actual investment spending is the sum of planned investment spending and unplanned inventory investment.

47. Summary
In income–expenditure equilibrium, planned aggregate spending, which in a simplified model with no government and no trade is the sum of consumer spending and planned investment spending, is equal to real GDP. At the income–expenditure equilibrium GDP, or Y*, unplanned inventory investment is zero. The Keynesian cross shows how the economy self-adjusts to income–expenditure equilibrium through inventory adjustments.

48. Summary
After an autonomous change in planned aggregate spending, the inventory adjustment process moves the economy to a new income–expenditure equilibrium. The change in income–expenditure equilibrium GDP arising from an autonomous change in spending is equal to [1/(1 − MPC)] ×∆AE0.

49. Key Terms Marginal propensity to consume (MPC) Accelerator principle
Inventory investment
Marginal propensity to save (MPS)
Unplanned inventory investment
Autonomous change in aggregate spending
Actual investment spending
Planned aggregate expenditure
Multiplier
Individual consumption function
Income–expenditure equilibrium
Aggregate consumption function
Income–expenditure equilibrium GDP
Planned investment spending
Keynesian cross