Chapter 27: Basic Macro. Relationships
We begin this chapter by examining the relationship between 3 different
pairs of economic aggregates which include;
• Income and consumption and income and saving relationship
• Interest rate and investment relationship
• Changes in spending and changes in output relationship
Income/Consumption & Saving Relationship
The relationship between income and consumption is one of the best
established relationships in macroeconomics. In examining that
relationship, we are also exploring the income- saving relationship.
Remember that DI = C + S from chapter 24 so rearranging the terms we get
S = DI – C.
As (DI) increases consumption increases, or in other words, as we make
more money we tend to spend more. Savings also increases as income
increases.
At breakeven C=DI, S=0
Consumption
45%
%
saving
C
390
Breakeven pt.
dissaving
0
390
DI=GDP
The consumption(C) line shows how much households are planning to
spend at each level of income. The 45° line is a reference line. Because it
bisects the 90° angle formed by the 2 axes of the graph, each point on it is
equidistant from both axes. At each point on the 45° line, consumption
would equal DI, or C = DI. Therefore, the vertical distance between the 45°
line and any point on the horizontal axis measures either consumption or
DI.
If we let it measure (DI), the vertical distance between it and the
consumption line labeled (C) represents the amount of saving (S) in that
year. Saving is the amount by which actual consumption in any year falls
short of the 45° line, S = DI – C.
Observe that the vertical distance between the 45° line and line (C)
increases as we move rightward along the horizontal axis and decreases as
we move leftward. Like consumption, saving varies directly with the level of
DI.
(1)
(2)
(3)
(4)
(5)
(6)
(7)
GDP=DI
Cons.
Saving
APC
APS
MPC
MPS
1−2
2∕ 1
3∕ 1
∆2∕ ∆1
∆3∕ ∆1
$370
$375
$−5
1.01
−.01
$390
$390
$0
1.00
.00
$410
$405
$5
.99
.01
$430
$420
$10
.98
.02
$450
$435
$15
.97
.03
$470
$450
$20
.96
.04
Notice the data verifies the direct relationship between consumption(C)
and (DI). Households increase their spending as their (DI) rises and they
spend a larger proportion/fraction of a small (DI) than of a large (DI).
Because saving equals (DI) less (C), we need only subtract (C) from (DI) to
find the amount saved at each level of (DI). So col. 1 minus col. 2 equals col.
3. We see that savings is also directly related to (DI) but that saving is a
smaller proportion of a small (DI) than of a large (DI). If households
consume a smaller and smaller proportion/fraction of (DI) as (DI) increases,
then they must be saving a larger and larger proportion/fraction.
Remembering that at each point on the 45° line C = DI, we see that
dissaving , consuming in excess of (DI) will occur at relatively low (DI)’s.
Households can consume more than their current incomes by liquidating
some of their wealth or by borrowing. Graphically, dissaving is shown as the
vertical distance of the consumption schedule above the 45° line.
The break-even income is $390 billion. This is the income level at which
households plan to spend their entire (DI), or where (C) = (DI) and (S) =0.
Graphically, the consumption schedule cuts/crosses the 45° line at the
break-even income level. At all levels of (DI) above $390 households will
plan to save part of their (DI)’s.
APC and APS (column 4 &5 above)
The fraction or percentage of total income that is consumed is the average
propensity to consume (APC), (APC = consumption ÷ Income).
The fraction of total income that is saved is the average propensity to save
(APS), (APS = saving ÷ Income).
The APC falls as (DI) increases, while the (APS) rises as (DI) goes up. Because
(DI) is either consumed or saved, the fraction of any (DI) consumed plus the
fraction saved must exhaust that income. Mathematically, APC + APS = 1 at
any level of DI.
MPC and MPS(column 6 &7 above)
The fact that households consume a certain proportion/fraction of a given
total income does not guarantee they will consume the same
proportion/fraction of any change in incomes they might receive.
The proportion, or fraction, of any change in income consumed is called the
marginal propensity to consume (MPC), (MPC = ∆C∕ ∆DI). Marginal means
additional or extra.
The fraction of any change in income saved is the marginal propensity to
save (MPS), (MPS = ∆S∕ ∆DI).
See columns 6 and 7 above and use the formulas just given to fill in the
blanks. Notice the MPC and the MPS are constant and that the
MPC + MPS = 1.
The (MPC) is the numerical value of the slope of the consumption schedule
and the slope of any line is the ratio of the vertical change to the horizontal
change, or rise over run.
Consumption
MPC=15/20=.75
C= MPC
Change C($15)
Change DI($20)
Change DI($20)
0
DI=GDP
Non-income Determinants
Certain determinants other than income might prompt households to
consume more or less at each level of (DI) and thereby change the location
of the consumption and saving schedules. Here we are releasing our other
things equal assumption, or ceteris paribus.
1. Wealth- A household’s wealth is the dollar amount of all the assets
that it owns minus the dollar amounts of its liabilities that it owes.
Households build wealth by saving money out of current income. The
larger the stock of wealth a household can build up, the larger will be
its present and future consumption possibilities.
Example- When the value of your home increases or stock market prices
rise, increasing your 401K retirement plan, households are now willing to
spend more out of their current income. The result is an upward shift in the
consumption schedule.
2. Borrowing- When a household borrows, it can increase current
consumption beyond what would be possible if its spending were
limited to its (DI). By allowing households to spend more, borrowing
shifts the current consumption schedule upward. But note there is no
free lunch. While borrowing in the present allows for higher
consumption in the present, it necessitates lower consumption in the
future when the debts that are incurred due to the borrowing must be
repaid.
3. Expectations- Household expectations about future prices and income
may affect current spending and saving. The expectation of higher
prices tomorrow may cause more spending today while prices are still
low so the consumption schedule shifts up and the saving schedule
shifts down. An expectation of a coming recession, which would lower
incomes, might lead households to reduce consumption and save
more today. Their increased current saving will help build wealth that
will help them ride out the expected bad times ahead.
4. Real Interest Rates- When real interest rates, those adjusted for
inflation fall, households tend to borrow more, consume more, and
save less. The lower interest rate causes consumers to purchase more
cars and other items on credit and the consumption schedule will shift
upward.
5. Taxes- a decrease in taxes will increase after tax (DI) and therefore
both (C) and (S) will increase. An increase in taxes will do the opposite.
C1
C
C
C1
Other Considerations
 The movement from one point to another point along the
consumption schedule is called a change in the amount consumed
and is solely caused by a change in (DI) or real GDP.
 On the other hand, an upward or downward shift in the entire
schedule is caused by changes in any one or more of the non-income
determinants of consumption just discussed.
 Changes in wealth, expectations, real interest rates, and household
debt will shift the consumption schedule in one direction and the
saving schedule in the opposite direction.
 In contrast, a change in taxes shifts the consumption and saving
schedule in the same direction. Higher taxes reduce both
consumption and saving, shifting both schedules downward.
Interest Rate/ Investment Relationship
Recall that investment consists of spending on new plants, capital
equipment, machinery and additions to inventory. The marginal benefit
from investment is the expected rate of return businesses hope to realize.
The marginal cost of the investment is the interest rate that must be paid
for borrowing the money.
1. Expected rate of return or net profit- Investment spending is guided by
the profit motive. Suppose a business purchases a new sanding machine
that costs $1000. The new machine will increase the firm’s output and
sales revenue. Let’s say the net expected revenue, after operating costs and
taxes are deducted, is $1100. Subtracting the $1000 cost from the net
revenue of $1100, we get an expected profit of $100. Dividing the $100
profit by the $1000 cost of the machine, gives us the expected rate of
return (r) on the machine which is 10%. Note that this is an expected rate of
return, not a guaranteed rate of return.
$100∕ $1000 = 10% expected rate of return
2. The real interest rate- The interest rate is the financial cost of borrowing
the $1000 to purchase the sanding machine. The interest cost of the
investment is computed by multiplying the interest rate (i) by the $1000
borrowed to buy the machine. If the interest rate is 7%, then the interest
cost is $70. This compares favorably with the net expected return of $100,
which produced the 10% expected rate of return.
Key Point: The firm should invest to the point for which r=I, because then it
will have undertaken all investments for which r>i. The real interest rate,
rather than the nominal rate, is crucial in making investment decisions.
Real interest rate = nominal interest rate – expected inflation
Ex. $1000 sanding machine w/ 10% expected rate of return
Nominal interest rate = 15%
Inflation rate = 10%
What is the real interest rate? (5%)
Investment Demand Curve
We now move from a single firm’s investment decision to the total demand
for investment goods by the entire business sector. Every firm has
estimated the expected rates of return from all the possible projects and
has recorded the data in the table and graph below.
Real interest rate
& expected ROR
16%
14%
12%
10%
8%
6%
4%
2%
0%
Cumulative amount of investment having
this rate of return or higher
$0
$5
$10
$15
$20
$25
$30
$35
$40
We can cumulate these data by asking: How many projects have an
expected rate of return of say 16% or more? The answer is zero. Next, how
many projects have an expected rate of return of 14% or more? The answer
if $5 billion, and so on.
r=i
The real interest rate is
inversely related to the amount
of investment.
16%
14%
12%
10%
Investment demand curve
8%
6%
4%
2%
Id
0
5
10
15
20
25
30
35
40
Investment
As you can see there is an inverse relationship between the real interest
rate and the quantity of investment demanded as shown on the horizontal
axis. The level of investment then depends on the expected rate of return
and the real interest rate. The graph above shows the relationship between
the interest rate and the amount of investment demanded, other things
equal.
Shifts in the Investment demand Curve
When factors other than interest rates change, the investment demand
curve shifts. In general, any factor that leads businesses collectively to
expect greater rates of return will increase the investment demand curve
shifting it rightward. Anything that leads businesses to expect lower rates
of return will decrease the investment demand curve.
r=i
Id2
Ido
Id1
Investment
1. Acquisition, maintenance, and operating costs- The initial costs of
capital goods, and the estimated costs of operating and maintaining
those goods, affect the expected rate of return. If these costs rise,
the expected rate of return will fall and the investment demand
curve shifts left. Lower costs will have the opposite effect.
2. Business taxes- Firm’s look at expected rates of return after taxes
have been taken out. Lower taxes will increase the investment
demand curve, whereas higher taxes will decrease the investment
demand curve.
3. Technological change- The development of new products,
improvements in existing products, and the creation of new
machinery and production processes will stimulate investment. A
more efficient machine, for example, will lower production costs and
increase the expected rate of return. The investment demand curve
will shift to the right.
4. Stock of capital goods on hand- When the economy is overstocked
with production facilities and when firms have excessive inventories
of finished goods, the expected rate of return on new investment
declines. The resulting investment demand curve shifts leftward.
5. Planned inventory changes- Our definition of investment includes
changes in inventories of unsold goods. If firms are planning to
increase their inventories, the investment demand curve shifts to the
right. If firms are planning on decreasing their inventories, the
investment demand curve shifts to the left. Firms make planned
changes to their inventory levels mostly because they are expecting
either faster or slower sales.
6. Expectations- Expected rates of return depends on a firm’s
expectations of future sales, future operating costs, and future
profitability of the products that the capital helps produce. It
essentially boils down to how optimistic or pessimistic businesses are
about the future.
Instability of Investment
In contrast to consumption, investment is unstable; it rises and falls quite
often. Investment, in fact, is the most volatile component of total spending.
The Multiplier Effect
A final basic relationship that requires discussion is the relationship
between changes in spending and changes in real GDP. More spending
results in a higher GDP and less spending results in a lower GDP. However,
a change in a component of total spending leads to a larger change in GDP.
The multiplier will determine how much larger that change will be.
• Multiplier = change in real GDP ÷ initial change in spending
• Change in GDP = multiplier × initial change in spending
3 Things About the Multiplier
 The initial change in spending is usually associated with investment
spending, but change in consumption, government, or net export
spending also lead to a multiplier effect.
 The initial change in spending associated with investment spending
results from a change in the real interest rate and/or a shift of the
investment demand curve.
 The multiplier works in both directions.
Rationale for the Multiplier
The multiplier effect follows from 2 facts. First, remember the circular flow
model tells us that one person’s spending is another person’s income.
Second, any change in income will change both consumption(C) and
saving(S) in the same direction as, and by a fraction of, the change in
income (DI). It follows that an initial change in spending will set off a
spending chain throughout the economy.
(2)
(3)
(1)
Change in
Change in
Change in Consumption Saving
Income
(MPC = .75) (MPS = .25)
Increase in investment of
$5.00
$5.00
Second round
3.75
Third round
2.81
Fourth round
2.11
Fifth round
1.58
All other rounds
4.75
Total
$20.00
$3.75
$1.25
2.81
2.11
1.58
1.19
3.56
$15.00
.94
.70
.53
.39
1.19
$5.00
The fractions of an increase in income consumed (MPC) and saved (MPS)
determine the cumulative re-spending effects of any initial change in
spending and therefore determine the size of the multiplier.
Key Point: The (MPC) and the multiplier are directly related and the (MPS)
and the multiplier are inversely related. The larger the (MPC) the larger the
multiplier, or the smaller the (MPS) the larger the multiplier.
Multiplier = 1∕ 1−MPC
Multiplier = 1∕ MPS
There is also a tax multiplier which is always 1 less than the spending
multiplier and negative. If the spending multiplier is 4, then the tax
multiplier would be − 3.
We can use our Aggregate Expenditures model to illustrate how a small
change in spending produces a larger change in real GDP. (AE) represents
all spending that makes up GDP including C + Ig + G + Xn.
Consumption/AE
45
C+I+G
G=+$5
C+I
C
I=+$20
225
0
300
?
?
DI=GDP
If we increase (Ig) by $20, how much will real GDP increase?
If we increase (G) by another $5, how much will real GDP increase?
If we cut taxes by $10, how much will real GDP increase?
Some Practice with the Multiplier
Given the following MPC’s, what is the multiplier?
 .20
.50
.67
.75
.80
.90
Given a $20 increase in spending and the following increases in GDP, what
is the multiplier and the MPC?
 $200
$80
$60
$40
$25
$0