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### 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.

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 averagepropensity 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.

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.

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.

- 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%)

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 Cumulative amount of investment having

& expected ROR this rate of return or higher

16% $0

14% $5

12% $10

10% $15

8% $20

6% $25

4% $30

2% $35

0% $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.

The real interest rate is inversely related to the amount of investment.

16%

14%

12%

Investment demand curve

10%

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.

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.

In contrast to consumption, investment is unstable; it rises and falls quite often. Investment, in fact, is the most volatile component of total spending.

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

- 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.

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.

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.

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

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