Chapter 10: Basic Macroeconomic Relationships

ECO 112 Principles of Macroeconomics

Today’s Roadmap

Key Concepts

The consumption and saving schedules, and how they relate to disposable income
The average propensity to consume (APC) and average propensity to save (APS)
The marginal propensity to consume (MPC) and marginal propensity to save (MPS)
Non-income factors that shift the consumption and saving schedules: wealth, borrowing, expectations, and real interest rates
The investment demand curve: how the real interest rate determines which investment projects get undertaken
Non-interest factors that shift the investment demand curve
Why investment spending swings much more sharply than consumption spending over the business cycle
The multiplier effect: how an initial change in spending leads to a larger change in real GDP

Consumption and Saving

Connecting Back: Chapter 6 and Disposable Income

Chapter 6 introduced the market for loanable funds, where households’ saving supplies the funds that businesses borrow to invest. This chapter opens up that saving decision.

Households receive disposable income (DI): income after taxes, the amount actually available to spend or save.
Every dollar of DI is either spent (consumption) or set aside (saving). There is no third option.

\[ DI = C + S \]

where $C$ is consumption and $S$ is saving.

The Consumption and Saving Schedules

The consumption schedule shows the amount households plan to spend at each level of disposable income. The saving schedule shows the amount households plan to save at each level of disposable income.

Both schedules are positively related to DI: as DI rises, both C and S rise.
Because $C + S = DI$ always, the two schedules are really two sides of the same coin.

Plotting the Schedules

Average Propensity to Consume and Save

\[ APC = \frac{C}{DI} \qquad APS = \frac{S}{DI} \]

Average propensity to consume (APC): the fraction of a given level of DI that is spent.
Average propensity to save (APS): the fraction of a given level of DI that is saved.

Since every dollar of DI is either spent or saved:

\[ APC + APS = 1 \]

Marginal Propensity to Consume and Save

\[ MPC = \frac{\Delta C}{\Delta DI} \qquad MPS = \frac{\Delta S}{\Delta DI} \]

Marginal propensity to consume (MPC): the fraction of an additional dollar of DI that goes to consumption.
Marginal propensity to save (MPS): the fraction of an additional dollar of DI that goes to saving.

Since any additional dollar of DI is also split between spending and saving:

\[ MPC + MPS = 1 \text{ always} \]

APC and MPC are different ideas: APC describes an entire level of income, MPC describes what happens to the next dollar.

Example: Computing MPC and MPS

Jordan’s disposable income was $40,000 last year, and Jordan consumed $37,000 of it. This year, after a raise, Jordan’s disposable income rose to $46,000, and consumption rose to $41,800.

What is the change in disposable income? The change in consumption?
What is Jordan’s MPC?
What is Jordan’s MPS?
Of the $6,000 raise, how many dollars went to additional saving?

Solution: Computing MPC and MPS

$\Delta DI = 46{,}000 - 40{,}000 = \$6{,}000$
$\Delta C = 41{,}800 - 37{,}000 = \$4{,}800$

$MPC = 4{,}800 / 6{,}000 = 0.8$
$MPS = 1 - 0.8 = 0.2$

Additional saving: $6{,}000 \times 0.2 = \$1{,}200$ (check: $\Delta C + \Delta S = 4{,}800 + 1{,}200 = 6{,}000$)

Consumption and Saving Rise Over Time

In the United States, both total consumption and total saving have grown substantially over past decades. This is mostly illustrative of a simple point rather than a specific statistic to memorize:

As real disposable income rises over time, both C and S rise along with it, exactly as the schedules predict.
A rising level of income, not a change in spending habits, explains most of that long-run growth in both C and S.

Real Data: Consumption Spending

Series PCEC

Does this series ever fall for a sustained period?

Answer: rarely and only briefly, since consumption is relatively stable compared to other spending categories, this chapter’s later section explains why.

What would you expect to happen to this line during a period when disposable income falls sharply?

Answer: the line should flatten or dip slightly, since the consumption schedule says C moves with DI, but consumption tends to fall by less than income does.

Is this chart showing the consumption schedule, or something else?

Answer: something else, this is total consumption spending over time, not consumption plotted against different levels of DI in the same period.

Non-Income Determinants of Consumption and Saving

Movements Along vs. Shifts of the Schedule

A change in disposable income itself causes a movement along the consumption and saving schedules, sliding to a different point on the same line.

Several other factors cause the entire schedule to shift, up or down, at every level of DI:

Wealth
Borrowing and debt
Expectations about future prices or income
Real interest rates

Keep these separate: a change in DI moves you along the line; a change in one of these factors moves the whole line.

Wealth and the Wealth Effect

The wealth effect is the tendency for households to consume more, at any given level of DI, when the value of what they own rises.

A booming stock market or rising home values makes households feel richer, even before they sell anything.
Feeling richer, households spend more and save less out of a given paycheck: the consumption schedule shifts up, the saving schedule shifts down.
The reverse happens when wealth falls, for example after a stock market decline.

Borrowing, Expectations, and Real Interest Rates

Borrowing and debt: easier access to credit cards, auto loans, or other credit lets households consume more than their current DI, shifting the consumption schedule up (and the saving schedule down).
Expectations: expecting prices to rise soon, or expecting higher income next year, tends to encourage spending now, shifting consumption up. Expecting a recession or job loss tends to do the opposite.
Real interest rates: recall the market for loanable funds from Chapter 6. A higher real interest rate rewards saving more generously, shifting the saving schedule up and the consumption schedule down. A lower real rate does the reverse.

Example: Movement or Shift?

For each scenario, decide whether it causes a movement along the consumption schedule or a shift of the whole schedule. If it is a shift, state the direction (up or down for consumption).

A worker receives a raise, increasing disposable income.
Home values in a household’s neighborhood jump 20 percent.
Real interest rates rise sharply as the Fed tightens policy.
Credit card companies lower borrowing standards, making credit easier to get.
Consumers hear a credible forecast that a recession is coming next year.

Movement along the schedule (DI itself changed).

Shift up (consumption): rising wealth triggers the wealth effect.

Shift down (consumption) and up (saving): a higher real interest rate rewards saving.

Shift up (consumption): easier borrowing lets households spend more at any given DI.

Shift down (consumption): expecting bad times ahead tends to encourage more precautionary saving now.

The Investment Demand Curve

From Saving to Investment

Chapter 6’s loanable funds market showed that household saving supplies the funds businesses borrow to invest. This section looks at the demand side: how businesses decide how much to invest.

Investment is spending on capital goods: machinery, equipment, factories, and buildings.
A firm undertakes an investment project only if it expects the project to be profitable.

Expected Rate of Return

Every potential investment project has an expected rate of return: the annual profit the project is expected to generate, as a percent of the project’s cost.

A firm compares a project’s expected rate of return to the real interest rate it must pay to borrow the funds.
Rule: undertake the project if its expected rate of return exceeds the real interest rate. Skip it if the expected return is below the real interest rate.

This is the same real interest rate from the loanable funds market in Chapter 6, now used from the borrower’s side.

The Investment Demand Curve

The investment demand curve shows an inverse relationship between the real interest rate and the quantity of investment demanded.

As the real interest rate falls, more projects clear the profitability bar, so the quantity of investment demanded rises.
Shaped like an ordinary demand curve, but on the horizontal axis is investment spending, not a single good.

Example: Which Projects Get Undertaken?

A firm is considering four possible investment projects, each with a different expected rate of return. The real interest rate in the loanable funds market is currently 6 percent.

Project	Expected rate of return
A	9%
B	7%
C	5%
D	3%

Which projects should the firm undertake?
If the real interest rate fell to 4 percent instead, which projects would then be undertaken?

Solution: Which Projects Get Undertaken?

At a 6% real rate: A (9%) and B (7%) are undertaken, their returns exceed the cost of borrowing. C (5%) and D (3%) are skipped.

If the real rate fell to 4%: A, B, and C all clear the bar, only D (3%) is skipped.
A lower real interest rate always weakly increases the quantity of investment undertaken.

Non-Interest Determinants of Investment Demand

A change in the real interest rate causes a movement along the investment demand curve. Several other factors shift the entire curve:

Cost of acquiring, operating, and maintaining capital: more expensive equipment or higher upkeep costs lower expected returns, shifting the curve left.
Business taxes: higher taxes on business profits reduce the after-tax return on a project, shifting the curve left.
Technological change: new, more productive technology raises expected returns, shifting the curve right.
Stock of capital goods on hand: if firms already have plenty of idle capacity, new investment looks less attractive, shifting the curve left.
Expectations about future business conditions: optimism about future sales shifts the curve right; pessimism shifts it left.

Real Data: Investment Spending

Series GPDI

Compare the shape of this line to the PCEC chart from earlier. Which looks bumpier?

Answer: investment (GPDI) is visibly bumpier, with sharper drops around recessions, while consumption (PCEC) looks much smoother.

What would falling business confidence about the future do to this series, according to the investment demand curve?

Answer: it would shift investment demand left at every real interest rate, so total investment spending would tend to fall.

During a recession, would you expect this series to fall by more or less than GDP overall?

Answer: usually by more, investment is one of the most volatile components of GDP, which the next section explains.

Why Investment Is Unstable

Investment Swings More Than Consumption

Over the business cycle, investment spending fluctuates much more sharply than consumption spending. Several reasons why:

Durability: capital goods are durable (Chapter 9), so a firm can postpone replacing worn-out equipment during a downturn, exactly like a household postponing a new car.
Uneven innovation: new technologies and business ideas do not arrive at a steady pace, so waves of investment cluster around major innovations.
Variable profits: profits, the fuel for investment, swing more sharply than income over the business cycle.
Volatile expectations: expectations about future business conditions can shift quickly and are inherently uncertain, unlike the fairly steady habits behind everyday consumption.

Illustrating the Volatility Gap

Illustrative pattern only, not real historical data. Notice the blue consumption line stays close to a smooth upward path, while the orange investment line swings sharply up and down around the same general trend.

Connecting to the Business Cycle

This volatility is a big part of why recessions hit some sectors so much harder than others (Chapter 9).

When a recession begins, firms cut back investment spending fast, postponing projects and reducing purchases of new capital.
Consumption spending, especially on nondurable goods and services, holds up much better because households cannot easily cut back on groceries, utilities, or health care.
Investment’s instability is one reason it is often described as the most closely watched, and most forecasted, component of GDP.

The Multiplier Effect

One Person’s Spending Is Another’s Income

An initial change in spending does not stop with the first transaction. Recall from Chapter 6 that spending in the economy becomes income for someone else.

Suppose a business increases its investment spending by hiring a construction firm.
The construction firm’s workers and owners now have additional income.
They spend part of that additional income (according to their MPC), which becomes income for the businesses and workers they buy from, and so on.

This chain reaction means the total change in real GDP ends up being a multiple of the initial change in spending. This is the multiplier effect.

The Simple Multiplier

\[ \text{Multiplier} = \frac{1}{MPS} \]

\[ \Delta \text{Real GDP} = \text{Multiplier} \times \Delta \text{Initial spending} \]

The multiplier tells us how many total dollars of GDP result from one dollar of new spending, once all the rounds of re-spending are added up.
This section introduces the multiplier conceptually. Chapter 11 builds the full model where the multiplier and the consumption schedule together determine equilibrium real GDP.

Example: The Multiplier in Action

A local government increases spending on road repair by $1,000. The MPS in this economy is 0.25 (so the MPC is 0.75).

What is the multiplier?
What is the total change in real GDP once the full chain of re-spending plays out?
Show the first four rounds of the spending chain: the initial $1,000, then each successive round of re-spending.

Solution: The Multiplier in Action

Multiplier: $1 / 0.25 = 4$
Total change in real GDP: $1{,}000 \times 4 = \$4{,}000$

Round 1: $1{,}000$
Round 2: $1{,}000 \times 0.75 = 750$
Round 3: $750 \times 0.75 = 562.50$
Round 4: $562.50 \times 0.75 = 421.88$

Each round is smaller than the last, because 25 cents of every dollar leaks into saving instead of being re-spent. Added up across all rounds, the total comes to exactly $4,000.

A Larger MPS Means a Smaller Multiplier

A common point of confusion: a larger MPS produces a smaller multiplier, not a larger one.

Suppose MPS had instead been 0.5 (people save half of every new dollar). The multiplier would be $1/0.5 = 2$, not 4.
Why? A higher MPS means more of each round’s income leaks out into saving rather than being re-spent, so the chain of re-spending dies out faster and adds up to a smaller total.
A higher MPC (people spend more of each new dollar) means a bigger multiplier; a higher MPS means a smaller one, since MPC and MPS always add to 1.

Looking Ahead to Chapter 11

This chapter introduced the building blocks; the next chapter puts them to work.

Chapter 11 combines the consumption schedule from this chapter with government spending, investment, and net exports to build the full aggregate expenditures model.
The multiplier introduced here becomes the tool for finding exactly how much equilibrium real GDP changes when any type of spending changes.

Wrap Up

The consumption schedule and saving schedule both rise with disposable income; $C + S = DI$ always. MPC + MPS = 1 always, while APC + APS = 1 at any given income level.
Non-income factors, wealth, borrowing, expectations, and real interest rates, shift the whole schedule; a change in DI itself only moves you along it.
The investment demand curve slopes downward: as the real interest rate falls, more projects clear the profitability bar and quantity of investment demanded rises.
Non-interest factors, capital costs, business taxes, technology, capital stock on hand, and business expectations, shift the investment demand curve.
Investment is far more volatile than consumption, because capital purchases are postponable, innovation is uneven, profits vary, and expectations shift quickly.
The multiplier ($1/MPS$) shows how an initial change in spending leads to a larger total change in real GDP; a larger MPS means a smaller multiplier.

Looking ahead: Chapter 11 builds the full aggregate expenditures model, using the consumption schedule and the multiplier from this chapter to determine equilibrium real GDP.