Difficulty: Introductory-Intermediate | Prerequisites: GDP concepts (Chapter 7), basic algebra
Source: Principles of Macroeconomics, Case/Fair, 8e – Chapter 8, Section 8.1
Tags: aggregate expenditure, aggregate income, MPC, MPS, consumption function, saving function, marginal propensity to consume, marginal propensity to save, autonomous consumption, 45-degree line, Keynesian model
This section introduces the building blocks of the Keynesian income-expenditure model. You are learning how total spending in the economy relates to total output and total income, and how households split each additional pound (or dollar) of income between consumption and saving. These relationships, the consumption function and the saving function, are the foundation for everything else in this chapter: equilibrium output, the multiplier, and eventually fiscal policy. If you skipped Chapter 7 on GDP accounting, go back and read it first; you need to know what aggregate output means before you can model what determines it.
Every dollar of output generates a dollar of income. Households divide their income between consumption and saving, and the rates at which they do so (MPC and MPS) determine the consumption and saving functions. These functions, combined with planned investment, set total planned spending in the economy.
Aggregate expenditure (AE)
Total spending in the economy: consumption (C) + planned investment (I) + government spending (G) + net exports (EX − IM). In simple terms, it is everything that gets bought in the economy during a period.
Aggregate output (Y)
The total value of goods and services produced. Because every unit of output generates income for someone, aggregate output equals aggregate income.
Consumption (C)
Household spending on goods and services. Positively related to income, wealth, and expectations about the future; negatively related to interest rates.
Saving (S)
The portion of income not consumed: S = Y − C. Saving is a flow variable (measured per period). "Savings" (with an 's') is the stock, the accumulated total.
Saving vs. savings
"Saving" is a flow variable; "savings" is a stock variable. Think of saving as the water flowing into a bathtub each minute, and savings as the total water already in the tub.
Autonomous consumption
The amount households consume even when income is zero. This is the intercept (a) in the consumption function C = a + bY. People draw down savings, borrow, or receive transfers to keep consuming when they have no current income.
Marginal propensity to consume (MPC)
The fraction of each additional dollar of income that is spent on consumption: MPC = ΔC / ΔY. If you earn an extra $100 and spend $80 of it, your MPC is 0.80.
Marginal propensity to save (MPS)
The fraction of each additional dollar of income that is saved: MPS = ΔS / ΔY. Since every extra dollar is either consumed or saved, MPC + MPS = 1.
Consumption function
The equation relating consumption to income: C = a + (MPC × Y). The intercept is autonomous consumption; the slope is the MPC.
Saving function
The equation relating saving to income: S = −a + (MPS × Y). The intercept is negative autonomous consumption (dissaving at zero income); the slope is the MPS.
Planned investment (I)
Spending by firms on capital goods, new construction, and planned additions to inventory. In the simplest model it is treated as fixed (not dependent on income).
Actual investment
Planned investment plus any unplanned inventory changes. Actual investment can differ from planned investment when firms sell more or fewer goods than expected.
Unplanned inventory investment
The difference between actual and planned investment. Positive when goods pile up unsold; negative when firms sell more than they produced.
Real GDP measures both total output produced and total income received. If real GDP is $5 trillion, then $5 trillion of income has been generated.
This identity is what links the production side of the economy to the spending side.
Every additional dollar of disposable income is either consumed or saved. If you earn an extra $100, the sum of your additional consumption and additional saving is exactly $100.
The split is governed by MPC and MPS, which always sum to 1.
MPS = 0.20 means MPC = 0.80.
MPS = 0.25 means MPC = 0.75.
MPS = 0.35 means MPC = 0.65.
a = autonomous consumption (the y-intercept)
b = MPC (the slope)
Example: C = 200 + 0.8Y means that when income is zero, consumption is 200, and for each additional dollar of income, 80 cents is consumed.
Derived directly from S = Y − C.
If C = 200 + 0.8Y, then S = −200 + 0.2Y.
Saving is negative (dissaving) at low income levels, zero at the break-even point, and positive above it.
Break-even is where S = 0, or equivalently where C = Y.
From S = −200 + 0.2Y: set S = 0, solve for Y = 1,000. At income of 1,000, the household consumes all its income.
Change in autonomous consumption (a): shifts the entire function up or down. An increase in a shifts consumption up and saving down.
Change in MPC: rotates the consumption function. A higher MPC makes it steeper (more of each extra dollar is consumed) and makes the saving function flatter.
Wealth: higher wealth increases consumption at every income level.
Expectations about the future: optimism raises spending; uncertainty reduces it.
Interest rates: higher rates discourage borrowing and spending, encouraging saving.
Consumption is still positive (autonomous consumption). The household dissaves, drawing on past savings or borrowing.
Saving is negative at zero income.
On a graph with income on the x-axis and consumption on the y-axis, the 45-degree line shows all points where C = Y.
Where the consumption function crosses the 45-degree line, saving is zero.
Above the 45-degree line: consumption exceeds income (dissaving).
Below the 45-degree line: consumption is less than income (positive saving).
In a closed economy with no government, aggregate expenditure = C + I.
Planned investment is treated as autonomous (a flat horizontal line, independent of income) in the basic model.
Firms have least control over inventory changes. You can plan to build a factory, but you cannot perfectly plan how many units customers will buy.
Actual investment = planned investment + unplanned inventory change.
If a firm manufactures 10,000 units and sells 8,000, unplanned inventory rises by 2,000.
If a firm manufactures 20,000 and sells 21,000, inventory drops by 1,000.
In macroeconomics, "investment" means buying capital goods (machines, factories) or adding to inventories. Purchasing stocks or bonds is not investment in this sense.
Formula | Meaning |
|---|---|
C = a + (MPC × Y) | Consumption function |
S = −a + (MPS × Y) | Saving function |
MPC + MPS = 1 | The two propensities always sum to one |
MPC = ΔC / ΔY | Marginal propensity to consume |
MPS = ΔS / ΔY | Marginal propensity to save |
S = Y − C | Saving equals income minus consumption |
Actual I = Planned I + Unplanned inventory change | Investment identity |
AE = C + I (simple model) | Aggregate expenditure in a closed economy, no government |
Example 1 – Finding MPC and MPS from data: Consumption is $25,000 when income is $26,000. Consumption rises to $26,100 when income rises to $28,000.
ΔC = 26,100 − 25,000 = 1,100
ΔY = 28,000 − 26,000 = 2,000
MPC = 1,100 / 2,000 = 0.55
MPS = 1 − 0.55 = 0.45
Example 2 – Using the consumption function: C = 200 + 0.8Y. What is consumption at Y = 1,300?
C = 200 + 0.8(1,300) = 200 + 1,040 = 1,240
Saving = 1,300 − 1,240 = 60
Example 3 – Unplanned inventory: Planned investment is $50 billion, actual investment is $40 billion.
Unplanned inventory change = 40 − 50 = −$10 billion (inventories fell by $10 billion because firms sold more than planned).
When consumers become nervous about a recession, they cut spending and raise saving. This is exactly the consumption function at work: a drop in confidence shifts autonomous consumption downward, reducing C at every income level. Central banks respond by cutting interest rates to push spending back up, because interest rates are one of the key non-income determinants of consumption.
Students often confuse "saving" (a flow, what you set aside this month) with "savings" (a stock, total accumulated). They are related but measured differently.
The MPC is the change in consumption divided by the change in income, not total consumption divided by total income. Mixing up marginal and average is a common exam mistake.
Buying shares of stock is not "investment" in macro. Investment means physical capital or inventories.
When income is zero, consumption is not zero. Autonomous consumption keeps people spending through borrowing or drawing down savings.
You will be asked to calculate MPC and MPS from numerical examples, from graphs, and from equations. Practise all three formats.
The relationship MPC + MPS = 1 appears in nearly every problem. If you know one, you know the other.
Graph-reading questions on the 45-degree diagram are common: know where saving is positive, negative, and zero.
Understand the difference between planned and actual investment, and be able to compute unplanned inventory changes. This feeds directly into Section 8.2 on equilibrium.
True or false: MPC + MPS = 1. (True)
If the MPS is 0.25, the MPC is ________. (0.75)
True or false: Buying a government bond counts as "investment" in macroeconomics. (False)
If a firm planned to invest $60 billion and actual investment was $80 billion, unplanned inventory change was ________. ($20 billion)
Saving is a ________ variable; savings is a ________ variable. (flow; stock)
Q: If the consumption function is C = 80 + 0.5Y, what is the MPS?
A: MPS = 1 − MPC = 1 − 0.5 = 0.5.
Q: If the saving function is S = −20 + 0.3Y, what is consumption at an income level of 120?
A: S at 120 = −20 + 0.3(120) = −20 + 36 = 16. Consumption = Y − S = 120 − 16 = 104.
Q: If Heather's consumption function is C = 100 + 0.75Y, at what income level does her saving equal zero?
A: Saving = 0 when C = Y. So Y = 100 + 0.75Y, which gives 0.25Y = 100, so Y = 400.
Q: Higher interest rates are likely to do what to consumer spending and saving?
A: Decrease consumer spending and increase consumer saving.
Q: Suppose consumption is $4,000 when income is $6,000 and the MPC is 0.9. What is consumption when income rises to $7,000?
A: The increase in income is $1,000. Additional consumption = 0.9 × 1,000 = $900. New consumption = 4,000 + 900 = $4,900.
Q: If planned investment is $50 billion and actual investment is $55 billion, what is unplanned inventory investment?
A: Unplanned inventory investment = 55 − 50 = $5 billion (positive, meaning goods accumulated unexpectedly).
This material connects directly to Section 8.2 (equilibrium output), where you will use the consumption and saving functions to find the income level at which planned spending equals output. It also connects to Chapter 9 on fiscal policy: when the government enters the model, the consumption function is modified by taxes, and the multiplier changes. Understanding MPC and MPS here is essential for every multiplier calculation later in the course.
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