Difficulty: Intermediate | Prerequisites: Part 1 of these notes (spending components, MPC, MPS)
This is the second half of Chapter 13. It takes the four spending components from Part 1, stacks them into the aggregate expenditure (AE) model, and introduces the multiplier effect. The multiplier is one of the most-tested concepts in introductory macro, so this material is worth knowing cold. If you are not comfortable with MPC and MPS, go back to Part 1 first.
The aggregate expenditure (AE) model adds up C + I + G + NX into a single line plotted against Real GDP. The economy is in equilibrium where AE equals Real GDP (the 45-degree line). When autonomous spending changes, Real GDP changes by a larger amount thanks to the multiplier effect, because each dollar spent becomes someone else's income and gets partially re-spent.
Aggregate expenditure (AE)
The total planned spending in the economy: AE = C + I + G + NX. In the simplified model (no taxes or imports), the slope of the AE line equals the MPC. Think of it as the economy's total spending plan at each level of Real GDP.
45-degree line (Y = X line)
A reference line on the AE diagram where every point represents Real GDP equal to aggregate expenditure. Equilibrium occurs where the AE line crosses this line.
Macroeconomic equilibrium (in the AE model)
The point where aggregate expenditure equals Real GDP. At this point, firms are selling exactly what they produce, and inventories are stable. In simple terms, the economy is in balance: total spending matches total output.
Autonomous spending
The portion of aggregate expenditure that does not depend on Real GDP. It is the y-intercept of the AE line. Changes in autonomous spending are what trigger the multiplier effect.
Multiplier effect
The process by which a change in autonomous spending produces a larger change in equilibrium Real GDP. It works because one person's spending is another person's income, and that income is partly spent again, and so on. In simple terms, a dollar of new spending ripples through the economy and ends up generating more than a dollar of total output.
Spending multiplier
The number that tells you how much equilibrium Real GDP changes for each dollar change in autonomous spending. Formally: change in equilibrium Real GDP / change in autonomous spending. It can also be calculated as 1 / (1 - slope of the AE line).
The AE line is built by vertically stacking the four spending components: C + I + G + NX.
In the simplified case (no taxes, no imports), the slope of the AE line equals the MPC, because consumption is the only component that rises with income. I, G, and NX (when imports are zero) are flat and just shift the line up.
The y-intercept of the AE line is total autonomous spending: autonomous consumption + investment + government purchases + net exports.
Equilibrium is where the AE line crosses the 45-degree line (Y = X). At this single point, Real GDP equals aggregate expenditure.
There is only one equilibrium point.
Real GDP below equilibrium: AE is greater than Real GDP. Spending exceeds production. Firms see inventories shrinking, so they respond by increasing production and hiring. The economy moves back toward equilibrium.
Real GDP above equilibrium: AE is less than Real GDP. Production exceeds spending. Firms see inventories piling up, so they cut back production and employment. The economy moves back toward equilibrium.
The inventory adjustment mechanism is what pulls the economy back to equilibrium in both cases.
When autonomous spending changes (say, the government increases G by $100), the AE line shifts up by $100.
But equilibrium Real GDP increases by more than $100. Why? Because that $100 becomes income for someone, who spends part of it (MPC x $100), which becomes income for someone else, who spends part of that, and so on.
The total change in Real GDP = the initial change in autonomous spending x the multiplier.
A steeper AE line (higher MPC) means a larger multiplier, because more of each round of spending is re-spent.
General formula: Multiplier = 1 / (1 - slope of AE line). This always works.
Simplified case (no taxes, no imports): The slope of AE = MPC, so the multiplier = 1 / (1 - MPC) = 1 / MPS.
Example: if MPC = 0.8, multiplier = 1 / (1 - 0.8) = 1 / 0.2 = 5. Every $1 increase in autonomous spending raises Real GDP by $5.
With taxes or imports: Both taxes and imports make the AE line flatter (they pull money out of the spending stream at each round). A flatter AE line means a smaller multiplier.
Imports reduce AE because as income rises, more is spent on foreign goods (leaking out of the domestic economy).
Taxes reduce disposable income at each round, so less is available to be re-spent.
In either case, the multiplier will be less than 1 / (1 - MPC).
The slope of AE is always less than 1. This is important because it ensures that the multiplier is finite and the model has a stable equilibrium.
Without taxes or imports, slope of AE = MPC.
With taxes or imports, slope of AE < MPC.
Aggregate expenditure:
AE = C + I + G + NX
Equilibrium condition:
AE = Real GDP (the 45-degree line)
Spending multiplier (general):
\text{Multiplier} = \frac{1}{1 - \text{slope of AE line}}Spending multiplier (no taxes, no imports):
\text{Multiplier} = \frac{1}{1 - MPC} = \frac{1}{MPS}Change in equilibrium Real GDP:
\Delta Y = \text{Multiplier} \times \Delta \text{Autonomous Spending}Diagram notes:
The AE diagram has Real GDP on the x-axis and aggregate expenditure (in dollars) on the y-axis.
The 45-degree line represents AE = Real GDP.
The AE line starts above the origin (autonomous spending) and slopes upward with slope < 1.
Equilibrium is at the intersection of AE and the 45-degree line.
A parallel upward shift of AE (increase in autonomous spending) moves the equilibrium to the right along the 45-degree line by a multiple of the shift.
The multiplier effect is the theoretical basis for fiscal stimulus. When a government increases spending during a recession, the idea is that every dollar of new government spending generates more than a dollar of additional GDP. The size of the multiplier determines how cost-effective that stimulus is.
The observation that taxes and imports shrink the multiplier explains why small, open economies (with high import ratios) tend to get less domestic bang from fiscal stimulus than large, relatively closed economies do.
Students often assume the multiplier equals 1 / (1 - MPC) in all cases. It does not. That formula only applies when there are no taxes and no imports. With taxes or imports, the multiplier is smaller.
Students confuse the multiplier with the MPC. The MPC is a fraction (between 0 and 1). The multiplier is a whole number or larger (always greater than 1 in this model).
Students sometimes think that when AE is above the 45-degree line, the economy is "doing well." It means spending exceeds output, inventories are falling, and firms will ramp up production. It is a disequilibrium, not a desirable state.
Students forget the sign convention. The multiplier works in both directions: a decrease in autonomous spending reduces Real GDP by the multiplier times the decrease. The multiplier amplifies contractions as well as expansions.
Multiplier calculations are among the most common numerical questions on macro exams. Be ready to compute the multiplier given MPC or MPS, and to use it to find the change in equilibrium Real GDP.
Know the inventory adjustment story cold. Exam questions often describe a scenario ("firms notice inventories rising") and ask you to identify whether the economy is above or below equilibrium.
Understand why imports and taxes reduce the multiplier. This is a common conceptual question.
Remember that the slope of the AE line is always less than 1. If you calculate a slope of 1 or greater, something has gone wrong.
True or false: Equilibrium in the AE model occurs where the AE line crosses the 45-degree line. (True)
Fill in the blank: If MPC = 0.75 and there are no taxes or imports, the spending multiplier is __________. (4, because 1 / (1 - 0.75) = 1 / 0.25 = 4)
True or false: When Real GDP is above equilibrium, firms see their inventories shrinking. (False, inventories grow because production exceeds spending.)
Fill in the blank: Adding imports or taxes to the model makes the AE line __________ and the multiplier __________. (flatter; smaller)
True or false: A $50 decrease in autonomous spending with a multiplier of 4 reduces equilibrium Real GDP by $200. (True, because $50 x 4 = $200)
Q: The MPC is 0.9 and there are no taxes or imports. Government spending increases by $10 billion. What is the change in equilibrium Real GDP?
A: Multiplier = 1 / (1 - 0.9) = 1 / 0.1 = 10. Change in Real GDP = 10 x $10 billion = $100 billion increase.
Q: In the AE model, firms notice that their inventories are unexpectedly shrinking. Is actual Real GDP above or below the equilibrium level? What will firms do in response?
A: Real GDP is below equilibrium. Aggregate expenditure exceeds production, so inventories are being drawn down. Firms will respond by increasing production and employment, moving the economy back toward equilibrium.
Q: Explain why introducing an income tax reduces the size of the spending multiplier.
A: An income tax takes a fraction of each round of new income before it can be spent. This reduces the amount re-spent at each stage of the multiplier process, making the AE line flatter. A flatter AE line means a smaller multiplier because less of each initial dollar of spending gets recycled through the economy.
Q: Country A has no imports and MPC = 0.8. Country B has imports and the same MPC. Which country has the larger multiplier, and why?
A: Country A. Imports act as a leakage from the domestic spending stream (income spent on foreign goods does not become domestic income). This makes Country B's AE line flatter than Country A's, producing a smaller multiplier.
Q: The spending multiplier is 5. Autonomous consumption falls by $20 billion. What happens to equilibrium Real GDP?
A: Equilibrium Real GDP falls by $100 billion (5 x $20 billion). The multiplier works in both directions.
The multiplier concept carries straight into fiscal policy (Ch. 14-15). Tax multipliers and government spending multipliers are variations on the same idea, and the intuition you build here, that spending ripples through the economy in rounds, is the foundation.
This chapter also sets up the link to the AD-AS model. The multiplier tells you how far the AD curve shifts when autonomous spending changes. A larger multiplier means a larger horizontal shift in AD for any given change in spending, which matters for understanding how policy affects output and the price level.
Aggregate expenditure, AE model, aggregate expenditure model, 45-degree line, macroeconomic equilibrium, Keynesian cross, multiplier effect, spending multiplier, expenditure multiplier, autonomous spending, induced spending, MPC, MPS, inventory adjustment, fiscal stimulus, leakages, injections, taxes and the multiplier, imports and the multiplier, ECO 2013, Principles of Macroeconomics, Chapter 13, University of Florida macroeconomics