Source: Principles of Macroeconomics, Case/Fair, 8e
Difficulty: Intermediate Prerequisites: Chapter 8 notes (the basic income-expenditure model without government). You should be comfortable with the concepts of aggregate expenditure, planned investment, MPC, MPS, and equilibrium output before starting here.
Tags: fiscal policy, government spending, taxation, net taxes, disposable income, aggregate expenditure, budget deficit, budget surplus, consumption function with government, equilibrium output, leakages, injections, inventory change
This section introduces the government sector into the simple income-expenditure model you built in earlier chapters. Up to now, the model included only consumption and investment. Adding government purchases (G) and net taxes (T) changes how equilibrium output is determined and gives policymakers two main levers for influencing the economy. If you missed the earlier material on planned aggregate expenditure and the 45-degree line, go back to Chapter 8 first; everything here builds on that framework.
Fiscal policy is the government's use of spending and taxation to influence the economy. When government is added to the model, aggregate income becomes Y = C + I + G, disposable income becomes Y - T, and the consumption function adjusts accordingly. Equilibrium occurs where planned aggregate expenditure equals output, and any gap between the two shows up as unplanned inventory changes.
Fiscal policy
The spending and taxing policies used by the government to influence the economy. In simple terms, it is the set of decisions about how much the government buys, how much it collects in taxes, and how much it hands out in transfers.
Net taxes (T)
Total tax revenue minus transfer payments (such as unemployment benefits and welfare). Think of it as the net amount the government actually pulls out of household income.
Disposable income (Yd)
Income remaining after net taxes have been subtracted: Yd = Y - T. This is what households have available to spend or save.
Government purchases (G)
Spending by the government on goods and services. This enters planned aggregate expenditure directly, unlike transfer payments, which work through disposable income.
Transfer payments
Payments from the government to individuals for which no good or service is received in return (unemployment benefits, welfare, social security). These are subtracted from gross taxes to arrive at net taxes.
Budget deficit
Occurs when government spending exceeds tax revenue in a given year (G > T). The government must borrow to cover the difference.
Budget surplus
Occurs when tax revenue exceeds government spending in a given year (T > G). The excess can be used to pay down existing debt.
Aggregate expenditure (AE) with government
The total planned spending in the economy once government is included: AE = C + I + G.
Planned aggregate expenditure
The total amount that all sectors of the economy (households, firms, government) plan to spend in a given period.
Unplanned inventory change
The difference between output and planned aggregate expenditure. If output exceeds AE, inventories pile up (positive unplanned change). If AE exceeds output, inventories are drawn down (negative unplanned change).
Fiscal policy falls into three categories:
Government purchases of goods and services
Taxation
Transfer payments and welfare benefits
Government policies regarding the money supply are not fiscal policy. That is monetary policy, handled by the central bank (the Federal Reserve in the US). This distinction comes up frequently on exams.
Tax revenue depends on two things: the tax rate and the income of households. Both matter. A higher rate collects more per pound of income; higher household income means a larger base to tax. The money supply does not determine tax revenue.
Tax revenues fall during recessions, not rise. Incomes drop, so the tax base shrinks. At the same time, government spending tends to increase during recessions because unemployment payments rise automatically.
Disposable income increases when income increases and decreases when net taxes increase. Saving is a use of disposable income, not a determinant of it.
Worked example: if Bill's income is $1,000 and his net taxes are $350, his disposable income is $1,000 - $350 = $650.
When the government sector is included, the equation for aggregate income is:
Y = C + I + G
This replaces the simpler Y = C + I from the two-sector model. Adding G increases planned aggregate expenditure at every level of output.
After government is added, the consumption function becomes:
C = a + b(Y - T)
Where a is autonomous consumption, b is the MPC, and (Y - T) is disposable income. The key change from the earlier model is that taxes reduce the income available for consumption.
Worked examples:
C = 100 + 0.6Yd. If Y = $1,000 and T = $300, then Yd = $700, so C = 100 + 0.6(700) = 100 + 420 = 520.
C = 800 + 0.8Yd. If Y = $2,000 and T = $500, then Yd = $1,500, so C = 800 + 0.8(1,500) = 800 + 1,200 = 2,000.
C = 100 + 0.8Yd. If Y = $600 and T = 0, then Yd = $600, so C = 100 + 0.8(600) = 100 + 480 = 580.
C = 1,000 + 0.9Yd. If Y = $3,600 and T = $600, then Yd = $3,000, so C = 1,000 + 0.9(3,000) = 1,000 + 2,700 = 3,700.
The difference between what a government spends and what it collects in taxes in a year is the government budget deficit or surplus.
If taxes collected > spending, there is a surplus.
If spending > taxes collected, there is a deficit.
Worked examples:
Canfield collects $500,000 in taxes and spends $450,000. Surplus = $500,000 - $450,000 = $50,000 surplus.
Miketown collects $250,000 and spends $350,000. Deficit = $350,000 - $250,000 = $100,000 deficit.
Equilibrium occurs where output (Y) equals planned aggregate expenditure (AE = C + I + G). At that point, there is no unplanned inventory change.
If output < AE, inventories fall unexpectedly, signalling firms to increase production. Output tends to rise.
If output > AE, inventories pile up unexpectedly, signalling firms to cut production. Output tends to fall.
At equilibrium (assuming no foreign trade):
I + G = S + T
Injections (investment plus government purchases) equal leakages (saving plus net taxes). This is an alternative way to find equilibrium and a common exam question format.
For the economy to be in equilibrium, government purchases plus investment must equal saving plus tax revenue. Equivalently, government purchases must equal saving plus net taxes minus investment: G = S + T - I.
Using Table 9.1 as an example (all figures in $ billion, with net taxes = 100, investment = 200, government spending = 100 at every output level):
At Y = 600: AE = C(400) + I(200) + G(100) = 700. Since 700 > 600, inventories fall by 100 and output tends to rise.
At Y = 1,000: AE = C(600) + I(200) + G(100) = 900. Since 900 < 1,000, inventories rise by 100 and output tends to fall.
Equilibrium is at Y = 800, where AE = 800.
At equilibrium, disposable income at Y = 400 is 400 - 100 = $300. Saving at Y = 1,000 is Yd - C = 900 - 600 = $300. Leakages at equilibrium (Y = 800) = S + T = 200 + 100 = $300.
Formula | Meaning |
|---|---|
Yd = Y - T | Disposable income |
C = a + b(Y - T) | Consumption function with government |
Y = C + I + G | Aggregate income (equilibrium condition) |
I + G = S + T | Leakages = injections (equilibrium, no trade) |
Budget position = T - G | Positive = surplus, negative = deficit |
When a recession hits and unemployment rises, the government does not need to pass new legislation for some fiscal responses to kick in. Unemployment payments increase automatically, raising government spending, while falling incomes reduce tax revenues. Both effects push the budget toward deficit but help cushion household income. This is the basic mechanism behind automatic stabilisers, explored more fully in Part 3.
Students often think tax revenues rise during recessions because the government "needs more money." They do not. Revenues fall because incomes fall.
Students sometimes confuse fiscal policy with monetary policy. If it involves the money supply or the central bank, it is monetary policy, not fiscal.
Saving does not reduce disposable income. Saving is a use of disposable income, not a subtraction from it.
The budget deficit and the national debt are not the same thing. The deficit is a flow (one year's gap), the debt is a stock (the accumulated total owed).
Expect questions asking you to calculate disposable income, consumption, and equilibrium output using the consumption function with taxes.
Be ready to identify whether there is a surplus or deficit given spending and revenue figures.
Know the equilibrium condition both ways: Y = C + I + G and I + G = S + T.
Table-based questions will ask you to find equilibrium, compute unplanned inventory changes, and determine whether output will rise or fall at a given level.
True or false: The economy is in equilibrium when aggregate output equals consumption spending. False. Equilibrium is when aggregate output equals planned aggregate expenditure (C + I + G), not consumption alone.
True or false: For equilibrium, G + I = S + T. True.
True or false: Disposable income is income less net taxes. True.
Fill in the blank: If Y = $2,000, T = $400, a = 500, and MPC = 0.8, then C = ____. C = 500 + 0.8(2,000 - 400) = 500 + 1,280 = 1,780.
Q: Fiscal policy refers to what?
A: The spending and taxing policies used by the government to influence the economy.
Q: If income is $1,000 and net taxes are $350, what is disposable income?
A: $650. Yd = Y - T = 1,000 - 350 = 650.
Q: The aggregate consumption function is C = 100 + 0.6Yd. If income is $1,000 and net taxes are $300, what does consumption equal?
A: 520. Yd = 700, so C = 100 + 0.6(700) = 520.
Q: If output is less than planned aggregate expenditure, what happens to inventories?
A: There is an unplanned decrease in inventories. Firms sell more than they produce, drawing down stock.
Q: A city collects $500,000 in taxes and spends $450,000. What is its budget position?
A: A budget surplus of $50,000.
Q: Assuming no foreign trade, what is the equilibrium condition using leakages and injections?
A: I + G = S + T. Injections equal leakages.
This material builds directly on the two-sector (C + I) equilibrium model from Chapter 8. The multiplier effects introduced in Part 2 of these notes extend the logic here by showing how changes in G or T ripple through the economy. The budget concepts (deficit, surplus, debt) connect forward to discussions of the national debt and long-run fiscal sustainability covered in later chapters.
fiscal policy, government spending, net taxes, transfer payments, disposable income, Yd, budget deficit, budget surplus, aggregate expenditure with government, Y = C + I + G, consumption function with taxes, C = a + b(Y - T), equilibrium output, unplanned inventory change, leakages and injections, I + G = S + T, Case Fair Chapter 9, Principles of Macroeconomics Chapter 9, ECO 2013