Week 7 · Chapter

Chapter 7 — Fiscal Policy

Principles of Macroeconomics Free sample edition

The module's primary reading · ~40–50 minutes · Objective 6 (analyze fiscal policy — government spending, taxes, expansionary and contractionary stances, and automatic stabilizers — apply the spending and tax multipliers, and distinguish the deficit (a flow) from the national debt (a stock)), with Objective 5 (use the aggregate-demand and aggregate-supply model to analyze short-run fluctuations and the business cycle — name which curve shifts, in which direction, and what happens to the price level and real output — and measure recessionary and inflationary gaps) · Read it first this week; the lecture, the slides, the tutorial, the quiz, and the Model Workshop all build on it.

In plain language

This week is about fiscal policy (a government's choices about how much to spend and how much to tax), one of the two big levers it can pull when the economy stalls or overheats. When a government spends a dollar, that dollar becomes someone's paycheck, and part of the paycheck gets spent again. So the first dollar can grow into several dollars of output, and the spending multiplier (the number that says how many dollars of output one new dollar of spending creates) measures that chain. A government that spends more than it collects runs a budget deficit (the shortfall in one year), and every deficit adds to the national debt (the total still owed). Economists agree on that arithmetic, and they argue hard about when the government should use this lever, so you will hear both sides at full strength.

Why you already care about this

Picture three people in an illustrative town. A road-crew worker learns that a new bridge project will keep her employed for 18 more months. A café owner across the street notices that her lunch line is 12 people longer on weekdays now that the crew is working nearby. A retiree reads a headline that the government borrowed again this year and wonders whether his 2 grandchildren will pay for it. All three are living inside one week's worth of economics.

The worker's job came from government spending. The café owner's longer line came from the worker spending her paycheck, which is the multiplier at work. The retiree's worry is about the gap between what the government spends and what it collects, and about the pile of past borrowing that gap adds to. One chapter ties the three stories together.

You will follow an illustrative road project of 20 billion dollars as it moves through the economy, and you will see why it can raise output by 100 billion dollars in a simple model. You will see why a tax cut of the same size does a little less. And you will meet the honest disagreement among economists about whether, and when, a government should try.

By the end of this chapter you will be able to:

name a fiscal policy move as expansionary or contractionary and say which way it shifts aggregate demand;
compute the spending multiplier from the marginal propensity to consume and use it to find the change in output;
compute the tax multiplier and explain why a tax cut is weaker dollar for dollar than a spending increase;
tell the spending multiplier from the money multiplier and say which question each one answers;
identify an automatic stabilizer and explain how it works with no new law;
separate a budget deficit (a flow) from the national debt (a stock) and update the debt from a deficit;
lay out the Keynesian case for fiscal action and the classical and monetarist case for caution, labeling positive and normative claims.

Carry this line with you: a deficit is the water pouring in; the debt is the water level.

Where we are

Already covered: Week 1, The Macro Perspective, separated positive from normative claims. Week 2, Measuring Output, built GDP = C + I + G + NX. Week 3, Measuring Inflation & Unemployment, measured the price level and joblessness. Week 4, Economic Growth & Productivity, named potential output. Week 5, Aggregate Demand & Aggregate Supply, drew the AD–AS diagram, and Week 6, Business Cycles & Short-Run Fluctuations, read recessions and booms as gaps from potential output.
This week: fiscal policy, the spending and tax multipliers, automatic stabilizers, the deficit and the debt, and the debate over using fiscal policy.
How they connect: government purchases G are one of the four parts of spending from Week 2, so a change in G shifts Week 5's aggregate demand curve. The size of that shift is what can close Week 6's recessionary gap.
Where we're going next: Week 8, Midterm Review & Exam, gathers Weeks 1 to 7 by the one calculation and the one curve each topic asks for, and adds the flow-versus-stock habit you start this week.

Three earlier ideas carry this chapter. From Week 2, government purchases G are government spending on goods and services, such as a public teacher's pay or a new bridge, and they count in GDP. A transfer payment, such as an unemployment check, does not count in G. From Week 5, anything other than the price level that changes spending shifts the whole aggregate demand curve, and an aggregate demand shift moves the price level and real output in the same direction. From Week 6, a recessionary gap means actual output sits below potential output, with workers and machines standing idle. This week asks what the government's budget can do about that gap.

1. Define fiscal policy: who holds the budget lever

Think about a household that hits a rough patch. It can change what it spends, and it can change what it brings in. A government has the same two levers on a much larger scale: what it spends, and what it collects in taxes. When it uses those levers to steer the whole economy, that is fiscal policy.

Fiscal policy is the government's use of its spending and taxes to influence the whole economy; it is set by the legislature, not by the central bank.

In this course, government purchases are written G and taxes are written T. Both are in billions of dollars. The legislature passes the budget and the tax laws, so fiscal policy belongs to the legislature. The central bank's tools, which you meet in Weeks 9 to 11, are monetary policy, a separate lever.

Fiscal policy comes in two directions.

Expansionary fiscal policy is raising government spending or cutting taxes to add to total spending, which shifts the aggregate demand curve to the right.
Contractionary fiscal policy is cutting government spending or raising taxes to reduce total spending, which shifts the aggregate demand curve to the left.

Worked example — naming the stance and the shift. For each illustrative move, name the stance, the curve, and the direction, then say what happens to the price level and real output.

The legislature funds a new 20-billion-dollar road project. Government purchases G rise. That is expansionary. Aggregate demand shifts right, so the price level and real output both rise.
The legislature raises the income-tax rate. Taxes T rise, households keep less of each paycheck, and consumption C falls. That is contractionary. Aggregate demand shifts left, so the price level and real output both fall.
The legislature cuts spending on new office buildings. G falls. That is contractionary. Aggregate demand shifts left, and P and Y both fall.
The legislature cuts the payroll tax. T falls, take-home pay rises, and C rises. That is expansionary. Aggregate demand shifts right, and P and Y both rise.

In words: every fiscal move works by changing spending, so every one of them shifts aggregate demand, and an aggregate demand shift moves P and Y together.

Misconception check. Students often say "the Fed cut spending" or "the central bank passed a tax cut." It is an easy mix-up, because both the legislature and the central bank are in the news when the economy wobbles. The cure is to ask who holds the lever. Spending and taxes are fiscal policy, set by the legislature. The central bank's tools are monetary policy, a different lever for Weeks 9 to 11.

Memory hook: the budget lever sits with lawmakers, not the central bank.

2. Measure the marginal propensity to consume

Suppose you get an unexpected 100-dollar bonus at work. What do you do with it? Maybe you buy groceries, pay for a concert ticket, and put the rest in savings. Most people spend part of an extra dollar and save part of it. Economists give the spent part a name.

The marginal propensity to consume is the fraction of an extra dollar of income that a household spends rather than saves, written MPC; at an MPC of 0.8, 80 cents of each extra dollar is spent.

The word "marginal" means "the next one." The MPC is about the next dollar you earn, not about every dollar. The saved fraction is what is left over, 1 − MPC.

Worked example — the bonus. In the illustrative economy you will follow all week (constructed for this course, not real data), the MPC is 0.8. A household earns 100 extra dollars.

Find the spent part. 0.8 × 100 = 80 dollars.
Find the saved part. The saved fraction is 1 − 0.8 = 0.2, and 0.2 × 100 = 20 dollars.
Check. 80 + 20 = 100, so every extra dollar is either spent or saved.

In words: out of each extra 100 dollars of income, this household spends 80 and saves 20.

Misconception check. Students often read an MPC of 0.8 as "people spend 80 percent of everything they earn." That reading is tempting, because the number looks like a share of income. But the MPC describes only the extra dollar. A household could spend nearly all of its regular paycheck on rent and food and still save a large share of a surprise bonus. The MPC is about the next dollar, which is the one fiscal policy hands out.

Memory hook: MPC is the next dollar, not every dollar.

3. Follow the rounds of re-spending

Picture a 20-dollar bill moving through a neighborhood. You pay it to a barber. The barber spends 16 of it at a food truck and saves the rest. The food-truck owner spends part of the 16 at a hardware store. The same original bill keeps creating new sales, and each new sale is a little smaller than the one before.

That chain is the heart of the multiplier. When the government spends, its spending is someone's income. That person spends part of it, which is someone else's income, and the chain continues.

Worked example — the road project, round by round. In the illustrative economy, the government spends 20 billion dollars on a road project, and the MPC is 0.8.

Round one. The 20 billion dollars is income to the road crew and the firms that supply them.
Round two. The road crew spends 0.8 of it: 0.8 × 20 = 16 billion dollars, spent at shops and cafés.
Round three. The café owners and shopkeepers spend 0.8 of their new income: 0.8 × 16 = 12.8 billion dollars.
Running total so far. 20 + 16 + 12.8 = 48.8 billion dollars after three rounds, and the chain is still going.
Every round added up. Each round is 0.8 of the one before, so the rounds shrink toward zero. Their total is 20 ÷ (1 − 0.8) = 20 ÷ 0.2 = 100 billion dollars.

In words: a 20-billion-dollar road project creates 100 billion dollars of new output once every round of re-spending is added up, in this simple model.

The first three rounds of re-spending from a 20-billion-dollar road project at an MPC of 0.8, in billions of dollars (illustrative)
Round	Who receives the income	New spending in this round
One	the road crew and its suppliers	20
Two	shops and cafés	16
Three	the café owners' own suppliers	12.8

Misconception check. Students often think the road project adds only 20 billion dollars to output, because that is all the government spent. That would be true if the road crew saved every dollar. But the crew spends 80 cents of each dollar, and each of those cents becomes someone else's paycheck. The cure is to follow the money past the first stop.

Memory hook: one person's spending is another person's income.

4. Use the spending multiplier to size the change in output

Adding round after round by hand is slow. Economists use a shortcut that adds up the whole chain at once.

The spending multiplier is the number 1 ÷ (1 − MPC), which tells how many dollars of output one extra dollar of spending creates once every round of re-spending is added up.

A change is written with the Greek letter delta, Δ. So ΔG is the change in government purchases and ΔY is the change in real output, both in billions of dollars. The rule is ΔY = spending multiplier × ΔG.

Worked example — the shortcut. In the illustrative economy, the MPC is 0.8 and ΔG = 20 billion dollars.

Find the saved fraction. 1 − 0.8 = 0.2.
Find the spending multiplier. 1 ÷ (1 − 0.8) = 1 ÷ 0.2 = 5.
Find the change in output. ΔY = 5 × 20 = 100 billion dollars.

In words: each dollar of new government spending becomes 5 dollars of output in the simple model, so the 20-billion-dollar road project raises output by 100 billion dollars, the same total the rounds gave.

The size of the multiplier depends on the MPC. The more of each extra dollar people spend, the longer the chain runs.

The spending multiplier at four values of the marginal propensity to consume (illustrative)
MPC	Saved fraction	Spending multiplier
0.6	0.4	2.5
0.75	0.25	4
0.8	0.2	5
0.9	0.1	10

The closer the MPC is to 1, the bigger the multiplier, because less of each round leaks into saving.

The multiplier works in reverse too. Worked example — the contractionary mirror. The legislature cuts spending by 20 billion dollars, so ΔG = −20. Then ΔY = 5 × (−20) = −100 billion dollars. In words: the cut lowers output by 100 billion dollars in the simple model, and aggregate demand shifts left.

The multiplier also tells you how big a project would need to be to close a gap. Worked example — sizing a project. Suppose the illustrative economy has a recessionary gap of 50 billion dollars. Divide the gap by the multiplier: 50 ÷ 5 = 10 billion dollars of new spending would close it in the simple model.

Here is an honesty note. The simple model leaves out two leaks. Households pay part of each extra dollar in taxes, and they spend part of it on imports made abroad. Both leaks cut the chain short, so the real-world multiplier is smaller than 1 ÷ (1 − MPC). How much smaller is an open question that economists study and argue about; this course teaches the simple model as a model and never grades a real-world multiplier as one number.

In practice (your tools). In Google Sheets, type the four MPC values 0.6, 0.75, 0.8, and 0.9 in cells B2 through B5. In C2, type =1/(1-B2) and copy it down to C5. The column shows 2.5, 4, 5, and 10. In D2, type =C2*20 and copy it down to see how much output a 20-billion-dollar project would add at each MPC; the row for 0.8 shows 100.

Misconception check. Students often compute the multiplier as 1 ÷ MPC, which gives 1 ÷ 0.8 = 1.25. That is tempting, because the MPC is the number in the problem. But the chain is cut short by saving, so the formula divides by the saved fraction, 1 − MPC. Dividing by the MPC badly understates the effect: 1.25 instead of 5. A quick check helps: a bigger MPC must give a bigger multiplier, and only 1 ÷ (1 − MPC) does that.

Memory hook: divide by what leaks out, not by what stays in.

5. Compare a tax cut with a spending increase

Imagine two ways to put 20 dollars into a neighborhood. In the first, the city buys 20 dollars of paint for the community center. In the second, the city sends a resident a 20-dollar tax refund. The paint purchase is spending right away. The resident saves part of the refund first and spends only the rest. So the refund starts its chain one step smaller.

That difference has its own multiplier.

The tax multiplier is the number −MPC ÷ (1 − MPC), which tells how much output changes for each dollar change in taxes; it is negative because a tax increase lowers output and a tax cut raises it.

ΔT is the change in taxes, and a tax cut is a negative ΔT. The rule is ΔY = tax multiplier × ΔT.

Worked example — a tax cut. In the illustrative economy, the MPC is 0.8.

Find the tax multiplier. −0.8 ÷ (1 − 0.8) = −0.8 ÷ 0.2 = −4.
A tax cut of 25 billion dollars. ΔT = −25, so ΔY = −4 × (−25) = 100 billion dollars.
A tax cut of 20 billion dollars, the same size as the road project. ΔY = −4 × (−20) = 80 billion dollars.
Compare. The 20-billion-dollar road project raised output by 100 billion dollars, and the 20-billion-dollar tax cut raises it by 80. The tax cut does 100 − 80 = 20 billion dollars less.

In words: a tax cut of 25 billion dollars adds the same 100 billion dollars of output as a spending increase of 20 billion, because households save a fifth of the tax cut before any of it is spent.

Misconception check. Students often treat a 20-billion-dollar spending increase and a 20-billion-dollar tax cut as equal in effect. It sounds fair, because the same number of dollars changes hands. But the government's spending is spent in full in round one, while households save a fifth of the tax cut first. The cure is to use the right multiplier for each: 5 for spending, −4 for taxes.

There is a second multiplier you will meet later, and it must stay fenced off. The money multiplier, 1 ÷ RR, where RR is the required reserve ratio, belongs to banking in Week 9. It describes how bank lending can expand the money supply. It never answers a question about government spending or taxes.

Misconception check — two multipliers. Students often reach for 1 ÷ RR on a fiscal-policy question because both formulas are called "multipliers." The cure is to ask what is being injected. New spending into output uses 1 ÷ (1 − MPC). New reserves into the money supply use 1 ÷ RR, a banking idea for Week 9.

Memory hook: spending is spent at once; a tax cut is partly saved first.

6. Let automatic stabilizers work with no new law

Picture a ride-share driver whose fares drop in a slow month. Two things happen at once, and nobody has to vote on either. The income tax the driver owes falls with the fares. And if a worker in the same city loses a job, unemployment insurance starts paying out. Both cushion spending when times are hard, and both are already written into law.

Automatic stabilizers are taxes and transfer programs already on the books, such as income taxes and unemployment insurance, that cushion spending in a downturn and restrain it in a boom without any new law.
Discretionary fiscal policy is a deliberate new decision by the legislature to change spending or taxes, as opposed to the automatic changes that happen under existing law.

Worked example — a household's tax cushion. An illustrative household (constructed for this course) pays a 20% income tax. Its monthly income falls from 5,000 dollars to 4,000 dollars.

Tax before. 0.20 × 5,000 = 1,000 dollars, so after-tax income is 5,000 − 1,000 = 4,000 dollars.
Tax after. 0.20 × 4,000 = 800 dollars, so after-tax income is 4,000 − 800 = 3,200 dollars.
The drop in after-tax income. 4,000 − 3,200 = 800 dollars.

In words: the household's income fell by 1,000 dollars, but its after-tax income fell by only 800, because its tax bill shrank on its own. Multiply that cushion across millions of households and spending falls less in a recession than it otherwise would.

The cushion works in a boom too. When incomes rise, tax bills rise with them and unemployment payments fall, which takes some steam out of spending without any new vote.

Misconception check. Students often think every change in the budget is a policy decision. It looks that way in the headlines, where the deficit "grew" or "shrank." But much of the change in a recession is automatic: tax revenue falls and unemployment payments rise under laws already in place. The cure is to ask whether anyone voted. If not, it is an automatic stabilizer, not discretionary fiscal policy.

Here is a caveat about speed. Automatic stabilizers start working right away, with no lag for a vote. They may not be large enough to close a deep gap on their own, which is why the debate in Section 8 is about discretionary policy.

Memory hook: stabilizers act before anyone votes.

7. Separate the deficit from the debt: a flow versus a stock

Picture a bathtub. The faucet runs, and the water level rises. The faucet's flow is measured per minute. The water level is measured at one moment. A government's budget works the same way.

A budget deficit is the amount by which government spending exceeds revenue in one year; it is a flow, measured per year, and the government borrows to cover it.
The national debt is the total the government owes at a point in time from past borrowing not yet repaid; it is a stock, and each year's deficit adds to it.

The deficit is the faucet. The debt is the water level.

Worked example — one year's budget. In the illustrative budget (constructed for this course, not real data, in billions of dollars), the government collects revenue of 400 and spends 450. It began the year owing 1,000.

Find the deficit. Spending − revenue = 450 − 400 = 50 billion dollars for the year. That is a flow.
Update the debt. The government borrows the 50 to cover the deficit, so the debt is 1,000 + 50 = 1,050 billion dollars at the end of the year. That is a stock.

In words: this government ran a deficit of 50 billion dollars this year, and its debt rose from 1,000 billion to 1,050 billion dollars.

A deficit adds to the debt; that is arithmetic, not a school of thought. A smaller deficit still adds to the debt, only more slowly. The debt shrinks only in a year when revenue is larger than spending.

Misconception check. Students often use "deficit" and "debt" as if they meant the same thing, and say "the government cut the debt" when it only shrank the deficit. The two words sound alike and both describe borrowing. The cure is the bathtub: the deficit is how fast water pours in this year, and the debt is how high the water stands. Turning the faucet down is not the same as draining the tub.

Memory hook: deficit per year, debt at a point in time.

8. Weigh the case for and against fiscal stimulus

Picture a town during a slump. Shops have empty aisles. Builders have idle cranes. Workers want hours they cannot find. Should the government step in with a big spending program? Thoughtful economists answer that question differently, and this course gives you both answers at full strength.

First, two more terms the debate uses.

Crowding out is the worry that government borrowing competes with private borrowers for saving, pushes up interest rates, and reduces private investment, offsetting part of a fiscal stimulus.
Policy lags are the delays between a change in the economy and a policy's effect on it: the time to recognize the problem, the time to decide and pass a response, and the time for the response to take effect.

The Keynesian case for fiscal action. In a recessionary gap, workers and machines sit idle. Extra government spending puts them back to work, and the multiplier spreads the gain. With so much idle capacity and so little demand for loans, the extra borrowing pushes interest rates up only a little, so crowding out is small. Waiting has a cost too: every month the gap stays open, people lose jobs and income they will not get back. The positive claim here is that a spending increase raises output when resources are idle. The normative judgment is that the lost jobs are a harm worth borrowing to prevent.

The classical and monetarist case for caution. Government borrowing draws on the same pool of saving that firms use to build factories and buy equipment. It can push up interest rates and crowd out private investment, so part of the stimulus is offset. Fiscal policy also faces long lags. It takes time to recognize a downturn, more time for the legislature to agree on a bill, and more time for a road project to break ground. By then the economy may have recovered on its own, and the extra spending can push it past potential output. And every deficit adds to the debt. The positive claims here are that crowding out and lags exist and can weaken or mistime a stimulus. The normative judgment is that the risk of mistimed help and a larger debt outweighs the cost of waiting.

The two cases on using fiscal policy in a recessionary gap, sorted into positive and normative claims
Question	Keynesian case for action	Classical and monetarist case for caution
Positive: does extra spending raise output?	Yes, strongly, when resources are idle	Yes, but crowding out offsets part of it
Positive: how fast does it work?	Fast enough to help while the gap lasts	Often late, after recognition, legislative, and implementation lags
Normative: what is the bigger risk?	Leaving people out of work for longer	Mistimed help and a growing debt

Both sides accept the same toolkit. Both agree that a deficit adds to the debt. They disagree about how large the real-world multiplier is, how big crowding out is, how long the lags are, and how to weigh jobs today against debt tomorrow. Some of those disagreements can be tested with evidence; others rest on values. Neither side is "right" by decree, and the course leaves the verdict to the evidence and to you.

Misconception check. Students often think one side of this debate must be outdated or plain wrong. It is tempting to pick a team, because the topic is political. But the disagreement is mostly about sizes and timing, such as how much crowding out happens in a given slump, which economists study with evidence, plus a value judgment about which risk matters more. The cure is to sort each claim: is it positive, testable against evidence, or normative, resting on values?

Pause and reflect. Choose one of these two prompts and write a few sentences.

(a) Think of a large public project you have seen built near you, such as a road, a transit line, or a school. Who earned income from it in the first round, and where might they have spent that income in the second?
(b) Think of a time a household you know had to choose between borrowing now and waiting. Which argument in this section does that choice remind you of, and why?

Memory hook: agree on the arithmetic; argue about the sizes and the values.

Key terms

fiscal policy — The government's use of its spending and taxes to influence the whole economy; it is set by the legislature, not by the central bank. (first used: 1. Define fiscal policy: who holds the budget lever)
expansionary fiscal policy — Raising government spending or cutting taxes to add to total spending, which shifts the aggregate demand curve to the right. (first used: 1. Define fiscal policy: who holds the budget lever)
contractionary fiscal policy — Cutting government spending or raising taxes to reduce total spending, which shifts the aggregate demand curve to the left. (first used: 1. Define fiscal policy: who holds the budget lever)
marginal propensity to consume — The fraction of an extra dollar of income that a household spends rather than saves, written MPC; at an MPC of 0.8, 80 cents of each extra dollar is spent. (first used: 2. Measure the marginal propensity to consume)
spending multiplier — The number 1 ÷ (1 − MPC), which tells how many dollars of output one extra dollar of spending creates once every round of re-spending is added up. (first used: 4. Use the spending multiplier to size the change in output)
tax multiplier — The number −MPC ÷ (1 − MPC), which tells how much output changes for each dollar change in taxes; it is negative because a tax increase lowers output and a tax cut raises it. (first used: 5. Compare a tax cut with a spending increase)
automatic stabilizers — Taxes and transfer programs already on the books, such as income taxes and unemployment insurance, that cushion spending in a downturn and restrain it in a boom without any new law. (first used: 6. Let automatic stabilizers work with no new law)
discretionary fiscal policy — A deliberate new decision by the legislature to change spending or taxes, as opposed to the automatic changes that happen under existing law. (first used: 6. Let automatic stabilizers work with no new law)
budget deficit — The amount by which government spending exceeds revenue in one year; it is a flow, measured per year, and the government borrows to cover it. (first used: 7. Separate the deficit from the debt: a flow versus a stock)
national debt — The total the government owes at a point in time from past borrowing not yet repaid; it is a stock, and each year's deficit adds to it. (first used: 7. Separate the deficit from the debt: a flow versus a stock)
crowding out — The worry that government borrowing competes with private borrowers for saving, pushes up interest rates, and reduces private investment, offsetting part of a fiscal stimulus. (first used: 8. Weigh the case for and against fiscal stimulus)
policy lags — The delays between a change in the economy and a policy's effect on it: the time to recognize the problem, the time to decide and pass a response, and the time for the response to take effect. (first used: 8. Weigh the case for and against fiscal stimulus)

Summary

Fiscal policy is the legislature's spending and taxes; monetary policy is the central bank's.
Expansionary fiscal policy shifts aggregate demand right; contractionary fiscal policy shifts it left.
The MPC is the share of the next dollar of income that is spent.
The spending multiplier is 1 divided by the saved fraction, 1 minus the MPC.
The tax multiplier is smaller in size, so a tax cut does less per dollar than new spending.
The money multiplier is a banking idea and never answers a fiscal question.
Automatic stabilizers cushion the economy with no new law.
The deficit is a yearly flow; the debt is the stock it adds to.
Keynesian and classical or monetarist economists share the arithmetic and differ on crowding out, lags, and values.

Check your understanding

Work these before looking at the answers — they are ungraded, and the answers (with reasoning) are at the bottom of the page.

In an illustrative island economy (not real data), the MPC is 0.5. Find the spending multiplier, and find how much output rises if the island's government spends 30 billion dollars more on a new harbor.
In the same island economy, the government instead cuts taxes by 30 billion dollars. Find the tax multiplier and the change in output, and compare it with the harbor project.
An illustrative city (not real data) begins the year owing 200 million dollars. It collects 80 million dollars in revenue and spends 95 million. Find the city's deficit for the year and its debt at the end of the year, and say which one is a flow and which is a stock.
Sort each change as an automatic stabilizer or discretionary fiscal policy: (a) unemployment-insurance payments rise as layoffs rise; (b) the legislature votes to fund new school buildings; (c) income-tax collections fall as paychecks shrink in a slump.

Answers (worked reasoning — read after attempting)

The saved fraction is 1 − 0.5 = 0.5, so the spending multiplier is 1 ÷ 0.5 = 2. The change in output is 2 × 30 = 60 billion dollars. In words: the harbor project raises the island's output by 60 billion dollars in the simple model. A student who divides by the MPC gets 1 ÷ 0.5 = 2 here by coincidence, so check the formula, not only the number.
The tax multiplier is −0.5 ÷ (1 − 0.5) = −0.5 ÷ 0.5 = −1. A tax cut is ΔT = −30, so ΔY = −1 × (−30) = 30 billion dollars. The harbor raised output by 60, so the tax cut does 60 − 30 = 30 billion dollars less, because islanders save half of the tax cut before spending any of it.
The deficit is spending − revenue = 95 − 80 = 15 million dollars for the year, a flow. The debt at the end of the year is 200 + 15 = 215 million dollars, a stock. In words: the city borrowed 15 million dollars this year, and its total debt rose to 215 million.
(a) Automatic stabilizer: the payments rise under existing law, with no new vote. (b) Discretionary fiscal policy: the legislature made a new decision. (c) Automatic stabilizer: tax collections fall on their own as incomes fall.

Next up in this module: the Readings & Resources page, the lecture tutorial, the practice set, and the quiz — and next week the midterm review gathers the spending multiplier rule with every model from Weeks 1 to 7.

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