Week 8 · Chapter

Chapter 8 — Midterm Review & Exam

Principles of Macroeconomics Free sample edition

The module's primary reading · ~30–40 minutes · Objective 1 (apply the tools of macroeconomic modeling — scarcity, opportunity cost, the production possibilities frontier, and the circular-flow model — and distinguish positive statements (what is) from normative statements (what ought to be)), Objective 2 (measure an economy's output with gross domestic product by the expenditure approach (C + I + G + NX), decide what counts and what does not, distinguish real from nominal GDP, and compute and interpret the GDP deflator), Objective 3 (measure the price level and the labor market — compute and interpret the CPI, the inflation rate, a real wage change, the unemployment rate, and the labor-force participation rate — and classify frictional, structural, and cyclical unemployment), Objective 4 (explain the sources of long-run economic growth and productivity, and compute and interpret growth rates, doubling times by the rule of 70, and per-capita growth), 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), 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)) · Read it early this week, before the review activities and well before the midterm.

In plain language

This week you look back at the first seven weeks and see how they fit together. Each topic so far asks for one calculation, one curve, or one key distinction, such as real versus nominal or a level versus a rate. You also learn one new habit, the flow-vs-stock habit (a one-question check that asks whether a number is an amount per year or an amount at a moment). It sorts a yearly deficit from the debt it adds to, a year's investment from the machines an economy owns, and a year's inflation from the level prices have reached. That habit carries you into the second half of the course, where money and debt take center stage.

Why you already care about this

An illustrative economy you have followed all term produced 1,100 billion dollars of output in one year. An illustrative government budget ran a deficit of 50 billion dollars in one year. That government's debt stood at 1,050 billion dollars when the year ended. Three numbers, three sizes, and one of them is not like the other two.

You have met every one of those figures already. Now picture three reactions to them. A friend at a family dinner says, "The debt is 1,050, so the government borrowed 1,050 this year." A coworker on a lunch break says, "The deficit fell, so the debt must be shrinking." A neighbor reading the news says, "Prices are up 108 percent." Each reaction mixes up a number measured over a year with a number measured at a moment, or a level with a rate.

Each slip is easy to make and easy to fix. This chapter walks back through Weeks 1 to 7, one calculation and one curve per topic, and then gives you a tool for catching that slip before it costs you points on the midterm or sense in a news story.

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

rerun the one calculation each of Weeks 1 to 7 asks for, with every step shown, and say the result in words;
name the curve, the direction, and the new price level and real output for an aggregate demand or short-run aggregate supply shift;
measure a gap in units and as a percentage of potential;
tell a positive statement from a normative one in an applied-policy claim;
sort any economic number as a flow or a stock and say what the flow adds to.

Carry this line with you: a deficit fills the tub; the debt is the water level.

Where we are

Already covered: Weeks 1 to 7 built the macro way of thinking: the frontier and positive versus normative (Week 1), GDP and the deflator (Week 2), the CPI and the labor market (Week 3), growth and the rule of 70 (Week 4), the AD–AS model (Week 5), the business cycle and gaps (Week 6), and fiscal policy and the multiplier (Week 7).
This week: a review of all seven weeks, one calculation and one curve or distinction per topic, plus one new tool, the flow-vs-stock habit, and the midterm.
How they connect: the habit grows out of Week 7's deficit and debt, and it also sorts Week 2's GDP and investment and Week 3's inflation rate and price level.
Where we're going next: Week 9, Money & the Banking System, opens the second half of the course, where the flow-vs-stock habit keeps money, banking, and debt straight.

Week 1 gave you models and the frontier. Weeks 2 to 4 gave you the three big measures: output, prices and jobs, and growth. Weeks 5 to 7 gave you the one diagram the rest of the course runs on, and put government spending and taxes onto it. Every section below reuses a value you have already met, from illustrative datasets constructed for this course, not real data.

1. Read the frontier: points, slope, and the positive-normative line

Picture a town you know that could run its print shops and its repair garages at full tilt, but half of its workers are home with no shifts. The town is not short of people or tools. It is wasting them. That is the first picture macroeconomics gave you.

A production possibilities frontier is a diagram showing the largest combinations of two goods an economy can produce with all of its resources and its current technology.

In the illustrative labor-hours frontier, the economy has 24 million labor-hours. A unit of consumer goods takes 3 hours and a unit of capital goods takes 6 hours. Every combination that uses all the hours sits on the line 3x + 6y = 24, where x counts consumer goods and y counts capital goods, both in millions of units.

Worked example — testing two points. The one calculation Week 1 asks for is plugging a point into the frontier.

The point (4, 2). 3 × 4 + 6 × 2 = 12 + 12 = 24 million labor-hours. That is exactly the 24 available, so the point is on the frontier and efficient.
The point (2, 2). 3 × 2 + 6 × 2 = 6 + 12 = 18 million labor-hours. That is fewer than 24, so the point is inside the frontier.
The idle hours. 24 − 18 = 6 million labor-hours sit unused.

In words: at (2, 2) you could make more of both goods, and the 6 million idle hours are the frontier's picture of unemployment.

The one curve you need is the frontier itself, and its slope is opportunity cost. Moving from (8, 0) to (0, 4) gives up 8 consumer goods to gain 4 capital goods, so one capital good costs 8 ÷ 4 = 2 consumer goods.

Week 1 also gave you one distinction you will need on every policy question. A positive statement is a claim about how the economy is, was, or will be, which evidence can confirm or refute. A normative statement is a claim about how the economy ought to be, which rests on values. "The point (2, 2) leaves 6 million hours idle" is positive; you can check it with arithmetic. "The economy ought to put those hours to work" is normative; it rests on a value judgment, even one most people share.

Misconception check. Students often think a point inside the frontier is "impossible." It is tempting, because the outside points really are out of reach. But (2, 2) is attainable and wasteful; only points outside the line, such as (6, 3), are unattainable. A second trap is reading "positive" as "good" and "normative" as "bad." Positive means testable; normative means value-laden.

Memory hook: inside is wasteful; outside is out of reach.

2. Measure output: GDP by spending, real versus nominal

Every time your family buys groceries, a shop buys a new oven, a city pays a bus driver, or a buyer overseas orders a crate of goods made here, the economy's output shows up as spending. Week 2 added those four kinds of spending into one number.

Gross domestic product is the market value of all final goods and services produced within a country during a given period, such as a year; it is written GDP.

Worked example — the illustrative expenditure account. All values are in billions of dollars: C = 700, I = 200, G = 250, X = 100, and IM = 150.

Net exports first, with the sign. NX = X − IM = 100 − 150 = −50. More came in than went out, a trade deficit.
Add the four parts. GDP = 700 + 200 + 250 − 50 = 1,100.
Say it in words. The economy produced 1,100 billion dollars of final goods and services in the year.

The key distinction you carry from Week 2 is real versus nominal. Nominal GDP values output at the prices of the year it was made, so it rises when output or prices rise. Real GDP values the same output at fixed base-year prices, so it moves only when the amount of output moves. In the account, the same output at base-year prices is 1,000 billion dollars. The GDP deflator compares the two:

(1,100 ÷ 1,000) × 100 = 110.

In words: prices in this economy sit 10 percent above the base year, and 100 of the 1,100 is higher prices, not more stuff.

Misconception check. Students often read a rise in nominal GDP as a rise in real output. It is tempting, because both are called GDP and both are in dollars. But nominal GDP can climb with no extra output at all, if prices alone rise. The cure is to convert to real terms before you compare years. A second trap is adding a trade deficit; net exports of −50 lower GDP.

Memory hook: nominal counts dollars; real counts stuff.

3. Measure prices and jobs: a level versus a rate

Picture your receipt for the same weekly grocery run, kept for two years. The total went up. Week 3 turned that rising total into two different numbers, and mixing them up is a classic slip the midterm checks for.

The Consumer Price Index is a price index that compares the cost of a fixed market basket of goods and services in a given year with the cost of the same basket in the base year, times 100; it is written CPI.
The inflation rate is the percentage change in a price index from one period to the next: the new level minus the old level, divided by the old level, times 100.

Worked example — the illustrative market basket. The basket costs 200 dollars in the base year and 216 dollars in year 2.

The level. CPI = (216 ÷ 200) × 100 = 108. A level carries no percent sign.
The rate. (108 − 100) ÷ 100 × 100 = 8%. A rate carries a percent sign.
Year 3. The CPI reaches 113.4, and the rate from year 2 is (113.4 − 108) ÷ 108 × 100 = 5.4 ÷ 108 × 100 = 5%.

In words: your basket's prices rose 8% in the first year and 5% in the second, and by year 3 the basket costs 13.4 percent more than in the base year. The level kept climbing even as the yearly rate fell.

Jobs work the same way: one rate, one denominator. In the illustrative labor market, 114 million adults are employed and 6 million are unemployed, out of an adult population of 200 million.

Worked example — the labor-market rates. You use one denominator for each rate.

The labor force. 114 + 6 = 120 million people working or looking.
The unemployment rate. 6 ÷ 120 × 100 = 5%, so 5 of every 100 people in the labor force are without work and looking for it.
The participation rate. 120 ÷ 200 × 100 = 60%, so 60 of every 100 adults are working or looking.

A discouraged worker wants a job but has stopped looking, so the survey counts that person as outside the labor force, not as unemployed. If discouraged workers give up, the measured rate can fall with no one hired.

Misconception check. Students often read a CPI of 108 as "8% inflation this year," and then read 113.4 as "13.4% inflation." It is tempting, because 108 − 100 happens to equal the first year's rate. But that shortcut works only in the first year after the base year. The year-3 rate is 5%, not 113.4 − 108 = 5.4. A second trap is dividing the unemployed by the whole adult population; divide by the labor force.

Memory hook: the level has no percent sign; the rate always does.

4. Measure growth: the starting value and the rule of 70

Say your neighborhood bakery, in an illustrative example, sold 800 loaves last month and 840 this month. By how much did it grow? Week 4 answered with one rule about which number goes on the bottom.

A growth rate is the percentage change in a quantity from one period to the next, found as the new value minus the old value, divided by the old (starting) value, times 100.

Worked example — the illustrative growth economy. Real GDP rises from 800 billion to 840 billion dollars.

The change. 840 − 800 = 40.
Divide by the starting value. 40 ÷ 800 × 100 = 5%.
Say it in words. The economy produced 5 percent more real output than the year before.

Dividing by the new value instead, 40 ÷ 840 × 100 ≈ 4.76%, is the wrong-base error. It understates growth.

The rule of 70 is a shortcut that estimates doubling time as about 70 divided by the growth rate in percent; it is an approximation, close for the small rates economies usually grow at. At 7% growth, 70 ÷ 7 = 10 years to double. Honesty note: the rule gives "about," never "exactly," so write the answer with the word about.

Misconception check. Students often multiply instead of divide, and write 70 × 7 = 490 "years." It is tempting, because the rule has two numbers and a rate in it. The check is common sense: faster growth must mean a shorter doubling time, so the rate goes on the bottom.

Memory hook: divide by where you started, not where you ended.

5. Shift the AD–AS model and size the gap

Picture your city announcing a big road project. Crews are hired, suppliers get orders, and the crews spend their pay at shops and cafés. Prices and output in the city both start to climb. Weeks 5 and 6 gave you the picture that explains why, and the habit that reads it.

On the AD–AS diagram, real output Y (real GDP in billions of dollars) runs across, and the price level P (an index) runs up. Comparative statics is the habit of comparing two equilibriums before and after one change: name the curve that moves, name the direction, then read the new price level and real output.

Worked example — the illustrative linear pair. Aggregate demand is P = 20 − Y⁄100 and short-run aggregate supply is P = 4 + Y⁄100.

Before. Setting the curves equal, 20 − Y⁄100 = 4 + Y⁄100, gives Y = 800 and P = 12.
Name the curve and the direction. Government spending rises, so aggregate demand shifts right, to P = 22 − Y⁄100.
After. The new crossing is Y = 900 and P = 13.
Read the change. Output rose 900 − 800 = 100 billion dollars, and the price level rose 13 − 12 = 1 index point.

In words: you named aggregate demand, it shifted right, and real output and the price level rose together, walking up the fixed short-run aggregate supply line. A short-run aggregate supply shift is different: it moves P and Y apart, as in an oil-price shock where prices rise and output falls.

Week 6 added where the crossing sits. Potential output is the real output an economy can produce when its labor, capital, and technology are in normal, full use, and the vertical long-run aggregate supply line stands there. A recessionary gap is the shortfall of actual output below potential output.

Worked example — the illustrative gap. Potential output is 1,000 billion dollars and actual output is 950.

In units. 1,000 − 950 = 50 billion dollars.
As a percentage of potential. 50 ÷ 1,000 × 100 = 5% of potential.

In words: the economy is producing 50 billion dollars less than its idle workers and machines could make, a recessionary gap of 5% of potential.

Misconception check. Students often draw a change in the price level as a shift of aggregate demand. It is tempting, because the price level is right there on the axis. But a price-level change is a movement along a curve; only something other than P, such as government purchases, shifts the whole line. A second trap is reporting the gap as a bare 50; every gap needs its units and its percentage of potential.

Memory hook: a price-level change slides along; anything else shifts the line.

6. Use the fiscal tools: the multiplier and the two cases

When a road crew gets paid, the crew spends part of its pay at a café, and the café owner spends part of hers at a hardware store. One dollar of new spending turns into several dollars of income. Week 7 put a number on that chain.

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.

Worked example — the illustrative multiplier. The marginal propensity to consume, MPC, is 0.8, and government purchases rise by ΔG = 20 billion dollars.

The multiplier. 1 ÷ (1 − 0.8) = 1 ÷ 0.2 = 5.
The change in output. ΔY = 5 × 20 = 100 billion dollars.
Say it in words. A 20 billion road project raises output by 100 billion dollars in the simple model, and aggregate demand shifts right.

Dividing 1 by the MPC itself, 1 ÷ 0.8 = 1.25, is the classic slip. The wrong 1.25 versus the right multiplier of 5 is a 4-fold gap, so the slip badly understates the effect you are trying to measure. Expansionary fiscal policy, more spending or lower taxes, shifts aggregate demand right; contractionary fiscal policy, less spending or higher taxes, shifts it left.

Caveat: the simple multiplier is a model. Taxes and imports leak out of each round, so the real-world multiplier is smaller, and how much smaller is a question economists still study.

Week 7 also left you with a debate, and your job is to keep both sides at full strength. The Keynesian case says that in a recessionary gap, idle workers and machines can be put back to work, crowding out is small, and waiting leaves the gap open longer. The classical and monetarist case for caution says government borrowing can push up interest rates and crowd out private investment, policy lags can make the help land late, and every deficit adds to the debt. Which risk weighs more is a normative judgment resting on values and on how you read the evidence; this course hands down no verdict.

Misconception check. Students often grab the money multiplier, 1 ÷ RR, for a fiscal-policy question. It is tempting, because both are called multipliers. But 1 ÷ RR belongs to banking, which starts next week, and never answers a question about government spending. The fiscal multiplier is 1 ÷ (1 − MPC).

Memory hook: spending ripples; the money multiplier waits for the banks.

7. Sort flows from stocks: the habit for the second half

Picture a bathtub with the faucet running. You can describe the water two ways, and you will need both. One is how fast it pours in, a number per minute. The other is how high it stands right now, a number at one moment. Both are true, and they answer different questions.

That is the one new tool this week.

A flow is an amount measured per period of time, such as a year's GDP, a year's investment, a year's budget deficit, or a year's inflation rate; it only makes sense with a time period attached.
A stock is an amount measured at a point in time, such as the national debt at the end of a year, the capital stock, or the price level; flows over a period raise or lower it.
The flow-vs-stock habit is a one-question check run on any economic number: whether it needs a period such as "per year" to make sense, which makes it a flow, or a moment such as "at the end of the year," which makes it a stock.

Three pairs you met in the first half of the course show the habit at work.

Worked example — three flows and the stocks they feed. You sort each number by asking whether it needs "per year" or "as of."

The budget. Spending − revenue = 450 − 400 = 50 billion dollars for the year. The deficit is a flow. It raises the debt from 1,000 to 1,000 + 50 = 1,050 billion dollars at the end of the year. The debt is a stock.
Investment. In the expenditure account, investment is 200 billion dollars in one year. That is a flow of new machines, equipment, and buildings. It adds to the capital stock, the total amount of machines, equipment, and buildings an economy has at a point in time; each year's investment adds new capital goods to it. The capital stock is a stock.
Prices. Inflation of 8% from the base year to year 2 is a flow, a rate of change over a year. The CPI of 108 is the price level in year 2, a stock-like level. In year 3 the flow is 5% and the level is 113.4: the level keeps what every past year added.

In words: each flow you meet is a "per year" number that changes a stock, and each stock is an "as of" number that the flows have built up.

Now you can go back to the three reactions from the opening. The dinner remark reads a stock as if it were a flow. The debt of 1,050 is everything still owed as of the end of the year; only the deficit of 50 was borrowed during the year. The lunch-break remark confuses a smaller flow with a falling stock: a smaller deficit still adds to the debt, so the debt keeps growing, only more slowly. The news remark reads a level of 108 as a rate; the rate was 8%.

Limitation: the habit does not tell you whether a debt is too large or a deficit too risky. Those are questions economists argue about, and some of the argument is normative. The habit only makes sure you know which kind of number you are arguing over.

Pause and think. Choose one of these two prompts and answer it in a few sentences of your own.

(a) Name one flow and one stock in your own money life, such as a paycheck and a savings balance, and say how the flow changes the stock over a month.
(b) Find one number in a recent headline about the economy. Say whether it is a flow or a stock, and what words in the headline tell you which.

Misconception check. Students often think a falling deficit means a falling debt. It is tempting, because "the deficit is down" sounds like good news about borrowing. But as long as the deficit is above zero, the government still borrows that year, and the debt still rises. Turning the faucet down is not the same as draining the tub.

The midterm checks Weeks 1 to 7, Objectives 1 to 6, as they were taught. As the syllabus states, AI is not permitted on the midterm; it confirms that you personally can compute the measures, read the curves, and say what the results mean.

Memory hook: ask "per year?" or "as of?" — then compare.

Key terms

Production possibilities frontier — A diagram showing the largest combinations of two goods an economy can produce with all of its resources and its current technology. (first used: 1. Read the frontier: points, slope, and the positive-normative line)
Positive statement — A claim about how the economy is, was, or will be, which evidence can confirm or refute. (first used: 1. Read the frontier: points, slope, and the positive-normative line)
Normative statement — A claim about how the economy ought to be, which rests on values and cannot be settled by evidence alone. (first used: 1. Read the frontier: points, slope, and the positive-normative line)
Gross domestic product — The market value of all final goods and services produced within a country during a given period, such as a year; it is written GDP. (first used: 2. Measure output: GDP by spending, real versus nominal)
Consumer Price Index — A price index that compares the cost of a fixed market basket of goods and services that households buy in a given year with the cost of the same basket in the base year, times 100; it is written CPI. (first used: 3. Measure prices and jobs: a level versus a rate)
Inflation rate — The percentage change in a price index from one period to the next: the new level minus the old level, divided by the old level, times 100. (first used: 3. Measure prices and jobs: a level versus a rate)
Growth rate — The percentage change in a quantity from one period to the next, found as the new value minus the old value, divided by the old (starting) value, times 100. (first used: 4. Measure growth: the starting value and the rule of 70)
Comparative statics — The habit of comparing two equilibriums before and after one change: name the curve that moves, name the direction, then read the new price level and real output. (first used: 5. Shift the AD–AS model and size the gap)
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: 6. Use the fiscal tools: the multiplier and the two cases)
Flow — An amount measured per period of time, such as a year's GDP, a year's investment, a year's budget deficit, or a year's inflation rate; it only makes sense with a time period attached. (first used: 7. Sort flows from stocks: the habit for the second half)
Stock — An amount measured at a point in time, such as the national debt at the end of a year, the capital stock, or the price level; flows over a period raise or lower it. (first used: 7. Sort flows from stocks: the habit for the second half)
Flow-vs-stock habit — A one-question check run on any economic number: whether it needs a period such as "per year" to make sense, which makes it a flow, or a moment such as "at the end of the year," which makes it a stock. (first used: 7. Sort flows from stocks: the habit for the second half)
Capital stock — The total amount of machines, equipment, and buildings an economy has at a point in time; each year's investment adds new capital goods to it. (first used: 7. Sort flows from stocks: the habit for the second half)

Summary

Week 1: inside the frontier is wasteful; outside is out of reach.
Week 2: GDP adds C, I, G, and NX; compare years in real terms.
Week 3: the CPI is a level; inflation is a rate.
Week 4: divide growth by the starting value; the rule of 70 is approximate.
Weeks 5 and 6: name the curve, the direction, the new P and Y.
Week 7: the spending multiplier is one over one minus the MPC.
New: a flow is per year; a stock is as of a moment.
New: a deficit adds to the debt, even when the deficit shrinks.

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.

An illustrative island economy (not real data) has household spending of 60, business investment of 15, government purchases of 20, exports of 10, and imports of 25, all in millions of dollars. Find its GDP, and say what the sign of net exports does to the total.
An illustrative town's price index (not real data) reads 125 one year and 130 the next. Is 130 a level or a rate? Find the inflation rate between the two years.
In an illustrative economy (not real data) with an MPC of 0.75, the government cuts its purchases by 12 billion dollars. Find the change in output, and name the curve that moves and its direction.
Sort each item as a flow or a stock: (a) a family's 3,000 dollars of take-home pay last month; (b) the 18,000 dollars left on a car loan today; (c) a shop's 40 new chairs bought this year; (d) the 400 chairs the shop owns now.

Answers (worked reasoning — read after attempting)

Net exports first: 10 − 25 = −15. Then GDP = 60 + 15 + 20 − 15 = 80 million dollars. The negative sign means the island bought more from abroad than it sold abroad, so net exports lower GDP; adding 15 instead would overstate output by 30.
130 is a level; it carries no percent sign. The rate is (130 − 125) ÷ 125 × 100 = 5 ÷ 125 × 100 = 4%. Subtracting 130 − 125 = 5 gives index points, not the rate.
The multiplier is 1 ÷ (1 − 0.75) = 1 ÷ 0.25 = 4. The change in output is ΔY = 4 × (−12) = −48 billion dollars. Aggregate demand shifts left, so real output and the price level both fall. Using 1 ÷ 0.75 by mistake would give a multiplier of about 1.33 and badly understate the drop.
(a) is a flow, pay per month. (b) is a stock, the amount owed as of today. (c) is a flow, investment during the year. (d) is a stock, the chairs owned now; the 40 new chairs are part of what built it up.

Next up in this module: the lecture, the slide deck, the Readings & Resources page, the practice set, the discussion, and the midterm — and next week the flow-vs-stock habit meets Money & the Banking System, where a new model shows how banks create money.

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