Week 11 · Chapter

Chapter 11 — Monetary Policy, Interest Rates & Aggregate Demand

Principles of Macroeconomics Free sample edition

The module's primary reading · ~35–45 minutes · Objective 7 (explain money, banking, and monetary policy — the functions of money, how fractional-reserve banking creates money and the money multiplier, the Federal Reserve's goals and tools, the money market, and the transmission mechanism from the money supply to interest rates, investment, and aggregate demand), 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 connects the central bank's bond trades to jobs, prices, and output. The path runs through borrowing. When the central bank adds money, interest rates fall, and businesses and families borrow and spend more. That chain of steps is the transmission mechanism (the series of links that carries a central-bank move out to the whole economy). By the end of the week you can say all five links in order, size each one with the course's numbers, run the chain backward, and explain why economists argue about how often a central bank should use it.

Why you already care about this

Picture three people this week. A bakery owner is pricing a new oven that costs 50,000 dollars, paid for with a bank loan. A couple is shopping for a used car with a 20,000-dollar loan. A city developer is deciding whether to break ground on a block of 40 apartments. Not one of them has ever met a central banker. Yet all three are watching the same number: the interest rate. They are illustrative people with made-up numbers, but their choices are real ones.

When that rate falls, the oven, the car, and the apartments all get cheaper to finance. Some plans that did not add up last month suddenly do. When the rate rises, some of those plans go back in the drawer. Multiply those choices across a whole country, and you get a change in total spending big enough to move output and prices.

Last week you watched the Fed buy bonds and push the interest rate from 6% down to 4% in the course's illustrative money market. This week you follow that two-point fall all the way out: through investment, through the spending multiplier, and onto the AD–AS diagram.

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

say the five links of the transmission mechanism in order, with no link skipped;
compute the change in investment from a change in the interest rate, using the course's engineered rule;
compute the change in output with the spending multiplier, and keep it apart from the money multiplier;
name the curve that shifts, its direction, and what happens to the price level and real output;
run the contractionary chain with every arrow reversed;
explain the inside lag, the outside lag, and why expectations can weaken the chain;
lay out the case for fine-tuning and the case for a policy rule at full strength, labelling positive and normative claims.

Carry this line with you: money, rate, investment, multiplier, AD; five links, said in order.

Where we are

Already covered: Week 5, Aggregate Demand & Aggregate Supply, gave you the AD–AS diagram and the habit of naming which curve moves. Week 7, Fiscal Policy, taught the spending multiplier 1 ÷ (1 − MPC). Week 9, Money & the Banking System, built the money supply from the monetary base with the money multiplier 1 ÷ RR. Week 10, The Federal Reserve & Monetary Policy, showed the Fed's tools and the money market, where the money supply sets the interest rate.
This week: the last week of the money unit. You trace how a change in the money supply travels through the interest rate and investment to aggregate demand, the price level, and real output. You also meet the lags and the debate over how actively to use it.
How they connect: this week chains the earlier tools together. Week 10's money market gives you link two, Week 7's multiplier gives you link four, and Week 5's diagram gives you link five.
Where we're going next: Week 12, Inflation, the Phillips Curve & Expectations, asks whether pushing output up with policy buys a lasting drop in unemployment or only higher inflation once expectations catch up.

Three earlier ideas carry this chapter. From Week 5, a shift of aggregate demand to the right raises both the price level and real output; a change in the price level alone is a movement along the curve. From Week 7, the spending multiplier turns one round of new spending into a larger change in output, because each dollar spent becomes someone's income. From Week 10, money demand M_d = 1,200 − 25r meets the vertical money supply M_s at the equilibrium interest rate, and the Fed's bond trades move M_s.

1. Restart from the money market: the Fed buys bonds and the rate falls

Think of the interest rate as the price of borrowing. Like any price, it moves when supply changes. When the Fed adds money to the banking system, borrowing gets cheaper.

You met this market last week. Here is the course's illustrative version, constructed for this course and not real data. Money demand is M_d = 1,200 − 25r, where r is the interest rate in percent. The Fed sets the money supply M_s, drawn as a vertical line.

Worked example — the starting rate and the bond purchase. Start with M_s = 1,050 dollars (Dataset B, illustrative).

Set supply equal to demand. 1,050 = 1,200 − 25r.
Move the r term. 25r = 1,200 − 1,050 = 150.
Solve. r = 150 ÷ 25 = 6%.
The Fed buys bonds. The monetary base rises 105 → 110, so M_s = 10 × 110 = 1,100 dollars.
The new rate. r = (1,200 − 1,100) ÷ 25 = 100 ÷ 25 = 4%.
The size of the move. 6 − 4 = 2, a fall of two percentage points.

In words: the Fed's bond purchase shifts the money supply right, and the interest rate falls from 6% to 4%, a two-point fall.

Picture the graph. The interest rate r runs up the vertical axis and the quantity of money runs along the horizontal axis. Money demand slopes down from upper left to lower right. The money supply is a vertical line. When the Fed buys bonds, the vertical line slides right, and the crossing slides down money demand to a lower rate.

Misconception check. Students often hear "the Fed buys bonds" and think it is tightening, because buying sounds like taking something away. It is the reverse. When the Fed buys a bond, it pays with new reserves, so the money supply rises and the interest rate falls. Buying loosens; selling tightens.

Memory hook: buying bonds loosens; selling bonds tightens.

2. Name the transmission mechanism: five links, said in order

A rate change at the central bank does not reach your paycheck in one jump. It travels like a message passed down a line of people. If anyone in the line drops the message, it never arrives.

The transmission mechanism is the chain of links that carries a monetary-policy move to the whole economy: the money supply moves the interest rate, which moves investment, which the spending multiplier scales into a shift of aggregate demand.

Here are the five links, with arrows meaning "leads to":

The Fed changes the money supply M_s.
→ The interest rate r moves.
→ Investment and other interest-sensitive spending respond, a change written ΔI.
→ The spending multiplier scales that change into a change in output, ΔY.
→ Aggregate demand shifts, and the price level P and real output Y move together.

The rest of this chapter sizes each link with the course's numbers. Notice which tool lives where. The money multiplier 1 ÷ RR belongs to link one, because it turns the monetary base into the money supply. The spending multiplier 1 ÷ (1 − MPC) belongs to link four, because it turns new spending into output.

Misconception check. Students often write "the Fed cut rates, so GDP rose." That is tempting, because it is how headlines talk. But it skips the link that does the work. A lower rate raises output only because someone borrows and spends more. Leave out investment, and you cannot say how much output changes, or why. Say every link, every time.

Memory hook: money, rate, investment, multiplier, AD.

3. Size the investment link: interest-sensitive spending

Go back to the bakery. The owner wants a 50,000-dollar oven and would borrow the full price. Interest is the yearly cost of that loan. The new oven would bring in an extra 2,500 dollars a year in sales of fresh bread. Is it worth it?

Worked example — the bakery's oven at two rates. These numbers are illustrative, constructed for this course and not real data.

Yearly interest at 6%. 0.06 × 50,000 = 3,000 dollars a year.
Compare at 6%. The oven earns 2,500 dollars, and 2,500 − 3,000 = −500 dollars. The loan costs more than the oven earns, so the owner waits.
Yearly interest at 4%. 0.04 × 50,000 = 2,000 dollars a year.
Compare at 4%. 2,500 − 2,000 = 500 dollars. Now the oven earns more than the loan costs, so the owner buys it.

In words: the same oven goes from "not yet" to "yes" when the rate falls from 6% to 4%. Nothing about the oven changed. Only the price of borrowing did.

That bakery is one firm. Across the economy, thousands of firms and households face the same kind of choice. Their purchases have a name.

Interest-sensitive spending is spending that is usually paid for with borrowed money, such as business equipment, new buildings, new homes, and cars bought on credit, so it rises when interest rates fall and falls when they rise.

Business investment is the biggest piece. To size it for the whole economy, the course uses one engineered rule. It is illustrative, built for this course, not a real-world estimate: investment rises 20 billion dollars for each one-point fall in the interest rate.

Worked example — the investment link. The rate fell from 6% to 4% in section 1 (Dataset Q, illustrative).

Size of the fall. 6 − 4 = 2, two percentage points.
Apply the rule. ΔI = 2 × 20 = 40 billion dollars.

In words: the two-point fall in the interest rate raises investment by 40 billion dollars.

Caveat: the real response of investment to a rate cut is not one fixed number. It depends on how confident firms feel and on what else is going on. Section 8 comes back to this.

Misconception check. Students often think a lower interest rate helps only savers or only banks. That is tempting, because "interest" sounds like a banking word. But the rate is a cost for every borrower. When it falls, a firm's oven, a family's car loan, and a developer's apartments all get cheaper to finance, and that spending is what carries the chain forward.

Memory hook: a cheaper loan turns "not yet" into "yes."

4. Size the output link with the spending multiplier

The 40 billion dollars of new investment does not stop where it lands. The oven maker hires workers. The workers spend part of their pay at shops. The shop owners spend part of theirs. You have seen this chain before: it is the spending multiplier from Week 7.

The course's illustrative MPC, the marginal propensity to consume, is 0.8. That means a household spends 80 cents of each extra dollar of income.

Worked example — the output link. Use ΔI = 40 billion dollars and MPC = 0.8 (Dataset Q with Dataset E, illustrative).

The spending multiplier. 1 ÷ (1 − 0.8) = 1 ÷ 0.2 = 5.
The change in output. ΔY = 5 × 40 = 200 billion dollars.
What it measures. The 200 billion dollars is how far aggregate demand shifts right at the old price level.

In words: 40 billion dollars of new investment, passed from paycheck to paycheck, adds 200 billion dollars to the spending the economy demands at the old price level.

Now the trap. This chain has two multipliers in it, and each one has its own job. The money multiplier, 1 ÷ RR = 10, already did its job in link one, turning the monetary base into the money supply. Link four belongs to the spending multiplier.

Misconception check. Students often grab the money multiplier for the output link, because 10 is the multiplier they used most recently. That gives 10 × 40 = 400 billion dollars: 400 versus the correct 200, a 2-fold miss. Ask what is being multiplied. Reserves into money means 1 ÷ RR. Spending into output means 1 ÷ (1 − MPC).

Memory hook: two multipliers, two links: money in link one, spending in link four.

5. Read the last link on the AD–AS diagram

Now put the chain on the diagram you have used since Week 5. Real output Y runs along the horizontal axis. The price level P runs up the vertical axis. Aggregate demand slopes down. Short-run aggregate supply slopes up. Where they cross is the short-run equilibrium.

New investment is new spending at every price level. So the whole aggregate demand curve shifts right, by the 200 billion dollars the multiplier gave you. The short-run aggregate supply curve does not move.

Worked example — reading the diagram. Follow the shift in words.

Name the curve. Aggregate demand.
Name the direction. Right, by 200 billion dollars at the old price level.
Find the new crossing. The economy walks up the short-run aggregate supply curve to a point higher and further right.
Read P and Y. The price level rises, and real output rises.

In words: expansionary monetary policy shifts aggregate demand right, so the price level and real output both rise, together.

This whole sequence has a name.

Expansionary monetary policy is a central-bank move that raises the money supply, such as buying bonds, so the interest rate falls, investment rises, and aggregate demand shifts right; in the short run the price level and real output rise.

Honesty note: because short-run aggregate supply slopes up, part of the push shows up as higher prices rather than more output. The diagram tells you the direction of both; the size of each depends on how steep the supply curve is.

Misconception check. Students often draw a Fed rate cut as a movement along aggregate demand, because Week 5's interest-rate effect also involved interest rates. But that effect came from a change in the price level, which moves you along the curve. Here the price level did not start the story; the Fed did. A change in anything other than P shifts the whole curve, so a rate cut from the Fed shifts aggregate demand.

Memory hook: AD right: P up, Y up, together.

6. Reverse every arrow: contractionary monetary policy

Now run the film backward. Suppose the Fed wants to cool an economy where prices are climbing. It sells bonds. Banks pay for them with reserves, so reserves leave the banking system.

Think of the couple shopping for a used car. Say the car loan is 20,000 dollars (illustrative, not real data). At 6%, a year's interest is 0.06 × 20,000 = 1,200 dollars. At 8%, it is 0.08 × 20,000 = 1,600 dollars, which is 1,600 − 1,200 = 400 dollars more each year. Some couples decide to keep the old car a while longer. Multiply that across the economy, and spending falls.

Worked example — the contractionary chain. The Fed sells bonds (Dataset Q, illustrative).

Money supply. The base falls 105 → 100, so M_s = 10 × 100 = 1,000 dollars.
Interest rate. r = (1,200 − 1,000) ÷ 25 = 200 ÷ 25 = 8%, a rise of 8 − 6 = 2, or two percentage points.
Investment. ΔI = −2 × 20 = −40 billion dollars.
Output. ΔY = 5 × (−40) = −200 billion dollars.
The diagram. Aggregate demand shifts left by 200 billion dollars at the old price level, and the economy walks down the short-run aggregate supply curve.
Check the symmetry. 200 + (−200) = 0, so the two chains are mirror images.

In words: the Fed's bond sale raises the interest rate from 6% to 8%, cuts investment by 40 billion dollars, and shifts aggregate demand left by 200 billion dollars, so the price level and real output both fall.

Contractionary monetary policy is a central-bank move that lowers the money supply, such as selling bonds, so the interest rate rises, investment falls, and aggregate demand shifts left; in the short run the price level and real output fall.

The two directions of the transmission chain, link by link (Dataset Q, illustrative; money in dollars, spending and output in billions of dollars)
Link	Expansionary: the Fed buys bonds	Contractionary: the Fed sells bonds
1. Money supply	Rises, 1,050 to 1,100	Falls, 1,050 to 1,000
2. Interest rate	Falls, 6% to 4%	Rises, 6% to 8%
3. Investment	Rises by 40	Falls by 40
4. Spending multiplier	5 × 40 = 200	5 × 40 = 200, as a fall
5. Aggregate demand	Shifts right; P and Y rise	Shifts left; P and Y fall

Read the table across each row. Every single arrow flips, not only the last one.

Misconception check. Students often flip only the final arrow: they keep "rate down, investment up" and then write "AD left." That is tempting, because the last step is the one the question asks about. But a chain with one flipped link is a broken chain. If the money supply falls, the rate rises, investment falls, output falls, and aggregate demand shifts left. Check each link on its own.

Memory hook: flip one, flip them all.

7. Check who sets what: reserves, not a decree

Headlines say "the Fed raised rates" as if the Fed typed a new number into everyone's loan. That is a handy shortcut, but it hides the mechanism.

Here is what actually happens. The Fed decides on a target and then acts on the banking system. It sets the quantity of reserves through its bond trades, and it sets the rate it pays banks on the reserves they keep at the Fed. Banks then set the rates on loans and deposits, and the market rate follows. In your chain, the interest rate moves because the money supply moved.

Worked example — tracing the cause. A news alert says "Fed policy pushes borrowing costs down." Trace it with the course's model.

What the Fed did. It bought bonds, so reserves and the money supply rose, 1,050 → 1,100 dollars.
What the market did. With more money supplied and money demand unchanged, the crossing slid down money demand, so r fell from 6% to 4%.
What the headline skipped. The rate is a market price that answered the Fed's move, not a number the Fed wrote down.

In words: the Fed moves the quantity of reserves and the rate it pays on them, and the market interest rate follows.

Misconception check. Students often think the Fed sets the interest rate by decree, the way a store sets a price tag. That is tempting, because the news reports a target rate as if it were a rule. But the Fed sets the quantity of reserves and the rate it pays on them; the market rate follows from the money market. If you draw it, you move the vertical money-supply line and read the new rate off the crossing.

Memory hook: the Fed moves the line; the market finds the rate.

8. Name the complications: lags and expectations

The chain on paper takes one page. In the real economy it takes time, and it can weaken along the way. Economists name two delays and one wild card.

Start with the first delay. Before the Fed can act, someone has to notice the problem. Data on output and jobs arrive with a delay and get revised. Then the Fed's committee has to meet and decide.

An inside lag is the time between a change in the economy and a policy decision about it: the time it takes to recognize the problem in the data and to decide on a response.

Here monetary policy has one advantage over fiscal policy. The Fed's committee can act without a new law, so its decision step skips the legislature. In Week 7, by contrast, a tax cut or a spending bill had to pass a vote.

Now the second delay. Even after the Fed acts, the city developer does not pour concrete the next morning. The developer has to redraw the budget, line up a loan, get permits, and hire a crew. Only then does the spending show up in output.

An outside lag is the time between a policy decision and its effect on the economy, while households and firms change their borrowing and spending and output responds.

The outside lag can be long, because firms and households take time to plan, borrow, and build.

Then the wild card: expectations. The chain assumes that a lower rate makes firms borrow more. But a firm borrows to build when it expects customers to show up. If firms expect weak sales, a lower rate may not move them to borrow, so the real chain can be weaker than the engineered rule.

Worked example — the bakery again, with gloomy expectations. Suppose the bakery owner now expects the extra sales from a new oven to be only 1,800 dollars a year, because the neighborhood is losing jobs (illustrative, not real data).

Yearly interest at 4%. 0.04 × 50,000 = 2,000 dollars, as before.
Compare. 1,800 − 2,000 = −200 dollars. The loan still costs more than the oven earns.
Decide. Even at the lower rate, the owner waits.

In words: the same two-point rate cut that tipped the oven decision in section 3 does not tip it now, because the owner's expectations changed.

Caveat: neither lag has one fixed length, and economists disagree about how long each runs. This course names the lags; it does not put a number on them.

Misconception check. Students often treat the five-link chain as instant and automatic, like flipping a light switch. That is tempting, because the arithmetic runs in five quick lines. But each link takes time, and the investment link depends on what borrowers expect. The chain describes the direction policy pushes; the lags and expectations decide how hard and how soon.

Pause and reflect — choose one. Pick either prompt; they count the same.

(a) Think of a big purchase you or your family put off or sped up because of a loan's cost. Which link of the chain were you, and what else besides the rate shaped the choice?
(b) Think of a business near you, such as a shop, a clinic, or a builder. What would it need to expect before a lower interest rate made it borrow to expand?

Memory hook: the chain points the way; lags and expectations set the pace.

9. Weigh fine-tuning against rules

So should the Fed use this chain often, leaning against every wobble in the economy? Or should it follow a steady, announced plan? This is a live debate. Both sides use the same five links and the same diagram. They disagree about lags, about how fast the economy heals itself, and about what matters most.

Fine-tuning is an activist approach to stabilization in which the central bank adjusts policy often, leaning against each gap as it appears, to keep output close to potential.
A policy rule is a predictable guide for setting policy that is announced in advance and followed from one period to the next, offered as an alternative to case-by-case discretion.

The Keynesian case for activism, at full strength. In a recessionary gap, workers and machines sit idle. Wages and prices are sticky, so the economy can stay below potential for a long time on its own. The central bank can move quickly, because its committee needs no new law. Leaning against the gap shortens the time people spend out of work, and that time is a real loss to real families.

The monetarist critique, at full strength. This view is associated with Milton Friedman, who argued that monetary policy works with long and variable lags.

Long and variable lags is the monetarist argument that the effects of monetary policy arrive late and after delays that differ from one episode to the next, so a move made now may land after the economy has already turned.

If that is right, a well-meant move can land late and add to the swings it meant to calm. On that view, a predictable policy rule announced in advance gives households and firms steadier expectations, which can make the economy calmer on its own.

Now separate the two kinds of claims, as the course asks you to every week.

Positive and normative claims on each side of the fine-tuning versus rules debate
Claim	Kind	Which side leans on it
A bond purchase lowers the interest rate and shifts aggregate demand right.	Positive, agreed by both	Both
Monetary policy affects output with lags that vary in length.	Positive, agreed by both	Both
The lags are short enough that a well-timed move usually helps.	Positive, disputed evidence	Keynesian
The lags are long and uncertain enough that active moves often arrive late.	Positive, disputed evidence	Monetarist
Shortening a spell of unemployment is worth the risk of a mistimed move.	Normative	Keynesian
Predictability is worth more than the chance to respond to each wobble.	Normative	Monetarist

Notice that the first two rows are not up for debate. The disagreement lives in how long the lags are, which is a question for evidence, and in how to weigh jobs now against stability later, which is a question of values. This course gives you both columns and leaves the verdict to the evidence and your own values.

Misconception check. Students often decide that one school is right and the other is outdated, usually whichever one they heard first. That is tempting, because a single answer feels tidier. But both sides accept the same chain; they differ on a measurable question and on a value judgment. A strong answer names the agreed ground first, then states each side's best case, then labels which parts are positive and which are normative.

Pause and reflect — choose one. Pick either prompt; they count the same.

(a) Write the strongest one-sentence case for fine-tuning, then the strongest one-sentence case for a rule, and label the normative part of each.
(b) Name one piece of evidence that would move you toward one side, and say whether that evidence is positive or normative.

Memory hook: same chain, different clocks, different values.

Key terms

transmission mechanism — The chain of links that carries a monetary-policy move to the whole economy: the money supply moves the interest rate, which moves investment, which the spending multiplier scales into a shift of aggregate demand. (first used: 2. Name the transmission mechanism: five links, said in order)
interest-sensitive spending — Spending that is usually paid for with borrowed money, such as business equipment, new buildings, new homes, and cars bought on credit, so it rises when interest rates fall and falls when they rise. (first used: 3. Size the investment link: interest-sensitive spending)
expansionary monetary policy — A central-bank move that raises the money supply, such as buying bonds, so the interest rate falls, investment rises, and aggregate demand shifts right; in the short run the price level and real output rise. (first used: 5. Read the last link on the AD–AS diagram)
contractionary monetary policy — A central-bank move that lowers the money supply, such as selling bonds, so the interest rate rises, investment falls, and aggregate demand shifts left; in the short run the price level and real output fall. (first used: 6. Reverse every arrow: contractionary monetary policy)
inside lag — The time between a change in the economy and a policy decision about it: the time it takes to recognize the problem in the data and to decide on a response. (first used: 8. Name the complications: lags and expectations)
outside lag — The time between a policy decision and its effect on the economy, while households and firms change their borrowing and spending and output responds. (first used: 8. Name the complications: lags and expectations)
fine-tuning — An activist approach to stabilization in which the central bank adjusts policy often, leaning against each gap as it appears, to keep output close to potential. (first used: 9. Weigh fine-tuning against rules)
policy rule — A predictable guide for setting policy that is announced in advance and followed from one period to the next, offered as an alternative to case-by-case discretion. (first used: 9. Weigh fine-tuning against rules)
long and variable lags — The monetarist argument that the effects of monetary policy arrive late and after delays that differ from one episode to the next, so a move made now may land after the economy has already turned. (first used: 9. Weigh fine-tuning against rules)

Summary

The transmission mechanism has five links: money supply, interest rate, investment, spending multiplier, aggregate demand.
A Fed bond purchase raises the money supply and lowers the interest rate.
A lower rate raises interest-sensitive spending, led by business investment.
The spending multiplier sizes the output link; the money multiplier belongs to link one only.
Expansionary policy shifts aggregate demand right, so the price level and real output both rise.
Contractionary policy flips every arrow, so the price level and real output both fall.
The Fed sets reserves and the rate it pays on them; the market rate follows.
Inside and outside lags, plus borrowers' expectations, slow and weaken the chain.
Fine-tuning and rules share the model; they differ on lags as evidence and on values as judgment.

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.

Put these scrambled links in the right order for an expansionary move: (a) investment rises; (b) aggregate demand shifts right; (c) the central bank buys bonds and the money supply rises; (d) the spending multiplier scales the new spending; (e) the interest rate falls.
In an illustrative island economy (not real data), a central-bank bond purchase lowers the interest rate from 7% to 4%. Investment there rises 15 billion dollars per one-point fall, and the MPC is 0.75. Find the change in investment, the spending multiplier, and the change in output, and say what happens to aggregate demand.
In an illustrative mountain economy (not real data), a central-bank bond sale raises the interest rate from 5% to 6%. Investment there falls 30 billion dollars per one-point rise, and the MPC is 0.6. Find the change in investment and the change in output, and name the direction of every link.
In an illustrative economy (not real data), the required reserve ratio is 0.125 and the MPC is 0.8. A rate cut raises investment by 25 billion dollars. A classmate multiplies 25 by 8 and reports that output rises 200 billion dollars. Explain the error and give the correct change in output.

Answers (worked reasoning — read after attempting)

The order is (c), (e), (a), (d), (b). The central bank buys bonds, so the money supply rises; the interest rate falls; investment rises; the spending multiplier scales that new spending into output; aggregate demand shifts right. Putting (a) before (e) skips the reason investment rose, which is the cheaper borrowing.
The rate falls by 7 − 4 = 3, so the change in investment is 3 × 15 = 45 billion dollars. The spending multiplier is 1 ÷ (1 − 0.75) = 1 ÷ 0.25 = 4. The change in output is 4 × 45 = 180 billion dollars. Aggregate demand shifts right by 180 billion dollars at the old price level, so the price level and real output both rise.
The rate rises by 6 − 5 = 1, so the change in investment is −1 × 30 = −30 billion dollars. The spending multiplier is 1 ÷ (1 − 0.6) = 1 ÷ 0.4 = 2.5, so the change in output is 2.5 × (−30) = −75 billion dollars. Every link points the contractionary way: the money supply falls, the interest rate rises, investment falls, output falls, and aggregate demand shifts left, so the price level and real output both fall.
The classmate used the money multiplier, 1 ÷ 0.125 = 8, on a spending change. That multiplier belongs to link one, where reserves become money. The output link uses the spending multiplier, 1 ÷ (1 − 0.8) = 5, so output rises by 5 × 25 = 125 billion dollars, not 200.

Next up in this module: the Readings & Resources page, the lecture tutorial, the practice set, and the quiz — and next week the Phillips curve model asks whether the output this chain adds lasts once expectations catch up.

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