Week 10 · Chapter

Chapter 10 — The Federal Reserve & Monetary Policy

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 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) · 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 the Federal Reserve (the central bank of the United States, often called the Fed) and the interest rates it helps set. The Fed runs monetary policy (changing the amount of money and the cost of borrowing to steer the whole economy). It has a short list of tools, and each one pushes the amount of money in the economy up or down. You will also meet the money market (the picture where the demand for money meets the supply of money), which shows how the amount of money sets an interest rate. By the end of the week you can name each tool, say which way it moves the money supply, and read the new interest rate off the picture.

Why you already care about this

Think about the last time you looked at an interest rate. Maybe it was a car loan at a dealership, a student-loan statement, or the rate a bank pays on a savings account. A single percentage of interest is not small. On a 10,000-dollar loan, one extra percent of interest costs you about 0.01 × 10,000 = 100 dollars in the first year. On a 3,000-dollar savings balance, one extra percent earns you about 0.01 × 3,000 = 30 dollars more.

So who decides whether rates go up or down? Not the bank on the corner by itself, and not the legislature that writes the budget. Much of that decision rests with the Federal Reserve. When the Fed acts, the change ripples into the rates on your loans and your savings.

Last week you saw where money comes from: banks build a large money supply on top of a small monetary base. This week you meet the institution that controls that base, and the model that turns the money supply into an interest rate. In this course's illustrative money market, a money supply of 1,050 dollars sets an interest rate of 6%, and one decision by the Fed can move it to 4% or to 8%.

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

name the three main parts of the Federal Reserve and the goals the law gives it;
connect the dual mandate to the unemployment rate and the inflation rate you learned to compute in Week 3;
explain what happens to bank reserves and the money supply when the Fed buys or sells bonds;
sort the discount rate, the reserve requirement, and interest on reserve balances by which way each moves the money supply;
solve the money market for the equilibrium interest rate and read the new rate after the money supply shifts;
tell a movement along money demand from a shift of money demand.

Carry this line with you: the Fed moves the line; the crossing sets the rate.

Where we are

Already covered: Week 3, Measuring Inflation & Unemployment, taught the unemployment rate and the inflation rate. Week 5, Aggregate Demand & Aggregate Supply, taught the difference between a movement along a curve and a shift of a curve. Week 7, Fiscal Policy, showed how the legislature uses spending and taxes. Week 9, Money & the Banking System, showed how banks turn a monetary base into a larger money supply with the money multiplier 1 ÷ RR.
This week: the second week of the money-and-central-bank unit: who the Fed is, what it is told to aim for, which tools it uses, and how the money market sets an interest rate.
How they connect: the Fed's tools work on the monetary base and the money multiplier from Week 9. Its goals are read with your Week 3 measures. The money market uses the movement-versus-shift habit you practiced on aggregate demand in Week 5.
Where we're going next: Week 11, Monetary Policy, Interest Rates & Aggregate Demand, follows the new interest rate into investment spending and the AD–AS diagram.

Two earlier ideas carry this chapter. From Week 9, the money supply is the money multiplier times the monetary base. With a required reserve ratio of 0.10, the multiplier is 1 ÷ 0.10 = 10, and a monetary base of 105 dollars supports a money supply of 10 × 105 = 1,050 dollars. From Week 5, a change in the thing on a graph's own axis slides you along a curve, while a change in anything else moves the whole curve. Both ideas come back this week.

1. Meet the Federal Reserve: who runs monetary policy

Most countries with their own currency have an institution that looks after the banks and the money supply. Think of it as the bank that banks use. It holds their reserves, it can lend to them, and it decides how much money the system should have.

A central bank is a country's official bank for the banking system and the government, which holds banks' reserves and runs the nation's monetary policy.
The Federal Reserve is the central bank of the United States, often called the Fed; it is made up of the Board of Governors, the regional Reserve Banks, and the Federal Open Market Committee.
Monetary policy is a central bank's use of its tools to change the money supply and interest rates in order to influence the whole economy; it is set by the central bank, not by the legislature.

Here is the Fed's structure, taken from the Fed's own description of itself. It has three main parts.

The Board of Governors is the governing board that leads the Federal Reserve System as a whole, one of the system's three main parts.
The Reserve Banks are the regional banks of the Federal Reserve System, each serving its own part of the country.
The Federal Open Market Committee is the Federal Reserve's policy-making committee, written FOMC, which decides the stance of monetary policy and directs the buying and selling of bonds.

The FOMC's main dial is an interest rate you may have seen in headlines.

The federal funds rate is the interest rate banks charge one another to borrow reserves overnight; the Federal Open Market Committee sets a target for it as its chief way of adjusting policy.

Worked example — fiscal or monetary? Sort three headlines about an illustrative economy by who acts.

"Lawmakers approve a new highway program." Spending is set by the legislature, so this is fiscal policy.
"The central bank's policy committee lowers its interest-rate target." A rate target is set by the FOMC, so this is monetary policy.
"Lawmakers cut the income-tax rate." Taxes are set by the legislature, so this is fiscal policy.

In words: spending and taxes belong to the legislature, and the money supply and interest rates belong to the central bank.

Misconception check. Students often write "the Fed cut spending" or "the Fed raised taxes." That is tempting, because both the Fed and the legislature are part of "the government" in everyday talk. But the Fed has no say over the budget. Fiscal policy is the legislature's spending and taxes. Monetary policy is the central bank's tools. If a sentence mixes them, ask who actually acted.

Memory hook: ask who acted — lawmakers or the central bank.

2. Name the Fed's goals: the dual mandate

Imagine you run a city bus system and the city council gives you two goals: keep as many buses running as possible, and keep fares steady. Sometimes the goals pull together and sometimes they pull apart. The Fed has a similar pair of goals, written into law.

The law directs the Fed to promote maximum employment, stable prices, and moderate long-term interest rates. The first two are named together so often that they have a nickname.

The dual mandate is the two goals the law gives the Federal Reserve that are named together: maximum employment and stable prices; the law also names moderate long-term interest rates.

You already know how to measure both goals yourself. Maximum employment is read with the unemployment rate. Stable prices are read with the inflation rate. You computed both in Week 3.

Worked example — the two readings behind the dual mandate. Use Week 3's illustrative labor market and illustrative market basket (constructed for this course, not real data).

Unemployment rate. The labor market has 6 unemployed people out of a labor force of 120, both counted in millions. The rate is 6 ÷ 120 × 100 = 5%.
Inflation rate. The price index rose from 100 in the base year to 108 in year 2. The rate is (108 − 100) ÷ 100 × 100 = 8%.
Match each reading to a goal. The 5% is the reading the maximum-employment goal watches. The 8% is the reading the stable-prices goal watches.

In words: the Fed's two goals are not vague wishes; each one is tracked by a number you can compute yourself.

Caveat: this chapter states the goals the law gives the Fed. Deciding how much weight each goal should get when they pull apart is a value judgment, and economists and citizens disagree about it. That debate is for the discussion, not for a formula.

Misconception check. Students often read the price index level of 108 as "108% inflation" or "8% inflation this year, no matter what." That is tempting, because the 8 sits right there in the number. But 108 is a level, measured against the base year's 100. The inflation rate is the percentage change between two periods, (108 − 100) ÷ 100 × 100 = 8%, and it is 108 − 100 only because the earlier year is the base year.

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

(a) Think of a job you or someone you know has looked for. In your own words, explain why a central bank would care about how long that search takes across a whole country.
(b) Think of a price you pay often, such as a bus fare or a sandwich. In your own words, explain why steady prices make it easier for a family to plan its budget.

Memory hook: two goals, two numbers: the unemployment rate and the inflation rate.

3. Use the main tool: open-market operations

Picture a regional bank with government bonds in its vault. A bond is a written promise by a borrower, such as the government, to repay a sum of money with interest over a set period; it can be bought and sold before it is repaid. The Fed can buy that bond from the bank, or sell it one of its own.

Open-market operations are the central bank's buying and selling of government bonds; buying adds reserves to banks and raises the money supply, and selling drains reserves and lowers it.

How does the Fed pay for a bond, you might ask? It credits the selling bank's account at the Fed with new reserves. The bank gives up a bond and gets reserves it can lend. Reserves are part of the monetary base, so the base grows. Then the money multiplier from Week 9 does the rest.

Worked example — an open-market purchase. Use the illustrative money-creation numbers (Dataset B, dollars; constructed for this course, not real data). The required reserve ratio is 0.10, so the money multiplier is 10.

Before. The monetary base is 105 dollars, so the money supply is M_s = 10 × 105 = 1,050 dollars.
The purchase. The Fed buys bonds from banks and pays with new reserves. The monetary base rises from 105 to 110 dollars.
After. The money supply is M_s = 10 × 110 = 1,100 dollars.
The change. 1,100 − 1,050 = 50 dollars more money.

In words: when the Fed buys bonds, banks hold more reserves, and the money supply rises from 1,050 to 1,100 dollars.

Worked example — an open-market sale. Start again from a base of 105 dollars (Dataset B, illustrative).

The sale. The Fed sells bonds to banks. Banks pay with their reserves, so reserves leave the banking system. The monetary base falls from 105 to 100 dollars.
After. The money supply is M_s = 10 × 100 = 1,000 dollars.
The change. 1,050 − 1,000 = 50 dollars less money.

In words: when the Fed sells bonds, reserves drain out, and the money supply falls from 1,050 to 1,000 dollars.

In practice (your tools). In Google Sheets, type 100, 105, and 110 in A2 to A4 as three possible monetary bases. In B2 type =10*A2 for the money supply and copy it down to B4. You should see 1,000, 1,050, and 1,100: a sale, the starting point, and a purchase.

Misconception check. Students often say "the Fed buys bonds, so it is spending, so that is fiscal policy." That is tempting, because "buying" sounds like government spending. But the Fed is not buying a road or a school. It trades reserves for a bond, which changes the money supply, so it is monetary policy. A second slip is reading "buying" as tightening. Buying bonds adds reserves and raises the money supply; it loosens.

Misconception check — the wrong multiplier. Students sometimes reach for Week 7's spending multiplier of 5 here. Using it on the new base gives 5 × 110 = 550 dollars, not the 1,100 the money multiplier of 10 gives: 1,100 versus 550, a 2-fold miss. Reserves turning into money is a banking question, so it takes 1 ÷ RR.

Memory hook: buying bonds adds reserves; selling bonds drains them.

4. Sort the other three tools by direction

The Fed has three more tools. You do not need numbers to use them in this course. You need the direction: does your tool push the money supply up or down?

The discount rate is the interest rate the central bank charges banks when it lends them reserves; a lower discount rate makes reserves cheaper to borrow and tends to raise the money supply.
The reserve requirement is the rule, used as a policy tool, that sets how large a share of deposits banks must hold as reserves; raising it shrinks the money multiplier and lowers the money supply.
Interest on reserve balances is the interest rate the Federal Reserve pays banks on the reserves they keep at the Fed; raising it makes holding reserves more attractive than lending and pushes interest rates up.

Think about each tool as if you sat in a bank manager's chair. If borrowing reserves from the Fed gets cheaper, the bank borrows more and lends more. If the rules say keep a bigger slice of each deposit, the bank lends less. If the Fed pays more for reserves parked at the Fed, the bank has less reason to lend them out.

Worked example — raising the reserve requirement. Use the illustrative monetary base of 105 dollars (Dataset B, illustrative).

Before. RR = 0.10, so the money multiplier is 1 ÷ 0.10 = 10 and the money supply is 10 × 105 = 1,050 dollars.
The change. The required reserve ratio rises from 0.10 to 0.20.
After. The money multiplier is 1 ÷ 0.20 = 5, and the base supports at most 5 × 105 = 525 dollars.

In words: doubling the share banks must keep cuts the multiplier from 10 to 5, so the money supply the base can support falls.

Here is your whole tool kit in one place, each tool read for direction only.

Each Federal Reserve policy tool, the action, and its effect on bank reserves, the money supply, and interest rates (directions only)
Tool	Action	Effect on the money supply	Effect on interest rates
Open-market operations	Buy bonds	Up: reserves flow in	Down
Open-market operations	Sell bonds	Down: reserves flow out	Up
Discount rate	Lower it	Up: borrowing reserves is cheaper	Down
Reserve requirement	Raise it	Down: the money multiplier shrinks	Up
Interest on reserve balances	Raise it	Down: banks hold reserves instead of lending	Up

Honesty note: the classroom version of these tools is tidier than the Fed as it now operates. In the United States, required reserve ratios have been zero since March 2020. The Fed now runs an ample-reserves system: banks hold plenty of reserves, and the Fed steers its federal funds rate target in part through interest on reserve balances. Open-market operations and the reserve requirement still teach the mechanism, but the classroom versions are simpler than the way the Fed steers rates day to day.

Misconception check. Students often think a higher reserve requirement lets banks lend more, because "more reserves" sounds like more money in the bank. That is tempting, but the rule works the other way. A higher requirement means banks must keep more of each deposit and can lend less, so the money multiplier shrinks and the money supply falls.

Memory hook: ask the bank manager: cheaper to borrow, lend more; told to keep more, lend less.

5. Build the money market: why money demand slopes down

Picture an illustrative student with 300 dollars that will not be needed for a year (a scenario constructed for this chapter). The student can keep it in checking, where it is easy to spend but earns no interest, or put it in a savings bond that pays interest. If the bond pays 6%, keeping the cash in checking gives up 0.06 × 300 = 18 dollars over the year. If the bond pays 2%, it gives up only 0.02 × 300 = 6 dollars.

That gap is the whole story of money demand. Holding money has an opportunity cost, the interest you give up by not holding a bond. When interest rates are high, that cost is high, so people hold less money. When rates are low, holding money is cheap, so people hold more.

Money demand is the amount of money people want to hold at each interest rate, written M_d; it slopes down because a higher interest rate raises the interest given up by holding money instead of bonds.
The money market is the model in which the demand for money meets the supply of money, with the quantity of money on the horizontal axis and the interest rate on the vertical axis.
The equilibrium interest rate is the interest rate at which the amount of money people want to hold equals the money supply, found where the money demand curve crosses the vertical money supply line.

Your money supply line, M_s, is drawn vertical. Why vertical? Because the amount of money is set by the Fed's tools and the banking system, not by the interest rate. Whatever the rate, the quantity is the same.

Describe the picture to yourself in words. Quantity of money runs along the bottom. The interest rate r runs up the side. Money demand slopes down from upper left to lower right. Money supply stands straight up at the quantity the Fed sets. The crossing point is the equilibrium interest rate.

Worked example — solving the illustrative money market. Money demand is M_d = 1,200 − 25r, with r in percent, and money supply is 1,050 dollars (Dataset B, illustrative).

Set them equal. 1,200 − 25r = 1,050.
Move the r term. 25r = 1,200 − 1,050 = 150.
Solve. r = 150 ÷ 25 = 6, so r is 6%.
Check on money demand. 1,200 − 25 × 6 = 1,200 − 150 = 1,050 dollars, equal to money supply.

In words: at an interest rate of 6%, people want to hold exactly the 1,050 dollars the system supplies, so 6% is the equilibrium interest rate.

In practice (your tools). In Desmos, put the interest rate on the vertical axis by typing y = (1200 - x)/25 for money demand, and type x = 1050 for the vertical money supply line. Click the point where they cross. Desmos shows (1050, 6): a money supply of 1,050 dollars and an interest rate of 6%.

Misconception check. Students often think money demand means "how much money people wish they had," which would be unlimited. That is tempting, because everyone would like more. But money demand is about how much of what you already own you choose to hold as money rather than in bonds. It is a choice about form, not a wish for more wealth, and the interest rate is its price.

Memory hook: holding money costs the interest you skip.

6. Shift money supply and read the new rate

Now let the Fed act while you watch the graph. When the Fed buys bonds, the money supply grows, so the vertical line moves right. People now hold more money than they want at 6%, so they try to buy bonds with it. That pushes interest rates down until people are content to hold the larger amount.

Worked example — after an open-market purchase. The money supply rises from 1,050 to 1,100 dollars (Dataset B, illustrative).

New crossing. Set 1,200 − 25r = 1,100, so r = (1,200 − 1,100) ÷ 25 = 100 ÷ 25 = 4%.
The change. The rate falls from 6% to 4%.

In words: the money supply line shifts right to 1,100, and the equilibrium interest rate falls from 6% to 4%. That is the kind of drop you would notice in the rate on your savings account and on your next loan.

Worked example — after an open-market sale. The money supply falls from 1,050 to 1,000 dollars (Dataset B, illustrative).

New crossing. Set 1,200 − 25r = 1,000, so r = (1,200 − 1,000) ÷ 25 = 200 ÷ 25 = 8%.
The change. The rate rises from 6% to 8%.

In words: the money supply line shifts left to 1,000, and the equilibrium interest rate rises from 6% to 8%.

The illustrative money market at three monetary bases: the money supply and the equilibrium interest rate (Dataset B, dollars and percent)
Fed action	Monetary base	Money supply M_s	Equilibrium interest rate r
Sell bonds	100	1,000	8%
No change	105	1,050	6%
Buy bonds	110	1,100	4%

In practice (your tools). Back in Desmos, replace x = 1050 with x = 10b. Desmos offers a slider for b; set it to run from 100 to 110. Drag it and watch the vertical line slide while the crossing walks along the money demand line: at b = 110 it sits at (1100, 4), and at b = 100 it sits at (1000, 8).

Misconception check. Students often say "the Fed sets the interest rate by decree, like a price tag." That is tempting, because news stories say the Fed "raised rates." But in this model the Fed moves the quantity of money, and the rate is where money demand crosses the new money supply. Even the federal funds rate target is reached by steering reserves and the rate the Fed pays on them; the market rate follows.

Memory hook: more money, lower rate; less money, higher rate.

7. Tell a movement along money demand from a shift

In section 6 the interest rate fell from 6% to 4%. Did money demand change? No. People, you included, slid down the same money demand line to a new point. The rate is on the vertical axis of this very graph, so a change in the rate is a movement along money demand, the same habit you used on aggregate demand in Week 5.

So what does shift your money demand? Something other than the rate. Picture a busy holiday season in an illustrative city: incomes rise and people make more purchases, so they want more money on hand at every interest rate. Or picture prices rising across the board: the same shopping trip takes more dollars. Even a small rise in income or prices means people want to hold a little more of each dollar they own as money, and you have looked at exactly this kind of shift before, on aggregate demand. Either way, money demand shifts right.

Higher income or a higher price level shifts money demand right.
Lower income or a lower price level shifts money demand left.
The Fed's tools shift money supply only.

Worked example — reading a money-demand shift in words. Incomes rise in the illustrative economy while the Fed holds the money supply at 1,050 dollars.

Name the curve. Rising income changes how much money people want at every rate, so money demand shifts.
Name the direction. More buying needs more money on hand, so money demand shifts right.
Read the result. With the vertical money supply fixed at 1,050, the new crossing sits higher, so the equilibrium interest rate rises above 6%.

In words: a rise in income shifts money demand right, and with the money supply unchanged the interest rate rises.

Misconception check. Students often draw an interest-rate change as a shift of money demand. That is tempting, because the rate and money demand appear together in every sentence. But the rate is the graph's own axis. A change in r is a movement along M_d; only a change in income or the price level shifts M_d. Before you move a line, ask what changed: if it was the Fed's tools, move M_s; if it was income or prices, move M_d.

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

(a) In your own words, explain to a friend why a rise in interest rates makes people hold less money, using a savings choice from your own life.
(b) In your own words, explain to a friend how you decide whether a news story moves money demand or money supply.

Memory hook: a rate change slides you along; income or prices move the line.

Key terms

central bank — A country's official bank for the banking system and the government, which holds banks' reserves and runs the nation's monetary policy. (first used: 1. Meet the Federal Reserve: who runs monetary policy)
Federal Reserve — The central bank of the United States, often called the Fed; it is made up of the Board of Governors, the regional Reserve Banks, and the Federal Open Market Committee. (first used: 1. Meet the Federal Reserve: who runs monetary policy)
monetary policy — A central bank's use of its tools to change the money supply and interest rates in order to influence the whole economy; it is set by the central bank, not by the legislature. (first used: 1. Meet the Federal Reserve: who runs monetary policy)
Board of Governors — The governing board that leads the Federal Reserve System as a whole, one of the system's three main parts. (first used: 1. Meet the Federal Reserve: who runs monetary policy)
Reserve Banks — The regional banks of the Federal Reserve System, each serving its own part of the country. (first used: 1. Meet the Federal Reserve: who runs monetary policy)
Federal Open Market Committee — The Federal Reserve's policy-making committee, written FOMC, which decides the stance of monetary policy and directs the buying and selling of bonds. (first used: 1. Meet the Federal Reserve: who runs monetary policy)
federal funds rate — The interest rate banks charge one another to borrow reserves overnight; the Federal Open Market Committee sets a target for it as its chief way of adjusting policy. (first used: 1. Meet the Federal Reserve: who runs monetary policy)
dual mandate — The two goals the law gives the Federal Reserve that are named together: maximum employment and stable prices; the law also names moderate long-term interest rates. (first used: 2. Name the Fed's goals: the dual mandate)
bond — A written promise by a borrower, such as the government, to repay a sum of money with interest over a set period; it can be bought and sold before it is repaid. (first used: 3. Use the main tool: open-market operations)
open-market operations — The central bank's buying and selling of government bonds; buying adds reserves to banks and raises the money supply, and selling drains reserves and lowers it. (first used: 3. Use the main tool: open-market operations)
discount rate — The interest rate the central bank charges banks when it lends them reserves; a lower discount rate makes reserves cheaper to borrow and tends to raise the money supply. (first used: 4. Sort the other three tools by direction)
reserve requirement — The rule, used as a policy tool, that sets how large a share of deposits banks must hold as reserves; raising it shrinks the money multiplier and lowers the money supply. (first used: 4. Sort the other three tools by direction)
interest on reserve balances — The interest rate the Federal Reserve pays banks on the reserves they keep at the Fed; raising it makes holding reserves more attractive than lending and pushes interest rates up. (first used: 4. Sort the other three tools by direction)
money demand — The amount of money people want to hold at each interest rate, written M_d; it slopes down because a higher interest rate raises the interest given up by holding money instead of bonds. (first used: 5. Build the money market: why money demand slopes down)
money market — The model in which the demand for money meets the supply of money, with the quantity of money on the horizontal axis and the interest rate on the vertical axis. (first used: 5. Build the money market: why money demand slopes down)
equilibrium interest rate — The interest rate at which the amount of money people want to hold equals the money supply, found where the money demand curve crosses the vertical money supply line. (first used: 5. Build the money market: why money demand slopes down)

Summary

The Federal Reserve is the U.S. central bank: the Board of Governors, the regional Reserve Banks, and the FOMC.
Monetary policy belongs to the central bank; fiscal policy belongs to the legislature.
The dual mandate is maximum employment and stable prices, read with the unemployment rate and the inflation rate.
Buying bonds adds reserves and raises the money supply; selling bonds drains reserves and lowers it.
A lower discount rate raises the money supply; a higher reserve requirement or higher interest on reserves lowers it.
The Fed now runs an ample-reserves system and steers its rate target in part through interest on reserve balances.
Money demand slopes down because holding money gives up interest; money supply is a vertical line.
The equilibrium interest rate is where money demand crosses money supply.
More money means a lower rate, and less money means a higher rate.
A change in the interest rate is a movement along money demand; only income or the price level shifts it.

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 central bank takes four actions. For each one, name the tool and say whether the money supply rises or falls. (a) It sells government bonds to banks. (b) It raises the interest rate it pays on reserve balances. (c) It lowers the rate it charges banks for loans of reserves. (d) It lowers the share of deposits banks must hold as reserves.
An illustrative island economy (not real data) has a monetary base of 35 dollars, a required reserve ratio of 0.05, and money demand M_d = 800 − 20r, with r in percent. Find the money supply and the equilibrium interest rate. Then the island's central bank buys bonds and the base rises to 36 dollars; find the new money supply and the new rate.
An illustrative river town (not real data) has a labor force of 50,000 people, of whom 2,000 are unemployed, and its price index rose from 125 last year to 130 this year. Find the unemployment rate and the inflation rate, and say which goal of the dual mandate each one speaks to. A classmate says the inflation rate is 30%; explain the slip.
A classmate sees the interest rate in a money-market graph rise from 3% to 5% and draws the money demand line shifting left to show it. Explain the error, and name two different events that could have raised the rate.

Answers (worked reasoning — read after attempting)

(a) Open-market operations: selling bonds drains reserves, so the money supply falls. (b) Interest on reserve balances: banks keep more reserves parked at the central bank instead of lending them. The money supply falls. (c) The discount rate: cheaper loans of reserves let banks lend more, so the money supply rises. (d) The reserve requirement: a lower required share makes the money multiplier bigger, so the money supply rises.
The money multiplier is 1 ÷ 0.05 = 20, so the money supply is 20 × 35 = 700 dollars. Set 800 − 20r = 700, so 20r = 800 − 700 = 100 and r = 100 ÷ 20 = 5%. After the purchase, the money supply is 20 × 36 = 720 dollars, and r = (800 − 720) ÷ 20 = 80 ÷ 20 = 4%. The money supply line shifts right and the rate falls from 5% to 4%.
The unemployment rate is 2,000 ÷ 50,000 × 100 = 4%, the reading for the maximum-employment goal. The inflation rate is (130 − 125) ÷ 125 × 100 = 5 ÷ 125 × 100 = 4%, the reading for the stable-prices goal. The classmate read the level 130 as if it were measured from 100; the rate is the percentage change from last year's 125, not 130 − 100.
A change in the interest rate is a movement along money demand, not a shift of it, because the rate is the graph's own axis. The rate could rise because the central bank sold bonds and the money supply line shifted left, or because incomes or prices rose and the money demand line shifted right. Either way, you first ask which line moved, then read the new crossing.

Next up in this module: the Readings & Resources page, the lecture tutorial, the practice set, and the quiz — and next week the transmission mechanism follows this new interest rate into investment, aggregate demand, and output.

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