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DSE Economics | Monetary Policy: Reserves, the Money Multiplier and Real Interest Rates — Tutor Prep Guide | Three formulas carry the chapter
Students chant that a rate cut stimulates the economy, then freeze when asked who moves first. This lesson draws the chain and names an actor at every step.
Objectives — Students can: (1) use a reserve ratio to find the money multiplier and maximum deposit creation; (2) order the chain from policy rate to interbank rate to best lending rate to spending, and name where it can break; (3) separate nominal from real interest rates and explain why a cut can fail when inflation is high.
01 Prerequisites (3-minute check)
If any of these fails, fix it before the lesson starts.
| Skill | Quick check | Pass mark |
|---|---|---|
| Functions of money | The three functions | Medium of exchange, unit of account, store of value |
| Supply and demand | How a higher rate affects borrowing | Borrowing costs rise, investment demand falls |
| Inflation | Nominal versus real | Real equals nominal minus the change in prices |
02 Lesson flow (45 minutes)
| Time | Stage | Tutor does | Student does |
|---|---|---|---|
| 0-5 min | Open with a ratio | Ask for the multiplier when the reserve ratio is 20% | They answer 0.2 or nothing |
| 5-16 min | Multiplier and deposit creation | 2000 deposited, up to 10000 of deposits | Multiplier 5, created 8000 |
| 16-28 min | The five-step chain | Policy rate, interbank, best lending rate, borrowing, aggregate demand | Every step names an actor |
| 28-38 min | Real interest rate | Nominal 5.0%, inflation 3.0% | Real about 1.94 percent |
| 38-45 min | Limits and exit questions | Liquidity trap, broken links, time lags | All three right |
03 Teaching script (read it out)
Scene 1: The multiplier is the reciprocal of the reserve ratio
A reserve ratio of 20% means 20 of every 100 deposited stays idle and the rest can be lent; lending returns as deposits round after round, so total deposits cap at 5 times the first deposit. 2000 of new deposits supports 10000 of total deposits, of which 8000 is newly created money.
Two limits belong here: the multiplier is a ceiling, not a forecast, because people hold cash; and the ratio is set by the central bank, not by commercial banks.
Two limits belong here: the multiplier is a ceiling, not a forecast, because people hold cash; and the ratio is set by the central bank, not by commercial banks.
Ask the student: if everyone keeps cash at home, is the multiplier still five?
Scene 2: A rate cut is a chain, and every link can snap
First the central bank moves the policy rate; second the interbank rate follows; third the best lending rate and mortgage rates fall; fourth firms and households borrow and spend more; fifth aggregate demand shifts right and output and prices rise.
Numbers first: the policy rate falls from 5.75 to 5.50 percent, a cut of 25 basis points. Any link can break: banks hold their lending rate for margin reasons, firms see weak prospects and refuse to borrow, households are already deleveraging. That sentence, intent is not outcome, is what earns the evaluation marks.
Numbers first: the policy rate falls from 5.75 to 5.50 percent, a cut of 25 basis points. Any link can break: banks hold their lending rate for margin reasons, firms see weak prospects and refuse to borrow, households are already deleveraging. That sentence, intent is not outcome, is what earns the evaluation marks.
Ask the student: a bank receives the rate cut, so why may it still not cut its best lending rate?
Scene 3: The real rate is what decides borrowing
With a nominal 5.0% and inflation at 3.0%, the Fisher relation puts the real rate near 1.94 percent, against a rough 2.0 percent. Under high inflation a nominal 5 percent can be 2 percent real, or negative. That is how a rate cut can coexist with a still-high real rate, and the policy effect is eaten by inflation.
Add the quantity equation: money 400 and velocity 5 give nominal output 2000; money at 440 with velocity unchanged gives 2200. Over long periods, printing money mostly moves prices rather than real output.
Add the quantity equation: money 400 and velocity 5 give nominal output 2000; money at 440 with velocity unchanged gives 2200. Over long periods, printing money mostly moves prices rather than real output.
Ask the student: with 3 percent inflation and a 5 percent nominal rate, what does a saver really earn?
04 Question types and worked steps
| Type | Example | Steps | Answer |
|---|---|---|---|
| Multiplier calculation | Find maximum deposits from a reserve ratio | Multiplier is one over the ratio, then multiply the initial deposit | 20% gives 5 |
| Chain ordering | Sequence policy rate to aggregate demand | Order by market level: central bank, interbank, retail bank, customer, demand | Name the actor at each step |
| Real interest rate | Convert nominal to real | Fisher: (1+i)/(1+pi) minus 1, or the rough i minus pi | About 1.94 percent |
| Policy evaluation | Assess whether a cut works | State intent, name two broken links, then state the condition | Liquidity trap and lags |
Sanity check (teach this): Three figures must cohere: 5 times 2000 is 10000, and minus the principal leaves 8000 created; the real rate of 1.94 percent must sit below the nominal 5.0% when inflation is positive; and the quantity equation moves both sides together, 400 times 5 equals 2000 against 440 times 5 equals 2200. A mismatch means a ratio was added as if it were a percentage.
05 Independent practice (3 questions)
| Question | Answer | What to watch |
|---|---|---|
| With a reserve ratio of 20% and 2000 deposited, what is maximum deposit creation? | 10000 | Whether one over r was used rather than r |
| Nominal 5.0% with inflation 3.0% gives what real rate? | 1.94 percent | Whether inflation was subtracted |
| The bank does not cut its best lending rate after the policy cut. Which link broke? | The retail pricing link | Name the link, not just policy failure |
06 Common mistakes and what to say
| Mistake | Student writes | Say this |
|---|---|---|
| Using the ratio as the multiplier | Answering 0.2 | The multiplier is the reciprocal, not the ratio. |
| Treating the multiplier as certain | Writing that deposits always rise fivefold | It is a ceiling; cash holding and excess reserves pull it down. |
| Confusing nominal and real | Calling 5 percent cheap borrowing with 3 percent inflation | Subtract inflation before judging. |
| Describing intent only | Writing that a cut stimulates the economy and stopping | Name the bank, firm or household step that fails. |
07 Homework (paper, section and question numbers)
- DSE Economics monetary policy practice paper — Questions 1 and 2: multiplier and maximum deposit creation, stating the excess reserve assumption.
- Same paper, chain and evaluation — Question 4: order the five steps and name two broken links; question 5: real rate from 5.0% nominal and 3.0% inflation.
08 Exit check (last 5 minutes)
| Question | Answer | Decision |
|---|---|---|
| Multiplier at a 20 percent reserve ratio | Five | Answering 0.2 means the formula is missing |
| Third link in the chain | Best lending rate and mortgage rates | Missing it means the chain is not formed |
| Real interest formula | (1+i)/(1+pi) minus 1 | Only i minus pi needs the difference explained |
09 Tutor FAQ
Why is the multiplier a ceiling?
The public may hold cash and banks may hold excess reserves; both leakages keep actual deposits below the theoretical maximum.
Does a hike always lower inflation?
Only if transmission works; when inflation is supply driven, a hike suppresses demand with a lag and limited effect.
Why does Hong Kong follow US rates?
Under the linked exchange rate with free capital flow, local rates must track dollar rates or arbitrage moves funds.
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A TutorZone lesson-prep guide. Written by the TutorZone team; questions and lesson flow are original and are not taken from any school or publisher material.