Money and Banking — Diagnostic Tests

Unit Tests

UT-1: Money Creation and the Money Multiplier

Question: A banking system has a required reserve ratio of 10%. A customer deposits \1000$ of cash into Bank A. (a) Calculate the maximum possible expansion of the money supply. (b) Show the first three rounds of the money creation process in a table. (c) What is the money multiplier? (d) Explain two leakages that would reduce the actual money creation below the theoretical maximum.

Solution:

(a) Maximum expansion = \frac{\1000\}\\{0.10\\} = $10,000$ (including the initial deposit).

(b) | Round | Deposit | Required Reserves | Loans | |---|---|---|---| | 1 | \1000$|$$100$|$$900$| | 2 |$$900$|$$90$|$$810$| | 3 |$$810$|$$81$|$$729$ |

Total after 3 rounds: Deposits = 1000 + 900 + 810 = \2710$. Loans$= 900 + 810 + 729 = $2439$.

(c) Money multiplier $= \frac{1}{rrr} = \frac{1}{0.10} = 10$.

(d) Two leakages:

1. Excess reserves: Banks may choose to hold more reserves than required (precautionary motive), especially during economic uncertainty. These reserves are not lent out, reducing the multiplier.
2. Cash leakages: When borrowers receive loans, they may withdraw some as cash rather than redepositing it. Cash held outside the banking system cannot be multiplied through lending.

UT-2: Functions of Money and Inflation

Question: (a) Identify and explain the three functions of money with a specific example for each. (b) If the money supply grows at 15% per year while real GDP grows at 3% per year, use the quantity theory of money to predict the inflation rate. (c) Explain why hyperinflation (e.g., prices doubling every month) causes money to lose its functions.

Solution:

(a) Three functions of money:

1. Medium of exchange: Money eliminates the need for double coincidence of wants inherent in barter. Example: A baker buys flour from a miller using money, without needing to find a miller who wants bread.
2. Unit of account: Money provides a standard measure of value, allowing prices to be expressed in a common unit. Example: A smartphone costs \5000$and a meal costs$$100$, making it easy to compare values.
3. Store of value: Money allows purchasing power to be saved and used in the future. Example: A worker saves \2000$ per month in a bank account to buy a car next year.

(b) Quantity theory: $MV = PY$. If velocity $V$ is constant: growth rate of $M$ $=$ growth rate of $P$ $+$ growth rate of $Y$. $\hat{M} = \hat{P} + \hat{Y}$. $15\% = \hat{P} + 3\%$, so $\hat{P} = 12\%$.

Predicted inflation rate: 12%.

(c) During hyperinflation:

• Medium of exchange: People refuse to accept money because it loses value between the time of transaction agreement and actual payment. They switch to barter or foreign currency.
• Unit of account: Prices change so rapidly that accounting in the domestic currency becomes meaningless. Firms may price in stable foreign currencies.
• Store of value: Money's purchasing power evaporates. Holding cash means guaranteed losses. People spend money immediately or convert to real assets.

UT-3: Interest Rate Determination

Question: The demand for money (liquidity preference) is $L = 500 - 20i + 0.5Y$, where $i$ is the interest rate (in %) and $Y$ is real income. The money supply is fixed at \600$billion. (a) Calculate the equilibrium interest rate when$Y = 1000$. (b) If the central bank increases the money supply to$$700$B, calculate the new equilibrium interest rate. (c) If real income rises to$Y = 1200$ with the original money supply, what happens to the interest rate? Explain the mechanism.

Solution:

(a) Equilibrium: $L = M_s$. $500 - 20i + 0.5(1000) = 600$. $500 - 20i + 500 = 600$. $1000 - 20i = 600$. $20i = 400$. $i = 20\%$.

(b) $500 - 20i + 500 = 700$. $1000 - 20i = 700$. $20i = 300$. $i = 15\%$.

The interest rate falls from 20% to 15% as the increased money supply creates an excess supply of money, causing people to buy bonds, driving bond prices up and yields (interest rates) down.

(c) $500 - 20i + 0.5(1200) = 600$. $500 - 20i + 600 = 600$. $1100 - 20i = 600$. $20i = 500$. $i = 25\%$.

Higher income increases the transactions demand for money (people need more cash for day-to-day transactions). With a fixed money supply, this excess demand for money causes people to sell bonds, driving bond prices down and interest rates up (from 20% to 25%).

---

Integration Tests

IT-1: Banking System and Monetary Policy (with Fiscal Policy)

Question: The central bank wants to stimulate the economy but the government is simultaneously running a large budget deficit. The required reserve ratio is 12.5%, and banks hold \200$B in required reserves with no excess reserves. (a) Calculate the current money supply. (b) The central bank buys$$10$B of government bonds. Calculate the maximum change in the money supply. (c) Explain how the government's bond issuance to finance its deficit might counteract the central bank's expansionary policy (crowding out through the banking system). (d) If the government finances its deficit by borrowing from the central bank, what is this called and what is the risk?

Solution:

(a) Money supply = \frac{\text{Reserves}}{ ext{rrr}} = \frac{200}{0.125} = \1600$B.

(b) \10$B open market purchase increases reserves by$$10$B. Maximum change$= \frac\\{10\\}\\{0.125\\} = $80$B. New money supply$= 1600 + 80 = $1680$B.

(c) When the government issues bonds to finance its deficit, it competes with the private sector for loanable funds. Banks that buy government bonds have fewer funds available for private lending. This absorbs bank reserves that could otherwise support money creation through the multiplier process. The government's borrowing may push up interest rates, partially offsetting the central bank's attempt to lower them. This is a form of financial crowding out.

(d) When the government borrows directly from the central bank (the central bank creates new money to buy government bonds), this is called monetising the debt or quantitative easing (when done on a large scale). The risk is inflation: the money supply increases without a corresponding increase in output, leading to excess demand and rising prices. If done excessively, it can lead to hyperinflation. This is why many central banks have operational independence from the government.

IT-2: Inflation and Interest Rates (with National Income)

Question: An economy has: nominal GDP = \2000$B, real GDP$= $1600$B, money supply$= $800$B. (a) Calculate the GDP deflator, inflation rate (base year deflator was 100), and velocity of money. (b) If the central bank targets 2% inflation and real GDP is expected to grow at 4%, calculate the required money supply growth rate. (c) A bank offers a nominal interest rate of 8% on deposits. Calculate the real interest rate. (d) If inflation unexpectedly rises to 10%, who benefits and who loses from this loan contract?

Solution:

(a) GDP deflator $= \frac{2000}{1600} \times 100 = 125$. Inflation $= \frac{125 - 100}{100} = 25\%$. Velocity $= \frac{\text{PY}}{ ext{M}} = \frac{2000}{800} = 2.5$.

(b) $\hat{M} = \hat{P} + \hat{Y}$ (assuming constant velocity). $\hat{M} = 2\% + 4\% = 6\%$. The money supply should grow at 6%.

(c) Real interest rate $= nominal rate - expected inflation = 8\% - 25\% = -17\%$. Depositors are effectively losing 17% of their purchasing power.

(d) With actual inflation at 10%: real interest rate $= 8\% - 10\% = -2\%$. Borrowers benefit (they repay loans in dollars worth less than when they borrowed) and lenders/depositors lose (they receive repayments with reduced purchasing power). This redistribution from lenders to borrowers is a key consequence of unexpected inflation and explains why lenders demand inflation premiums and why inflation uncertainty is harmful to financial markets.

IT-3: Financial Intermediation and Market Failure (with Market Failure)

Question: Banks perform financial intermediation, transforming short-term deposits into long-term loans. (a) Explain the problem of asymmetric information in banking, identifying both adverse selection and moral hazard. (b) A bank has deposits of \500$B, reserves of$$50$B, and loans of$$450$B. The required reserve ratio is 8%. Calculate: actual reserve ratio, excess reserves, and the maximum additional lending. (c) Explain how a bank run can occur and why deposit insurance addresses a market failure. (d) How does this relate to the concept of confidence in the monetary system?

Solution:

(a) Adverse selection occurs before a loan is made: borrowers with the riskiest projects are the most eager to seek loans because they have the most to gain if the project succeeds and limited liability if it fails. Banks cannot perfectly distinguish risky from safe borrowers. This leads to a higher average risk of loan applicants than the population as a whole.

Moral hazard occurs after a loan is made: once borrowers receive funds, they may engage in riskier behaviour than the bank agreed to (e.g., investing in speculative projects), because the bank bears part of the loss if the project fails while the borrower captures the upside.

(b) Actual reserve ratio $= 50/500 = 10\%$. Required reserves = 0.08 \times 500 = \40$B. Excess reserves$= 50 - 40 = $10$B. Maximum additional lending$= $10$B (these excess reserves can be lent out directly, subject to the multiplier process).

(c) A bank run occurs when depositors lose confidence in a bank's ability to repay their deposits. Since banks lend out most deposits (fractional reserve banking), they cannot repay all depositors simultaneously. When some depositors withdraw, others fear the bank will run out of reserves, creating a self-fulfilling panic. This is a market failure because individual rational behaviour (withdrawing deposits) leads to collectively irrational outcomes (bank failure, loss of value for all).

Deposit insurance (e.g., the Deposit Protection Scheme in Hong Kong, covering up to HK$500,000) eliminates the incentive to run: even if the bank fails, insured depositors will be repaid. This prevents self-fulfilling panics and protects the stability of the financial system.

(d) Confidence is fundamental to the monetary system. Money has value only because people believe others will accept it. Similarly, banks function only because depositors trust them to safeguard deposits. When confidence collapses (as in a bank run), the system breaks down rapidly. Deposit insurance, central bank lending as lender of last resort, and regulatory oversight all serve to maintain this confidence -- they are public goods that the private market would underprovide without government intervention.

Additional DSE Exam-Style Questions

EQ-1: Money Multiplier with Multiple Leakages

Question: A banking system has a required reserve ratio of 8%. Banks also hold excess reserves equal to 2% of deposits, and the public holds cash equal to 15% of deposits. (a) Calculate the effective money multiplier. (b) If the central bank injects \50$billion of new reserves through open market operations, calculate the maximum change in: (i) the monetary base, (ii) bank deposits, (iii) the broad money supply ($M2$). (c) If the public's currency ratio rises to 20% due to loss of confidence, recalculate the multiplier and explain the effect on the money supply.

Solution:

(a) The money multiplier accounting for excess reserves ($er$) and the currency-deposit ratio ($cr$):

$m = \frac{1 + cr}{rrr + er + cr} = \frac{1 + 0.15}{0.08 + 0.02 + 0.15} = \frac{1.15}{0.25} = 4.6$

(b) (i) Monetary base change = \50$ billion (the OMO directly changes reserves, part of the monetary base).

(ii) Deposits increase by \frac{1}{rrr + er + cr} \times \Delta R = \frac{1}{0.25} \times 50 = \200$ billion.

(iii) Broad money supply change = m \times \Delta B = 4.6 \times 50 = \230$ billion.

(c) With $cr = 0.20$:

$m = \frac{1 + 0.20}{0.08 + 0.02 + 0.20} = \frac{1.20}{0.30} = 4.0$

The multiplier falls from 4.6 to 4.0. The increase in the currency ratio means more money is held as cash outside the banking system, where it cannot be multiplied through lending. This is a leakage that reduces the effectiveness of monetary policy. If the central bank injected \50$B, the broad money supply would now increase by only$4.0 \times 50 = $200$billion instead of$$230$billion -- a reduction of$$30$ billion. This illustrates why confidence shocks can be self-reinforcing: higher cash withdrawals reduce the multiplier, contracting the money supply further.

EQ-2: Hong Kong's Currency Board System

Question: Hong Kong operates a Currency Board system pegging the HKD at 7.8 per USD. The HKMA's Exchange Fund holds US$180 billion in reserves. The monetary base is HK$1,500 billion. (a) Calculate the backing ratio and assess its adequacy. (b) If there is a capital outflow of US$5 billion, explain the automatic adjustment mechanism and calculate the change in the monetary base. (c) Suppose the HKMA decides to sell HK$20 billion of Exchange Fund Bills. Calculate the effect on the monetary base and explain why this is contractionary. (d) Evaluate whether Hong Kong should switch to a free-floating exchange rate.

Solution:

(a) The monetary base of HK$1,500 billion requires backing of$1500 / 7.8 = \text\\{US\\}$192.3$billion at the 7.8 peg. The actual reserves are US$180 billion.

Backing ratio $= 180 / 192.3 = 93.6\%$.

The backing ratio is below 100%, which may appear concerning. However, Hong Kong's full backing requirement applies to the Certificates of Indebtedness (which back banknotes), not the entire monetary base. The HKMA also earns investment returns on its reserves, and the Convertibility Zone (7.75--7.85) provides a buffer. The system remains credible as long as the market believes the HKMA can defend the peg.

(b) When US$5 billion flows out: investors sell HKD for USD. The HKMA buys HKD and sells USD from reserves to maintain the peg.

Change in monetary base = -5 \times 7.8 = -\text{HK}\39$ billion.

New monetary base = 1500 - 39 = \text{HK}\1,461$ billion.

The automatic contraction of the monetary base raises Hong Kong interest rates, which attracts capital back, stabilising the exchange rate. This is the self-correcting mechanism of the Currency Board.

(c) Selling HK$20 billion of Exchange Fund Bills absorbs HK$20 billion of liquidity from the banking system. The monetary base falls by HK$20 billion.

New monetary base = 1500 - 20 = \text{HK}\1,480$ billion.

This is contractionary because it reduces bank reserves, limiting banks' ability to lend and pushing up interbank interest rates (HIBOR).

(d) Arguments for keeping the peg:

• Provides exchange rate stability for trade (Hong Kong's trade-to-GDP ratio exceeds 300%), reducing transaction costs and uncertainty for importers and exporters.
• Anchors inflation expectations by tying monetary policy to the Federal Reserve, which has a strong inflation-fighting record.
• Maintains investor confidence; switching to a float could trigger capital flight and a sharp depreciation.

Arguments for switching to a float:

• Monetary policy would become independent, allowing the HKMA to set interest rates appropriate for Hong Kong's economic cycle rather than the US cycle.
• The US and Hong Kong economies are increasingly decoupled; US rate hikes designed to cool the US economy may unnecessarily contract Hong Kong's economy.
• Reserves could be used for domestic purposes rather than defending the peg.

Evaluation: For Hong Kong, the benefits of stability outweigh the costs of lost monetary independence. Hong Kong's role as an international financial centre depends on exchange rate certainty. The Currency Board has survived multiple crises (1997 Asian Financial Crisis, 2008 GFC, 2019 social unrest, COVID-19) and remains credible. A sudden switch would be highly disruptive.

EQ-3: Monetary Policy and the Transmission Mechanism in Hong Kong

Question: The US Federal Reserve raises the federal funds rate by 0.5 percentage points. (a) Trace the full transmission mechanism to Hong Kong, explaining each step from the Fed's decision to the effect on a Hong Kong small business seeking a bank loan. (b) If the Hong Kong economy is in recession while the US economy is overheating, explain the policy dilemma for Hong Kong. (c) Calculate the effect on a HK$2 million mortgage if the HIBOR rises by 0.5 percentage points, assuming the mortgage is at HIBOR + 1.5% and the original HIBOR is 2%. (d) Suggest non-monetary policy measures the Hong Kong government could use to stimulate the economy under these conditions.

Solution:

(a) Transmission mechanism:

1. Fed raises the federal funds rate by 0.5 percentage points.
2. Higher US rates attract capital out of Hong Kong (investors seek higher US returns).
3. Capital outflow puts downward pressure on the HKD exchange rate.
4. The HKMA must defend the peg by selling USD and buying HKD, reducing Hong Kong's monetary base.
5. The reduced monetary base pushes HIBOR (Hong Kong Interbank Offered Rate) up by approximately 0.5 percentage points to maintain the peg.
6. Banks raise their best lending rate (BLR) and prime rate, increasing borrowing costs.
7. The small business finds that bank loan interest rates have risen, increasing the cost of financing investment. The business may delay or cancel expansion plans.

(b) This is the fundamental dilemma of the Currency Board: Hong Kong's interest rates must follow US rates regardless of domestic conditions. When the US raises rates to fight inflation, Hong Kong must raise rates even if its economy is in recession. This deepens the Hong Kong recession by increasing borrowing costs precisely when stimulus is needed. The government cannot use monetary policy to address the downturn.

(c) Original mortgage rate $= \text{HIBOR} + 1.5\% = 2\% + 1.5\% = 3.5\%$. Monthly payment (assuming 25-year mortgage):

$M = P \times \frac{r(1+r)^n}{(1+r)^n - 1}$

where $P = 2,000,000$, $r = 0.035/12 = 0.002917$, $n = 300$.

M = 2\,000\,000 \times \frac{0.002917(1.002917)^{300}}{(1.002917)^{300} - 1} = 2\,000\,000 \times \frac{0.002917 \times 2.4066}{2.4066 - 1} = 2\,000\,000 \times \frac{0.00702}{1.4066} = \text{HK}\9,983$

After rate rise: new rate $= 2.5\% + 1.5\% = 4.0\%$, $r = 0.04/12 = 0.003333$.

M' = 2\,000\,000 \times \frac{0.003333(1.003333)^{300}}{(1.003333)^{300} - 1} = 2\,000\,000 \times \frac{0.003333 \times 2.7137}{2.7137 - 1} = 2\,000\,000 \times \frac{0.009046}{1.7137} = \text{HK}\10,558$

Increase in monthly payment = 10\,558 - 9\,983 = \text{HK}\575$per month ($+5.8%$).

(d) Non-monetary fiscal and supply-side measures:

1. Consumption vouchers: Direct cash transfers to residents (as used during COVID-19) to boost aggregate demand.
2. Infrastructure spending: Accelerate public works projects (e.g., Lantau development, Northern Metropolis) to create jobs and stimulate construction.
3. Tax rebates: Reduce salaries tax and profits tax temporarily to increase disposable income.
4. Land supply measures: Release more land for development to reduce housing costs, increasing real disposable income.
5. Tourism promotion: Attract mainland and international tourists to boost the services sector.
6. Innovation and technology investment: Government grants for tech startups and R&D to improve long-term productivity.

EQ-4: Interest Rate Parity and Exchange Rate Determination

Question: The interest rate in Country A is 2% and in Country B is 5%. The current spot exchange rate is 1 unit of A's currency $= 5$ units of B's currency. (a) Using uncovered interest rate parity (UIP), calculate the expected depreciation rate of A's currency. (b) Calculate the expected spot exchange rate in one year. (c) If covered interest rate parity holds and the one-year forward rate is 4.9, determine whether there is an arbitrage opportunity. (d) Explain why interest rate parity might fail to hold in practice.

Solution:

(a) Uncovered interest rate parity: $i_A = i_B + \frac{E^e - E}{E}$.

Rearranging: expected depreciation of A's currency $= i_A - i_B = 2\% - 5\% = -3\%$.

A negative value means A's currency is expected to appreciate by 3% (since A's interest rate is lower, the currency must appreciate to equalise returns).

(b) Expected spot rate in one year: $E^e = E \times (1 - 0.03) = 5 \times 0.97 = 4.85$.

A's currency appreciates: it now costs only 4.85 units of B's currency to buy 1 unit of A's currency.

(c) Covered interest rate parity: $F = E \times \frac{1 + i_A}{1 + i_B} = 5 \times \frac{1.02}{1.05} = 5 \times 0.9714 = 4.857$.

The theoretical forward rate is 4.857, but the actual forward rate is 4.9. Since $F_{actual} (4.9) > F_{theoretical} (4.857)$, there is an arbitrage opportunity:

1. Borrow in A's currency at 2%.
2. Convert to B's currency at the spot rate (5.0).
3. Invest in B's currency at 5%.
4. Sell the proceeds forward at 4.9.

Return from investing in B: borrow 1 unit of A, get 5 units of B, invest at 5% to get $5 \times 1.05 = 5.25$ units of B. Convert forward at 4.9: $5.25 / 4.9 = 1.0714$ units of A. Repay the loan: $1 \times 1.02 = 1.02$ units of A. Profit $= 1.0714 - 1.02 = 0.0514$ units of A (5.14% risk-free return).

(d) Interest rate parity may fail to hold because:

1. Transaction costs: Bid-ask spreads in foreign exchange and capital markets reduce arbitrage profits.
2. Capital controls: Government restrictions on cross-border capital flows prevent arbitrage.
3. Risk premium: Investors may demand a premium for holding assets in certain currencies (e.g., emerging market risk), causing a deviation from UIP.
4. Expectations errors: UIP depends on rational expectations of future exchange rates, but markets may systematically mispredict.
5. Liquidity differences: Some currencies are more liquid than others, affecting the ease of arbitrage.

EQ-5: Banking Regulation and Capital Adequacy

Question: A bank has the following balance sheet (in billions of HKD):

Assets	Liabilities + Equity
Reserves: 50	Deposits: 400
Loans: 300	Other liabilities: 50
Securities: 80	Equity (Tier 1 + Tier 2): 100
Other assets: 120
Total: 550	Total: 550

(a) Calculate the reserve ratio and the leverage ratio. (b) If the required reserve ratio is 10%, calculate excess reserves. (c) If the bank's risk-weighted assets are HK$350 billion, calculate the Basel III minimum capital ratios: (i) Common Equity Tier 1 (CET1) minimum 4.5$30 billion in bad loan losses, recalculate the leverage ratio and assess whether the bank remains solvent.

Solution:

(a) Reserve ratio $= \frac{\text{Reserves}}{\text{Deposits}} = \frac{50}{400} = 12.5\%$.

Leverage ratio $= \frac{\text{Equity}}{\text{Total Assets}} = \frac{100}{550} = 18.2\%$. (Basel III minimum leverage ratio is 3%, so this bank is well above the minimum.)

(b) Required reserves $= 0.10 \times 400 = 40$. Excess reserves = 50 - 40 = \text{HK}\10$ billion.

(c) Risk-weighted assets (RWA) $=$ HK$350$ billion.

• CET1 minimum: 4.5\% \times 350 = \text{HK}\15.75$ billion.
• Tier 1 minimum: 6\% \times 350 = \text{HK}\21$ billion.
• Total capital minimum: 8\% \times 350 = \text{HK}\28$ billion.

Assuming all equity is CET1 capital (HK$100$ billion), the bank far exceeds all minimum ratios: CET1 ratio $= 100/350 = 28.6\%$, Tier 1 ratio $= 28.6\%$, Total capital ratio $= 28.6\%$. These all exceed the Basel III minima comfortably, plus the capital conservation buffer (2.5%) and countercyclical buffer (0--2.5%).

(d) After HK$30$B losses: Equity falls to 100 - 30 = \text{HK}\70$billion. Total assets fall to$550 - 30 = \text\\{HK\\}$520$ billion.

New leverage ratio $= 70 / 520 = 13.5\%$ (still above 3%, so the bank remains solvent).

However, if the bank had less equity, losses could wipe it out. If losses exceeded HK$100$ billion (the equity buffer), the bank would become insolvent. This illustrates why capital adequacy requirements matter: they ensure banks have enough loss-absorbing capacity to survive adverse events.

EQ-6: Quantity Theory of Money and Hyperinflation

Question: Country Z has the following data: money supply M = \500$billion, velocity of money$V = 4$, price level$P = 125$, real output$Y = 16$billion units. (a) Verify that the quantity equation$MV = PY$ holds. (b) If the central bank increases the money supply by 25% while velocity and real output remain constant, calculate the new price level and inflation rate. (c) Suppose velocity increases to 5 (due to loss of confidence) and real output falls by 10% simultaneously. Calculate the new price level and inflation rate. (d) Using real-world examples (Zimbabwe 2008, Venezuela 2018, or Weimar Germany 1923), explain the mechanism of hyperinflation and why it is so difficult to stop once it begins.

Solution:

(a) $MV = 500 \times 4 = 2000$. $PY = 125 \times 16 = 2000$. The quantity equation holds: $MV = PY$.

(b) New $M = 500 \times 1.25 = 625$. $MV = 625 \times 4 = 2500$. Since $V$ and $Y$ are constant: $PY = 2500$. New $P = 2500 / 16 = 156.25$.

Inflation rate $= \frac{156.25 - 125}{125} \times 100\% = 25\%$.

When $V$ and $Y$ are constant, the inflation rate equals the money supply growth rate (the "neutrality of money" result).

(c) New $V = 5$, new $Y = 16 \times 0.90 = 14.4$. $M = 625$ (from part b). $MV = 625 \times 5 = 3125$. $P = 3125 / 14.4 = 217.0$.

Inflation rate from original: $\frac{217.0 - 125}{125} \times 100\% = 73.6\%$.

The combination of money growth (25%), velocity increase (25%), and output decline (10%) creates inflation of 73.6% -- far exceeding the money supply growth alone. This demonstrates how velocity and output changes can amplify or dampen the inflationary effect of money supply changes.

(d) Hyperinflation mechanism:

1. Initial trigger: The government runs a large fiscal deficit and finances it by printing money (monetising the debt). The money supply grows rapidly.

2. Price rises: $MV = PY$ means prices rise proportionally if velocity and output are stable.

3. Velocity accelerates: As people expect further inflation, they spend money immediately (reducing the holding period), which increases velocity. This causes prices to rise faster than the money supply.

4. Wage-price spiral: Workers demand higher wages to keep up with rising prices. Firms pass higher labour costs into prices. The government prints more money to meet its higher nominal spending obligations.

5. Fiscal dominance: The real value of tax revenue falls (the Tanzi effect -- there is a lag between when income is earned and when tax is collected, during which inflation erodes the real value). The deficit widens, requiring even more money creation.

6. Currency abandonment: People switch to foreign currency or barter. The domestic currency loses all three functions of money.

Why hyperinflation is hard to stop: Once velocity is rising and expectations are unanchored, simply stopping money creation may not suffice. Stopping money printing requires eliminating the fiscal deficit, which is politically difficult (cutting spending or raising taxes during an economic crisis). The social costs (unemployment, poverty) of the necessary fiscal adjustment are severe. Additionally, the loss of confidence in the currency can persist even after money growth stops, keeping velocity elevated. Stabilisation typically requires: (1) a credible fiscal consolidation plan, (2) a new currency or dollarisation, (3) central bank independence, and (4) international support (IMF programmes).

Real-world example -- Zimbabwe 2008: The government printed money to finance land redistribution and military spending. Inflation reached an estimated 79.6 billion percent month-on-month in November 2008. The government abandoned the Zimbabwe dollar in 2009 in favour of the US dollar and South African rand, which immediately stabilised prices.

Common Pitfalls

1. Confusing the money multiplier with the deposit multiplier: The simple deposit multiplier $\frac{1}{rrr}$ assumes no cash leakages and no excess reserves. The actual money multiplier $\frac{1 + cr}{rrr + er + cr}$ is always smaller because cash held outside banks and excess reserves held by banks both reduce the multiplier effect. Always use the full formula when the question mentions cash holdings or excess reserves.

2. Treating the monetary base and broad money supply as the same thing: The monetary base (M0) includes only currency in circulation and bank reserves. Broad money (M1, M2, M3) includes bank deposits created through the lending process. The money supply is the monetary base multiplied by the money multiplier. A change in reserves affects the monetary base directly but the broad money supply through the multiplier.

3. Misunderstanding the direction of causation in the quantity theory: $MV = PY$ is an identity (always true by definition). The quantity theory of money makes the causal claim that changes in $M$ cause changes in $P$ (assuming $V$ and $Y$ are stable in the short run). During hyperinflation, however, changes in $V$ (loss of confidence) can be the primary driver of inflation, with money supply growth following passively.

4. Forgetting that Hong Kong has no independent monetary policy: Under the Currency Board system, the HKMA does not set interest rates -- they follow the Fed. A common DSE error is to prescribe interest rate changes for Hong Kong. The only monetary tools available to the HKMA are: (i) adjusting the Convertibility Zone, (ii) changing the discount window rate (within narrow bounds), and (iii) foreign exchange interventions to maintain the peg.

5. Assuming that higher interest rates always reduce investment: While higher rates generally discourage borrowing, the effect depends on expectations. If a rate hike signals that the central bank is committed to controlling inflation, it may actually increase investment by improving business confidence and reducing uncertainty about future inflation. This is the "expectations channel" of monetary policy.