Money and Banking

Functions of Money

Money is anything that is generally accepted as a medium of exchange. It serves four key functions:

1. Medium of Exchange

Money eliminates the need for double coincidence of wants that exists in a barter system. In a barter economy, for trade to occur, both parties must want what the other has. Money serves as an intermediary that is universally accepted, making transactions far more efficient.

Example: Instead of a baker needing to find a shoemaker who wants bread, the baker sells bread for money and uses the money to buy shoes.

2. Unit of Account (Measure of Value)

Money provides a common measure of the value of all goods and services. It allows us to compare the value of different goods and to keep financial records.

Example: A laptop costs HKD 8,000 and a meal costs HKD 100. Money allows us to express both values in the same unit and compare them (the laptop is worth 80 meals).

3. Store of Value

Money allows people to save purchasing power for future use. Instead of consuming goods immediately, people can hold money and spend it later.

However, money is not a perfect store of value during inflation, because its purchasing power decreases as prices rise. Other stores of value include gold, property, stocks, and bonds.

4. Standard of Deferred Payment

Money allows debts to be contracted and repaid in the future. Borrowing and lending would be extremely difficult in a barter system because the value of goods changes over time.

Example: A bank lends HKD 500,000 to be repaid with interest over 20 years. Both parties agree on the value of the debt because it is denominated in money.

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Characteristics of Money

For a substance to function effectively as money, it should possess the following characteristics:

Characteristic	Description	Example
Acceptability	Generally accepted by all as a medium of exchange	Legal tender status, government backing
Durability	Does not deteriorate easily; can withstand repeated use	Coins, banknotes (vs perishable goods like bananas)
Portability	Easy to carry and transfer; convenient for transactions	Banknotes, electronic money
Divisibility	Can be divided into smaller units for transactions of different sizes	HKD 1, HKD 10, HKD 100, HKD 1000
Homogeneity	Each unit is identical in value to every other unit of the same denomination	Each HKD 100 note is worth the same
Scarcity	Supply is limited relative to demand; maintains value	Limited money supply by central bank
Stability of value	Relatively stable purchasing power over time	Low inflation preserves value

Types of Money

Commodity money: Money whose value comes from the commodity of which it is made (e.g., gold coins, cowrie shells, salt). The money has intrinsic value.

Fiat money: Money that has no intrinsic value but is declared legal tender by the government (e.g., modern banknotes and coins). Its value comes from government decree and public acceptance.

Representative money: Paper money backed by a commodity (e.g., gold certificates that could be exchanged for gold). The US dollar was backed by gold until 1971.

Electronic money (digital money): Money stored electronically and transferred through digital systems (e.g., bank transfers, credit cards, mobile payments like Octopus, Alipay, WeChat Pay).

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Evolution of Money

The evolution of money reflects the increasing complexity of economies:

1. Barter: Direct exchange of goods and services (limited by double coincidence of wants)
2. Commodity money: Gold, silver, cowrie shells used as a medium of exchange
3. Metallic money: Standardised coins made of precious metals
4. Paper money: Originally backed by gold; later became fiat money
5. Bank deposits: Cheques and bank transfers
6. Electronic money: Credit cards, debit cards, digital wallets
7. Cryptocurrencies: Decentralised digital currencies (e.g., Bitcoin) -- not widely accepted as money in most economies

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Types of Banks

Commercial Banks

Commercial banks are profit-making institutions that provide banking services to the public and businesses.

Functions of commercial banks:

1. Accepting deposits: Current accounts (demand deposits, low/no interest, easily accessible) and savings accounts (time deposits, higher interest, less accessible)
2. Making loans and advances: Lending to individuals and businesses at interest rates higher than the rates paid on deposits. The difference between the lending rate and deposit rate is the bank's profit margin (net interest margin).
3. Facilitating payments: Cheques, electronic fund transfers, credit/debit card services
4. Foreign exchange services: Buying and selling foreign currencies
5. Safe custody: Providing safe deposit boxes for valuables
6. Financial advice: Investment advice, wealth management
7. Credit creation: Creating new money through the lending process (see below)

Central Bank

The central bank is the government's bank and the banker's bank. It is responsible for managing the country's money supply, interest rates, and financial stability.

In Hong Kong, the de facto central bank is the Hong Kong Monetary Authority (HKMA).

Functions of the central bank:

1. Banker to the government: Manages government accounts, handles government debt issuance, and receives government revenue
2. Banker to commercial banks: Holds reserves of commercial banks, acts as lender of last resort
3. Issue of currency: Has the sole authority to issue banknotes (in HK, three commercial banks also issue banknotes under HKMA supervision)
4. Monetary policy: Controls the money supply and interest rates to achieve economic objectives (price stability, full employment, economic growth)
5. Exchange rate management: In HK, the HKMA maintains the Linked Exchange Rate System (USD/HKD at approximately 7.8)
6. Financial stability: Regulates and supervises banks to ensure the stability of the financial system
7. Management of foreign reserves: Holds and manages the country's foreign exchange reserves

Central Bank vs Commercial Bank

Feature	Central Bank	Commercial Bank
Objective	Public interest (stability, policy)	Profit maximisation
Ownership	Government	Private shareholders
Issues currency?	Yes (or supervises issue)	No (except in HK, three banks issue under supervision)
Regulates banks?	Yes	No
Accepts deposits?	Only from government and commercial banks	From the public and businesses
Lender of last resort?	Yes	No
Sets monetary policy?	Yes	No

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Money Creation by Commercial Banks

How Banks Create Money

Commercial banks create money through the process of credit creation (also called deposit creation). When a bank receives a deposit, it keeps only a fraction as reserves and lends out the rest. The lent money eventually returns to the banking system as a new deposit, and the process repeats.

The Money Multiplier

The money multiplier (also called the credit multiplier or deposit multiplier) shows the maximum potential expansion of the money supply from an initial deposit.

Key assumptions:

1. Banks lend out all excess reserves (no idle reserves)
2. The public does not hold cash (all money is deposited in banks)
3. There is only one type of deposit (simplified model)

Formula:

$\mathrm{Money Multiplier} = \frac{1}{\mathrm{Required Reserve Ratio (rrr)}}$

Or equivalently:

$\mathrm{Maximum increase in deposits} = \frac{\mathrm{Initial deposit}}{\mathrm{Required reserve ratio}}$

Example:

If the required reserve ratio is 10% (rrr = 0.1):

$\mathrm{Money multiplier} = \frac{1}{0.1} = 10$

An initial deposit of HKD 1,000 can potentially create:

$\mathrm{Maximum deposits} = \frac{1,000}{0.1} = 10,000$

Step-by-step process:

Round	New Deposit	Reserves (10%)	Loans (90%)
1	1,000	100	900
2	900	90	810
3	810	81	729
4	729	72.9	656.1
...	...	...	...
Total	10,000	1,000	9,000

The total increase in deposits forms a geometric series:

$\Delta D = 1,000 + 900 + 810 + 729 + \ldots = 1,000 \times \frac{1}{1 - 0.9} = \frac{1,000}{0.1} = 10,000$

Worked Example: Money Creation Step by Step

Suppose the required reserve ratio is 20% (rrr = 0.2). A customer deposits HKD 5,000 into Bank A.

Round 1: Bank A keeps 1000 (20%) and lends out 4000. Round 2: The 4000 is deposited into Bank B. Bank B keeps 800 and lends out 3200. Round 3: The 3200 is deposited into Bank C. Bank C keeps 640 and lends out 2560.

Money multiplier = 1/0.2 = 5.

Maximum increase in deposits = 5000 \times 5 = 25,000.

Total new loans = 25,000 - 5,000 = 20,000.

Factors Limiting Credit Creation

The actual money created is usually less than the theoretical maximum because:

1. Cash leakages: The public holds some cash outside the banking system (currency drain ratio)
2. Excess reserves: Banks may choose to hold reserves above the required minimum (for liquidity)
3. Willing borrowers: Banks can only lend if there are creditworthy borrowers who want to borrow
4. Willing lenders: Banks may be cautious about lending (especially during economic downturns)

With a currency drain ratio (c), the money multiplier becomes:

$m = \frac{1}{rrr + c}$

Where $c$ is the proportion of deposits held as cash by the public.

Example: If rrr = 0.1 and c = 0.2 (the public holds 20% of deposits as cash):

$m = \frac{1}{0.1 + 0.2} = \frac{1}{0.3} = 3.33$

The money multiplier falls from 10 to 3.33 due to cash leakages.

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Money Supply

Definition

The money supply is the total amount of money in circulation in an economy at a given time. It includes both cash (currency) and bank deposits.

Measures of Money Supply

Different measures of the money supply include different components:

M1 (Narrow Money):

$M1 = \mathrm{Currency in circulation} + \mathrm{Demand deposits}$

• Currency in circulation: banknotes and coins held by the public
• Demand deposits: current account balances that can be withdrawn on demand
• M1 is the most liquid measure of money supply

M2 (Broad Money):

$M2 = M1 + \mathrm{Savings deposits} + \mathrm{Time deposits}$

• Includes M1 plus less liquid deposits (savings accounts, fixed deposits)
• Savings and time deposits cannot be withdrawn on demand without penalty (less liquid)
• M2 is a broader measure that better reflects the total purchasing power in the economy

Liquidity

Liquidity refers to the ease with which an asset can be converted into cash without significant loss of value.

Asset	Liquidity
Cash	Highest
Current account	Very high
Savings account	High
Time deposit	Medium
Government bonds	Medium
Stocks/shares	Medium-low
Real estate	Low

M1 contains the most liquid assets; M2 includes less liquid assets as well.

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Monetary Policy

Definition

Monetary policy refers to the central bank's actions to control the money supply and interest rates in order to achieve macroeconomic objectives such as price stability, full employment, and sustainable economic growth.

Tools of Monetary Policy

1. Discount Rate (Base Rate / Policy Rate)

The discount rate (or base rate) is the interest rate at which the central bank lends to commercial banks.

Mechanism:

• If the central bank raises the discount rate:

  • Borrowing from the central bank becomes more expensive for commercial banks
  • Commercial banks raise their own lending rates
  • Borrowing becomes more expensive for businesses and consumers
  • Consumption and investment decrease
  • Aggregate demand decreases
  • Inflation is reduced

• If the central bank lowers the discount rate:

  • Borrowing becomes cheaper for commercial banks
  • Commercial banks lower their lending rates
  • Borrowing becomes cheaper for businesses and consumers
  • Consumption and investment increase
  • Aggregate demand increases
  • Economic growth is stimulated

2. Reserve Ratio (Required Reserve Ratio)

The reserve ratio is the fraction of customer deposits that commercial banks are required to hold as reserves (not lend out).

Mechanism:

• If the central bank raises the reserve ratio:

  • Banks must hold more reserves and can lend less
  • The money multiplier decreases
  • The money supply contracts
  • Interest rates tend to rise
  • Aggregate demand decreases

• If the central bank lowers the reserve ratio:

  • Banks can lend out a larger proportion of deposits
  • The money multiplier increases
  • The money supply expands
  • Interest rates tend to fall
  • Aggregate demand increases

Example: If the reserve ratio is raised from 10% to 20%:

$m_{\mathrm{old}} = \frac{1}{0.1} = 10$

$m_{\mathrm{new}} = \frac{1}{0.2} = 5$

The money multiplier falls from 10 to 5, significantly reducing the potential for credit creation.

Worked Example: Reserve Ratio Change and Money Supply

The central bank raises the reserve ratio from 10% to 25%. Total deposits in the banking system are HKD 500 billion, with banks holding exactly the required reserves.

Old multiplier = 1/0.1 = 10. New multiplier = 1/0.25 = 4.

Old required reserves = 500 \times 0.1 = 50 billion. New required reserves = 500 \times 0.25 = 125 billion.

The banking system now has a reserve shortfall of 125 - 50 = 75 billion. Banks must reduce lending by 75 \times 4 = 300 billion (using the new multiplier). The money supply contracts by up to HKD 300 billion.

3. Open Market Operations (OMO)

Open market operations involve the central bank buying or selling government securities (bonds) on the open market.

Buying government securities (expansionary):

• The central bank buys bonds from commercial banks or the public
• The central bank pays for the bonds by crediting bank reserves
• Bank reserves increase
• Banks can lend more
• The money supply expands
• Interest rates fall
• Aggregate demand increases

Selling government securities (contractionary):

• The central bank sells bonds to commercial banks or the public
• Buyers pay by transferring money from their bank accounts to the central bank
• Bank reserves decrease
• Banks can lend less
• The money supply contracts
• Interest rates rise
• Aggregate demand decreases

Expansionary vs Contractionary Monetary Policy

	Expansionary Monetary Policy	Contractionary Monetary Policy
Objective	Stimulate the economy	Reduce inflation
Discount rate	Lower	Raise
Reserve ratio	Lower	Raise
OMO	Buy government bonds	Sell government bonds
Money supply	Increase	Decrease
Interest rates	Fall	Rise
Effect on AD	Increases	Decreases
When used	Recession, high unemployment	High inflation, overheating economy

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The Hong Kong Monetary Authority (HKMA)

Linked Exchange Rate System (LERS)

Hong Kong operates a Linked Exchange Rate System, pegging the Hong Kong dollar (HKD) to the US dollar (USD) at a rate of approximately 7.8 HKD = 1 USD (more precisely, the HKD trades within a convertibility zone of 7.75 to 7.85).

How the LERS Works

The HKMA maintains the peg through:

1. Currency Board mechanism: Every HKD 7.8 in circulation must be fully backed by USD reserves. The Monetary Base (notes and coins in circulation + banks' balances at the HKMA) is 100% backed by foreign reserves.

2. Strong-side convertibility undertaking: If the HKD strengthens to 7.75, the HKMA is obligated to buy USD from licensed banks at 7.75, supplying HKD to the market and weakening the HKD.

3. Weak-side convertibility undertaking: If the HKD weakens to 7.85, the HKMA is obligated to sell USD to licensed banks at 7.85, absorbing HKD from the market and strengthening the HKD.

Implications of the LERS

• Hong Kong has no independent monetary policy -- it must follow the monetary policy of the US Federal Reserve (when the Fed raises rates, HK rates must also rise to maintain the peg)
• The LERS provides exchange rate stability, which is important for Hong Kong as an international financial centre and trading hub
• Loss of the ability to use monetary policy for domestic objectives (e.g., cannot lower interest rates independently during a local recession if the US is raising rates)

Functions of the HKMA

1. Maintaining monetary and banking stability
2. Maintaining the Linked Exchange Rate System
3. Managing the Exchange Fund (Hong Kong's official reserves)
4. Promoting the safety and soundness of the banking system
5. Developing Hong Kong as an international financial centre
6. Issuing coins (banknotes are issued by three commercial banks under HKMA supervision)

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Interest Rates

What Are Interest Rates?

Interest is the price of borrowing money. The interest rate is the percentage of the principal (the borrowed amount) that must be paid as interest per period (usually per year).

Types of Interest Rates

Nominal interest rate: The stated interest rate without adjustment for inflation.

Real interest rate: The nominal interest rate adjusted for inflation.

$\mathrm{Real interest rate} \approx \mathrm{Nominal interest rate} - \mathrm{Inflation rate}$

More precisely (Fisher equation):

$(1 + r) = \frac{(1 + i)}{(1 + \pi)}$

Where $r$ = real interest rate, $i$ = nominal interest rate, $\pi$ = inflation rate.

For small values of inflation:

$r \approx i - \pi$

Example: If the nominal interest rate is 5% and inflation is 2%:

Real interest rate $\approx 5\% - 2\% = 3\%$

Determinants of Interest Rates

1. Central bank policy rate: The base rate set by the central bank influences all other interest rates in the economy
2. Demand for and supply of loanable funds: Higher demand for borrowing pushes interest rates up; higher supply of savings pushes rates down
3. Inflation expectations: If lenders expect higher inflation, they demand higher nominal rates to compensate
4. Risk premium: Riskier borrowers pay higher interest rates to compensate for default risk
5. Duration: Longer-term loans typically carry higher interest rates (term premium)

Effects of Interest Rate Changes

Interest Rate Change	Effect on Borrowers	Effect on Savers	Effect on Exchange Rate
Increase	Borrowing more expensive; less consumption and investment	Higher returns on savings; more saving	Capital inflows; currency appreciates
Decrease	Borrowing cheaper; more consumption and investment	Lower returns; less saving	Capital outflows; currency depreciates

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Inflation Targeting

What Is Inflation Targeting?

Inflation targeting is a monetary policy framework where the central bank announces a specific inflation rate as its primary objective and adjusts monetary policy to achieve that target.

Most major central banks target an inflation rate of approximately 2% per year.

Why Target 2%?

• Low and stable inflation promotes economic certainty and planning
• 2% is high enough to avoid the risks of deflation (falling prices can lead to recession)
• 2% is low enough to prevent the erosion of purchasing power

How Central Banks Target Inflation

1. Monitor inflation: Track inflation indicators (CPI, core CPI)
2. Forecast inflation: Use economic models to predict future inflation
3. Adjust policy: If inflation is above target, use contractionary monetary policy. If below target, use expansionary monetary policy.
4. Communicate: Clearly communicate the target and policy decisions to manage expectations

Transmission Mechanism of Monetary Policy

The process by which monetary policy affects the economy:

1. Central bank changes the policy interest rate
2. This affects market interest rates (lending rates, mortgage rates, bond yields)
3. Changes in interest rates affect:
   • Consumption: Higher rates discourage borrowing for consumption (cars, houses)
   • Investment: Higher rates increase the cost of borrowing for firms; reduce expected returns on investment projects
   • Exchange rate: Higher rates attract foreign capital, causing currency appreciation (exports become more expensive, imports cheaper)
   • Asset prices: Higher rates reduce asset prices (bonds, stocks, property)
   • Expectations: Policy signals affect consumer and business confidence
4. These changes affect aggregate demand (AD)
5. Changes in AD affect output, employment, and ultimately inflation

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The Banking System and Financial Intermediation

Financial Intermediation

Banks act as financial intermediaries -- they channel funds from savers (those with surplus funds) to borrowers (those who need funds).

Benefits of financial intermediation:

1. Maturity transformation: Banks borrow at short maturities (deposits can be withdrawn on demand) and lend at long maturities (mortgages of 20-30 years). This allows savers to access their funds while borrowers receive long-term financing.
2. Risk transformation: Banks spread risk across many borrowers, reducing the risk to individual savers.
3. Size transformation: Banks pool many small deposits to make large loans that individual savers could not provide.
4. Convenience: Banks provide a convenient way to save and borrow.

The Balance Sheet of a Bank

Assets (Uses of Funds)	Liabilities (Sources of Funds)
Reserves (cash + deposits at central bank)	Demand deposits (current accounts)
Loans and advances	Savings deposits
Government securities	Time deposits
Other securities	Borrowing from central bank
Physical assets (buildings, equipment)	Shareholders' equity

Bank Runs and Deposit Insurance

A bank run occurs when many depositors simultaneously attempt to withdraw their deposits, usually because they fear the bank may become insolvent. Since banks lend out most of their deposits (fractional reserve banking), they cannot pay all depositors at once.

Deposit insurance protects depositors by guaranteeing that deposits up to a certain amount will be repaid even if the bank fails. This reduces the incentive for bank runs.

In Hong Kong, the Deposit Protection Scheme (DPS) covers deposits up to HKD 500,000 per depositor per bank.

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Common Pitfalls

1. Confusing the money multiplier formula direction: The money multiplier is the RECIPROCAL of the reserve ratio. A higher reserve ratio means a LOWER money multiplier, not a higher one.

   $m = \frac{1}{rrr}$

   If rrr = 0.2, then $m = 5$, not 0.2.

2. Stating that banks create money by printing notes: Banks create money through LENDING, not by printing currency. When a bank makes a loan, it creates a new deposit in the borrower's account. This new deposit is new money.

3. Confusing M1 and M2: M1 is narrow money (cash + demand deposits only). M2 is broad money (M1 + savings + time deposits). M2 is always larger than M1.

4. Forgetting the assumptions of the money multiplier: The theoretical maximum money multiplier assumes no cash leakages, no excess reserves, and willing borrowers. In practice, the actual money created is less than the theoretical maximum.

5. Confusing expansionary and contractionary open market operations: When the central bank BUYS bonds, it is expansionary (increases money supply). When it SELLS bonds, it is contractionary (decreases money supply). Think: buying puts money INTO the banking system; selling takes money OUT.

6. Stating that Hong Kong has an independent monetary policy: Under the Linked Exchange Rate System, Hong Kong's monetary policy is tied to that of the United States. The HKMA cannot independently set interest rates.

7. Confusing real and nominal interest rates: The nominal rate is what is stated; the real rate adjusts for inflation. A 10% nominal rate with 8% inflation gives only a 2% real rate. Always use real rates for economic decision-making.

8. Thinking the reserve ratio is the same as the cash ratio: The reserve ratio is set by the central bank (required reserves). The cash ratio (currency ratio) is the proportion of deposits the public holds as cash rather than in bank accounts. Both affect the money multiplier, but they are different concepts.

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Practice Problems

Question 1: Money Multiplier

Assume the required reserve ratio is 12.5%. A customer deposits HKD 8,000 into Bank A.

(a) Calculate the maximum possible increase in the total money supply. (b) Calculate the maximum total amount of new loans created in the entire banking system. (c) If the public holds 10% of any increase in deposits as cash (currency drain ratio = 0.1), calculate the revised money multiplier and the new maximum increase in the money supply.

(a) Money multiplier = $1 / 0.125 = 8$

Maximum increase in money supply = $8,000 \times 8 = 64,000$

(b) Maximum new loans = Maximum deposits - Initial deposit - Total reserves

Total new deposits = 64,000 Initial deposit = 8,000 Total reserves = 8,000 (the initial deposit is fully retained as reserves across the system)

Maximum new loans = 64,000 - 8,000 = 56,000

Alternatively: New loans = Initial deposit $\times$ (multiplier - 1) = $8,000 \times (8 - 1) = 56,000$

(c) Revised money multiplier = $1 / (0.125 + 0.1) = 1 / 0.225 = 4.44$

Maximum increase in money supply = $8,000 \times 4.44 = 35,556$

The currency drain reduces the money multiplier from 8 to 4.44, and the maximum increase in money supply falls from HKD 64,000 to approximately HKD 35,556.

Question 2: Open Market Operations

The central bank sells HKD 500 million worth of government bonds to commercial banks. Assume the required reserve ratio is 10% and there are no cash leakages.

(a) Calculate the change in bank reserves. (b) Calculate the maximum change in the money supply. (c) Is this an expansionary or contractionary policy? Explain.

(a) When the central bank sells bonds to commercial banks, the banks pay by transferring reserves to the central bank.

Change in bank reserves = -HKD 500 million (reserves decrease by HKD 500 million).

(b) Money multiplier = $1 / 0.1 = 10$

Maximum change in money supply = $-500 \times 10 = -5,000$ million

The money supply contracts by a maximum of HKD 5,000 million (HKD 5 billion).

(c) This is a contractionary monetary policy. By selling bonds, the central bank removes reserves from the banking system, reducing the ability of banks to create credit. The money supply contracts, interest rates rise, and aggregate demand decreases. This policy would be used to combat inflation.

Question 3: Reserve Ratio Change

The central bank lowers the required reserve ratio from 20% to 10%. Currently, total deposits in the banking system are HKD 100 billion and banks hold exactly the required reserves (no excess reserves). Assume no cash leakages.

(a) Calculate the money multiplier before and after the change. (b) Calculate the change in the maximum possible money supply. (c) Explain why the central bank might make this change.

(a)

Before: $m = 1 / 0.2 = 5$

After: $m = 1 / 0.1 = 10$

(b) The current deposits of HKD 100 billion are based on some initial deposit. However, the question asks about the change in the maximum possible money supply given the current level of deposits.

Before the change, required reserves = $100 \times 0.2 = 20$ billion. Excess reserves = 0.

After the change, required reserves = $100 \times 0.1 = 10$ billion. The previously required reserves of 20 billion now include 10 billion of excess reserves (since only 10 billion is now required).

The 10 billion of excess reserves can now be lent out: Additional lending potential = $10 \times 10 = 100$ billion.

So the maximum money supply increases by HKD 100 billion.

(c) The central bank would lower the reserve ratio to implement expansionary monetary policy. This would be appropriate during a recession or when economic growth is sluggish. By allowing banks to lend more from their existing reserves, the money supply expands, interest rates fall, and aggregate demand increases, stimulating economic activity and employment.

Question 4: Interest Rate Calculation

A bank offers a nominal interest rate of 6% per annum on a 1-year fixed deposit. If the inflation rate during the year is 4%:

(a) Calculate the real interest rate (approximate and exact). (b) If the inflation rate rises to 8% while the nominal rate stays at 6%, what happens to the real rate? Who benefits and who loses?

(a) Approximate real interest rate: $r \approx i - \pi = 6\% - 4\% = 2\%$

Exact real interest rate (Fisher equation):

$(1 + r) = \frac{(1 + 0.06)}{(1 + 0.04)} = \frac{1.06}{1.04} = 1.01923$

$r = 1.01923 - 1 = 0.01923 = 1.923\%$

(b) With inflation at 8%:

Approximate real rate = $6\% - 8\% = -2\%$

The real interest rate becomes negative (-2%). This means savers are losing purchasing power despite earning 6% nominal interest.

Borrowers benefit: They are repaying loans in money that is worth less than when they borrowed it (the real value of their debt decreases).

Savers lose: The interest they earn does not compensate for the erosion of purchasing power due to inflation. Their real return is negative.

Question 5: Hong Kong's Linked Exchange Rate

Explain how the HKMA maintains the Linked Exchange Rate System when there is downward pressure on the HKD (i.e., the HKD is weakening towards 7.85).

When there is selling pressure on the HKD (more people selling HKD and buying USD), the exchange rate tends to weaken (move from 7.80 towards 7.85).

At the weak-side convertibility rate of 7.85:

1. Licensed banks that have excess USD can sell USD to the HKMA at 7.85 HKD/USD.
2. The HKMA buys USD and pays HKD to the banks.
3. This removes HKD from circulation (the HKD paid to the HKMA is withdrawn from the banking system).
4. The reduction in the HKD money supply reduces liquidity in the banking system.
5. Interbank interest rates (HIBOR) rise due to the reduced supply of HKD.
6. Higher HKD interest rates attract capital inflows (investors seek higher returns).
7. The increased demand for HKD pushes the exchange rate back towards 7.80.
8. The convertibility undertaking is triggered at 7.85, so the HKD will not weaken beyond this level.

Additionally, the HKMA can use other tools:

• Adjusting the Base Rate to influence HIBOR
• Conducting open market operations to manage liquidity

Limitation: Because the HKD is pegged to the USD, Hong Kong must import US monetary policy. When the US Federal Reserve raises interest rates, the HKMA must also tighten monetary policy, even if Hong Kong's economy is in a downturn.

Question 6: Functions of Money Applied

For each of the four functions of money, explain whether Bitcoin performs that function well or poorly, with reasons.

Medium of exchange: Bitcoin performs POORLY as a medium of exchange. It is not widely accepted by shops and businesses for everyday transactions. Only a limited number of merchants accept Bitcoin. Transaction processing times can be slow and fees can be high relative to traditional payment methods.

Unit of account: Bitcoin performs POORLY as a unit of account. Its price is highly volatile -- it can change significantly within hours or days. Most goods and services are not priced in Bitcoin. A merchant cannot reliably set prices or keep accounts in Bitcoin because its value fluctuates too much.

Store of value: Bitcoin performs POORLY as a reliable store of value due to its extreme price volatility. An asset whose value can halve or double within months is not a good store of value. While some investors hold Bitcoin as a speculative asset, its volatility makes it unreliable for storing purchasing power over time. However, proponents argue its fixed supply (21 million cap) could make it a long-term store of value.

Standard of deferred payment: Bitcoin performs POORLY as a standard of deferred payment. Because its value is highly volatile, neither borrowers nor lenders would want to denominate long-term contracts in Bitcoin. A loan denominated in Bitcoin could become far more or far less expensive in real terms due to price fluctuations, creating unacceptable risk for both parties.

Question 7: Bank Balance Sheet

Bank A has the following balance sheet (in millions of HKD):

Assets:

• Reserves: 200
• Loans: 600
• Securities: 200

Liabilities:

• Deposits: 1,000

The required reserve ratio is 15%.

(a) Does Bank A have excess reserves? If so, how much? (b) What is the maximum amount Bank A can lend out? (c) If Bank A lends out its maximum, calculate the maximum total increase in the money supply for the entire banking system.

(a) Required reserves = $1,000 \times 0.15 = 150$ million

Actual reserves = 200 million

Excess reserves = $200 - 150 = 50$ million

Yes, Bank A has 50 million in excess reserves.

(b) Bank A can lend out its excess reserves of 50 million.

(c) When Bank A lends out 50 million, this creates a new deposit of 50 million in another bank. That bank must keep 15% in reserves and can lend out 85%. This process continues.

Maximum increase in money supply = $50 \times \frac{1}{0.15} = 50 \times 6.67 = 333.33$ million

So the maximum total increase in the money supply is approximately HKD 333.33 million.

Note: The initial 50 million is already part of the money supply (it was created as a new deposit when the loan was made). The total increase in deposits throughout the banking system is 333.33 million, of which 50 million is the initial new loan/deposit and 283.33 million is the subsequent credit creation.

Question 8: Nominal vs Real Interest Rates

A saver deposits HKD 100,000 in a 1-year fixed deposit at a nominal interest rate of 3% per annum. During the year, the inflation rate is 5%.

(a) Calculate the nominal amount the saver receives at maturity. (b) Calculate the real interest rate. (c) Has the saver gained or lost purchasing power? By how much?

(a) Nominal amount at maturity = $100,000 \times (1 + 0.03) = 103,000$

The saver receives HKD 103,000.

(b) Real interest rate $\approx 3\% - 5\% = -2\%$

Using the exact Fisher equation:

$(1 + r) = \frac{1.03}{1.05} = 0.98095$

$r = -0.01905 = -1.905\%$

(c) The saver has LOST purchasing power. Although the nominal amount increased by HKD 3,000, the purchasing power of HKD 103,000 after inflation is:

$\mathrm{Real value} = \frac{103,000}{1.05} = 98,095.24$

The saver's real purchasing power has fallen from HKD 100,000 to approximately HKD 98,095 -- a loss of about HKD 1,905. The negative real interest rate means inflation has eroded the value of the savings.

Question 9: Credit Creation with Cash Leakages

Bank B receives a new deposit of HKD 10,000. The required reserve ratio is 10%. The public holds cash equal to 15% of any increase in deposits.

(a) Calculate the effective money multiplier. (b) Calculate the maximum increase in the total money supply. (c) Explain why the actual increase would likely be less than this maximum.

(a) With cash leakages, the effective money multiplier is:

$m = \frac{1}{rrr + c} = \frac{1}{0.10 + 0.15} = \frac{1}{0.25} = 4$

(b) Maximum increase in money supply = $10,000 \times 4 = 40,000$

(c) The actual increase would likely be less than HKD 40,000 because:

• Banks may hold excess reserves above the required minimum (not lending out all excess reserves)
• Not all borrowers may immediately deposit their loans into bank accounts (some may hold cash)
• There may not be enough creditworthy borrowers who want to borrow
• Banks may be unwilling to lend due to economic uncertainty or risk aversion

Question 10: Monetary Policy Transmission

The central bank decides to raise the base rate by 0.5 percentage points. Trace the transmission mechanism and explain the likely effects on the economy, assuming the economy is currently operating above full employment with rising inflation.

1. Interest rate channel: Commercial banks raise their lending rates (mortgage rates, business loan rates) in response to the higher base rate.

2. Borrowing and spending: Higher lending rates make borrowing more expensive for households and firms. Mortgage payments increase, reducing disposable income for homeowners. Firms face higher costs of financing investment projects.

3. Consumption: Households reduce consumption spending, particularly on big-ticket items purchased with credit (houses, cars, durable goods). Saving becomes more attractive due to higher deposit rates.

4. Investment: Firms reduce investment spending because the cost of borrowing has increased and the expected return on investment projects may not justify the higher interest costs. Some marginal projects are cancelled.

5. Exchange rate: Higher domestic interest rates attract foreign capital inflows (investors seek higher returns). Increased demand for the domestic currency causes it to appreciate.

6. Net exports: Currency appreciation makes exports more expensive for foreign buyers and imports cheaper for domestic consumers. Export volumes fall and import volumes rise, reducing net exports.

7. Asset prices: Higher interest rates reduce the present value of future cash flows, leading to lower asset prices (bond prices fall, stock prices may decline, property prices face downward pressure).

8. Aggregate demand: Consumption, investment, and net exports all decrease, shifting the aggregate demand curve to the left.

9. Output and employment: Real GDP growth slows and unemployment may rise slightly as firms reduce production in response to lower demand.

10. Inflation: Reduced aggregate demand eases upward pressure on prices. Inflation gradually falls back towards the target level.

Since the economy was operating above full employment with rising inflation, this contractionary monetary policy is appropriate. It cools down an overheating economy and brings inflation under control.

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Problem Set

Problem 1: Money Multiplier with Cash Leakages

The required reserve ratio is 8%. An initial deposit of HKD 20,000 is made. The public holds cash equal to 25% of deposits.

(a) Calculate the effective money multiplier. (b) Calculate the maximum increase in the money supply. (c) Explain why this is less than the simple multiplier would suggest.

Solution

(a) With cash leakages: m = 1/(rrr + c) = 1/(0.08 + 0.25) = 1/0.33 = 3.03.

(b) Maximum increase = 20,000 \times 3.03 = 60,606.

(c) The simple multiplier (no leakages) = 1/0.08 = 12.5, giving 250,000. Cash leakages drain money from the banking system at each round, reducing the base for further lending.

If you get this wrong, revise: The Money Multiplier

Problem 2: Open Market Operations Calculation

The central bank buys HKD 300 million worth of government bonds from commercial banks. The required reserve ratio is 5%.

(a) What happens to bank reserves? (b) Calculate the maximum change in the money supply. (c) Is this expansionary or contractionary?

Solution

(a) Reserves increase by HKD 300 million (the central bank pays by crediting bank reserves).

(b) Money multiplier = 1/0.05 = 20. Maximum increase = 300 \times 20 = 6,000 million (HKD 6 billion).

(c) Expansionary -- buying bonds injects reserves, expanding the money supply and lowering interest rates.

If you get this wrong, revise: Open Market Operations (OMO)

Problem 3: Real vs Nominal Interest Rates

A bank offers 4% nominal interest on 1-year deposits. Inflation turns out to be 6%.

(a) Calculate the real interest rate (approximate and exact). (b) Who benefits from this situation -- borrowers or savers? (c) If a borrower takes a 1-year loan at 4% nominal, what is the real cost of the loan?

Solution

(a) Approximate: r = 4\% - 6\% = -2\%.

Exact: (1 + r) = 1.04/1.06 = 0.9811, so r = -1.89\%.

(b) Borrowers benefit. They repay loans in money that is worth less than when they borrowed. The real value of their debt falls.

(c) The real cost of the loan is -1.89\%. The borrower effectively pays back less in real terms than they received. This is a transfer of purchasing power from savers to borrowers.

If you get this wrong, revise: Interest Rates

Problem 4: Bank Balance Sheet and Lending

Bank X has the following (HKD millions): Reserves = 150, Loans = 600, Securities = 250. Deposits = 900. The required reserve ratio is 12%.

(a) Does the bank have excess reserves? (b) What is the maximum new loan the bank can make? (c) If the bank makes this loan and it is deposited in Bank Y (which had no excess reserves), what is the maximum total increase in the money supply for the whole system?

Solution

(a) Required reserves = 900 \times 0.12 = 108. Actual reserves = 150. Excess reserves = 150 - 108 = 42.

(b) Maximum new loan = 42 million.

(c) The 42 million becomes a new deposit in Bank Y. Bank Y must keep 42 \times 0.12 = 5.04 and can lend 36.96. This process continues with multiplier 1/0.12 = 8.33.

Maximum total increase = 42 \times 8.33 = 350 million.

If you get this wrong, revise: Money Creation by Commercial Banks

Problem 5: HKMA and the Linked Exchange Rate

Explain what the HKMA would do if there is upward pressure on the HKD (the exchange rate moves towards 7.75). Trace the mechanism step by step.

Solution

At the strong-side convertibility undertaking (7.75):

1. Licensed banks sell USD to the HKMA at 7.75 HKD/USD
2. The HKMA sells USD and receives HKD from the banks
3. This increases the HKD money supply (HKD flows into the banking system)
4. Increased HKD liquidity pushes interbank rates (HIBOR) down
5. Lower HKD rates reduce the attractiveness of HKD assets to foreign investors
6. Capital outflows reduce demand for HKD, easing the upward pressure
7. The exchange rate moves back towards 7.80

If you get this wrong, revise: The Hong Kong Monetary Authority (HKMA)

Problem 6: Functions of Money — Bitcoin Evaluation

Evaluate Bitcoin against each of the four functions of money. Is Bitcoin likely to replace conventional money in the foreseeable future?

Solution

Medium of exchange: Poor. Not widely accepted by merchants. Transaction processing can be slow and expensive.

Unit of account: Poor. Extreme price volatility makes it impossible to set reliable prices or maintain accounts in Bitcoin.

Store of value: Poor. Price can halve or double within months. Not reliable for storing purchasing power.

Standard of deferred payment: Poor. No lender or borrower would denominate long-term contracts in a currency whose value is so unpredictable.

Conclusion: Bitcoin does not perform the functions of money well. It functions more as a speculative asset or store of value hedge than as money. It is unlikely to replace conventional money unless its volatility decreases dramatically and acceptance increases significantly.

If you get this wrong, revise: Functions of Money

Problem 7: M1 vs M2

An economy has the following (HKD billions): Currency in circulation = 400, Demand deposits = 800, Savings deposits = 1200, Time deposits = 600.

(a) Calculate M1. (b) Calculate M2. (c) If people move HKD 200 billion from savings deposits to demand deposits, what happens to M1 and M2?

Solution

(a) M1 = Currency + Demand deposits = 400 + 800 = 1,200 billion.

(b) M2 = M1 + Savings deposits + Time deposits = 1,200 + 1,200 + 600 = 3,000 billion.

(c) Moving 200 from savings to demand deposits: M1 increases by 200 (to 1,400). M2 is unchanged (still 3,000) because both savings and demand deposits are components of M2.

If you get this wrong, revise: Measures of Money Supply

Problem 8: Transmission Mechanism

The central bank raises the base rate by 0.75 percentage points. The economy is experiencing rising inflation. Explain the expected effects on consumption, investment, net exports, and inflation.

Solution

Consumption: Higher lending rates make mortgages, car loans, and credit card borrowing more expensive. Disposable income falls for variable-rate borrowers. Consumption decreases, especially for big-ticket durables.

Investment: Higher borrowing costs reduce the expected return on investment projects. Some marginal projects become unprofitable and are cancelled. Business investment decreases.

Net exports: Higher rates attract foreign capital, appreciating the currency. Exports become more expensive for foreign buyers; imports become cheaper. Net exports decrease.

Inflation: Reduced consumption, investment, and net exports all decrease aggregate demand. With less demand-pull pressure, inflation gradually falls toward the target.

If you get this wrong, revise: Transmission Mechanism of Monetary Policy

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Extended Problem Set: Advanced Money and Banking

Problem 9: Banking Crisis and Contagion

Bank A has deposits of HK$500 billion, reserves of HK$40 billion, and loans of HK$460 billion. The required reserve ratio is 8$300 billion, reserves of HK$30 billion, and loans of HK$270 billion. Bank A and Bank B are major counterparties in the interbank market.

(a) Calculate each bank's actual reserve ratio, required reserves, and excess reserves. (b) A rumour causes depositors to withdraw HK$50 billion from Bank A. Calculate Bank A's new reserve ratio and explain whether it is solvent. (c) If Bank A sells HK$30 billion of its loans to Bank B at face value, can Bank B afford this purchase? What happens to Bank B's reserve ratio? (d) Explain how this scenario illustrates contagion risk and why the HKMA's lender of last resort function is important.

Solution

(a) Bank A: Actual reserve ratio $= 40/500 = 8\%$. Required reserves $= 0.08 \times 500 = 40$. Excess reserves $= 40 - 40 = 0$. Bank A has zero excess reserves and is fully loaned up.

Bank B: Actual reserve ratio $= 30/300 = 10\%$. Required reserves $= 0.08 \times 300 = 24$. Excess reserves $= 30 - 24 = 6$ billion.

(b) After HK$50B withdrawal: Deposits$= 450$. Reserves$= 40 - 50 = -10$.

Bank A's reserves are negative -- it cannot meet the withdrawal. It must either: (i) borrow from the interbank market, (ii) sell assets (loans), or (iii) borrow from the HKMA as lender of last resort. Bank A is technically solvent (assets $= 460 + 40 = 500 >$ liabilities $= 500$) but illiquid (cannot meet short-term obligations).

(c) If Bank A sells HK$30B of loans: it receives HK$30B in cash, raising reserves to $-10 + 30 = 20$. New deposits $= 450$. New reserve ratio $= 20/450 = 4.4\%$ (below the 8% requirement). Bank A still needs more liquidity.

For Bank B: it pays HK$30B, reducing reserves to$30 - 30 = 0$. Deposits unchanged at 300. New reserve ratio$= 0/300 = 0%$. Bank B now has zero reserves and cannot meet any withdrawals. The loan purchase has transmitted Bank A's liquidity crisis to Bank B.

(d) This illustrates contagion risk: the failure or distress of one bank can spread to other banks through interbank connections. When Bank A sells assets to Bank B, it transfers its liquidity problem to Bank B. If Bank B cannot absorb the shock, it may also fail, spreading the crisis further.

The HKMA's lender of last resort (LOLR) function is critical because: (i) it provides emergency liquidity to solvent but illiquid banks (like Bank A), preventing fire sales of assets at depressed prices; (ii) by lending to Bank A, the HKMA prevents the contagion from spreading to Bank B and the wider banking system; (iii) the mere existence of a LOLR reduces the likelihood of bank runs because depositors know the central bank stands behind the system. In Hong Kong, the HKMA operates a Discount Window for this purpose, and the Deposit Protection Scheme (covering up to HK$500,000 per depositor) provides additional confidence.

If you get this wrong, revise: Banking System Stability

Problem 10: Interest Rate Risk and Bank Profitability

A bank has the following balance sheet (in HK$ billion):

Assets	Liabilities
Fixed-rate loans (5 years, 4%): 400	Fixed-rate deposits (1 year, 2%): 300
Floating-rate loans (HIBOR + 2%): 200	Floating-rate deposits (HIBOR + 0.5%): 250
Reserves (0%): 50	Equity: 100

HIBOR is currently 3%. The bank expects HIBOR to rise to 5% over the next year.

(a) Calculate the bank's net interest margin (NIM) at the current HIBOR. (b) Calculate the bank's NIM if HIBOR rises to 5%. (c) Calculate the bank's duration gap and explain what it means for interest rate risk. (d) Suggest two strategies the bank could use to manage its interest rate risk.

Solution

(a) Interest income: Fixed-rate loans $= 400 \times 4\% = 16$. Floating-rate loans $= 200 \times (3\% + 2\%) = 200 \times 5\% = 10$. Total income $= 26$.

Interest expense: Fixed-rate deposits $= 300 \times 2\% = 6$. Floating-rate deposits $= 250 \times (3\% + 0.5\%) = 250 \times 3.5\% = 8.75$. Total expense $= 14.75$.

NIM $= (26 - 14.75) / 650 = 11.25 / 650 = 1.73\%$.

(b) At HIBOR $= 5\%$:

Interest income: Fixed-rate $= 16$ (unchanged). Floating-rate $= 200 \times (5\% + 2\%) = 14$. Total $= 30$.

Interest expense: Fixed-rate $= 6$ (unchanged). Floating-rate $= 250 \times (5\% + 0.5\%) = 250 \times 5.5\% = 13.75$. Total $= 19.75$.

NIM $= (30 - 19.75) / 650 = 10.25 / 650 = 1.58\%$.

NIM falls from 1.73% to 1.58% because the bank's floating-rate liabilities reprice faster than its floating-rate assets, and the fixed-rate assets do not reprice at all. The bank is asset-sensitive with a negative duration gap.

(c) The bank has more rate-sensitive liabilities (HK$250B floating + HK$300B fixed maturing in 1 year $=$ HK$550B within 1 year) than rate-sensitive assets (HK$200B floating + HK$0B fixed maturing within 1 year$=$HK$200B within 1 year). The repricing gap is 200 - 550 = -\text{HK}\350$ billion. This means when rates rise, the bank's interest expense rises faster than its interest income, compressing the NIM.

(d) Strategy 1 -- Interest rate swaps: The bank can enter a receive-fixed, pay-floating interest rate swap on a notional amount of HK$350 billion. This converts some of its floating-rate liabilities to fixed-rate, reducing its negative repricing gap.

Strategy 2 -- Increase floating-rate lending: The bank can issue more floating-rate loans (or convert some fixed-rate loans to floating) to increase its rate-sensitive assets. For example, offering mortgage products indexed to HIBOR rather than fixed rates.

Strategy 3 -- Lengthen deposit maturity: The bank can offer higher rates on longer-term fixed deposits, reducing the amount of deposits that reprice quickly.

If you get this wrong, revise: Bank Management

Problem 11: Monetary Policy and Asset Price Bubbles

The central bank observes that property prices have risen by 30% over the past two years while rent yields have fallen from 4% to 2.5%. The GDP deflator has risen by 6% over the same period. The base interest rate is 2%.

(a) Calculate the real appreciation of property prices (inflation-adjusted). (b) Calculate the rental yield and explain what the declining yield suggests about market conditions. (c) Explain the dilemma for the central bank: should it raise interest rates to address the property bubble, even if general inflation is low? (d) Evaluate the use of macroprudential tools (e.g., loan-to-value ratio caps, stress testing) as an alternative to interest rate policy for addressing asset price bubbles.

Solution

(a) Nominal property price increase $= 30\%$. General inflation $= 6\%$. Real appreciation $= \frac{1.30}{1.06} - 1 = 22.6\%$. Property prices have risen 22.6% in real terms over two years -- approximately 10.7% per year in real terms.

(b) Initial rental yield $= 4\%$. Current yield $= 2.5\%$. The rental yield has fallen by 37.5% relative. The declining yield (rising price-to-rent ratio) suggests that property prices are rising much faster than rents. This is a classic sign of a potential bubble: prices are being driven by speculative expectations of future price increases rather than fundamental rental value. If the yield falls below the cost of borrowing, the investment only makes sense if prices continue to rise.

(c) Dilemma: Raising interest rates to cool the property market would also slow the broader economy. If general inflation is low (6% over two years $=$ 3% per year), the central bank may not have a mandate to raise rates. Using interest rates to target asset prices risks causing unnecessary economic damage. However, not acting risks a larger bubble and a more painful correction later (as Hong Kong experienced in 1997 and 2008).

(d) Macroprudential tools evaluation:

Advantages over interest rate policy:

• Targeted: LTV caps and stress testing affect the property market directly without raising borrowing costs for the rest of the economy.
• Flexible: Can be tightened or loosened quickly in response to property market conditions.
• Address the root cause: By limiting leverage in property purchases, macroprudential tools reduce the fuel for speculative buying.

Disadvantages:

• Regulatory arbitrage: Buyers may find ways around the rules (e.g., using shell companies, offshore borrowing).
• May not prevent all bubbles: If buyers have sufficient cash (no leverage needed), LTV caps are ineffective.
• Complexity: Designing and enforcing macroprudential regulations requires significant regulatory capacity.

Hong Kong context: The HKMA has extensively used macroprudential tools including LTV ratio caps (currently 50--60% for most residential mortgages), stamp duties (Special Stamp Duty, Buyer's Stamp Duty, Ad Valorem Stamp Duty), and stress testing requirements for banks. These measures have been partially effective in cooling speculative demand while allowing the HKMA to maintain interest rates aligned with the Fed.

If you get this wrong, revise: Monetary Policy and Asset Prices

Problem 12: Digital Currencies and the Future of Money

Central banks worldwide are exploring Central Bank Digital Currencies (CBDCs). The HKMA has been researching the "e-HKD" since 2021.

(a) Explain three differences between a CBDC and a cryptocurrency like Bitcoin. (b) Explain two potential benefits and two risks of introducing a CBDC in Hong Kong. (c) If the HKMA introduces an e-HKD that pays interest, how would this affect the demand for bank deposits? What implications does this have for the banking system? (d) Evaluate whether Hong Kong should introduce a CBDC given its existing efficient payment systems (Octopus, FPS, Faster Payment System).

Solution

(a) Three differences:

1. Issuer: A CBDC is issued and backed by the central bank (sovereign money). Bitcoin is issued by a decentralised network with no backing.
2. Value stability: A CBDC is denominated in the national currency and maintains stable value (like cash). Bitcoin is highly volatile (its value fluctuates based on market sentiment).
3. Legal tender status: A CBDC would have legal tender status, meaning it must be accepted as payment for debts. Bitcoin has no legal tender status in Hong Kong.

(b) Benefits: (i) Financial inclusion: unbanked individuals can access digital payments directly through the central bank. (ii) Payment efficiency: faster, cheaper cross-border payments compared to the current correspondent banking system. (iii) Monetary policy transmission: the interest rate on CBDC could serve as a direct monetary policy tool (a floor on interest rates).

Risks: (i) Bank disintermediation: if consumers hold CBDC instead of bank deposits, banks lose a cheap funding source, reducing their ability to lend. (ii) Cybersecurity: a centralised digital currency system is a single point of failure; a successful cyberattack could be catastrophic. (iii) Privacy: CBDC transactions could be fully traceable by the government, raising surveillance concerns.

(c) If the e-HKD pays interest (say 2%), and bank deposits pay less (say 1.5%), rational depositors would shift funds from banks to CBDC. This reduces bank deposits, forcing banks to raise deposit rates or find alternative funding (wholesale funding, which is more expensive). The result is higher lending rates, reduced credit availability, and potentially a contraction of the money supply through the deposit multiplier.

The magnitude depends on the interest rate differential and the substitutability of CBDC for deposits. If the CBDC is designed with holding limits (e.g., maximum HK$100,000 per person), this limits the disintermediation effect.

(d) Evaluation:

Hong Kong already has efficient digital payment systems: the Octopus card (transit and retail), FPS (Faster Payment System for bank-to-bank transfers), and various mobile payment platforms. The marginal benefit of a CBDC in terms of payment efficiency is therefore relatively small.

However, a CBDC could provide: (i) a common digital infrastructure that interoperates with all existing systems, (ii) programmable money for smart contracts and conditional payments (e.g., government subsidies that can only be spent on designated goods), and (iii) a platform for cross-border payments with mainland China (connecting with the digital RMB).

The decision should weigh the costs of implementation against these incremental benefits, while carefully managing the risks to financial stability.

If you get this wrong, revise: Future of Money

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Additional Problems: DSE Exam-Style Money and Banking

Problem 13: Open Market Operations Step by Step

The central bank wants to reduce the money supply by HK$400 billion. The required reserve ratio is 10%. The banking system currently has zero excess reserves.

(a) Calculate the required open market sale of government bonds. (b) Trace the first three rounds of the contraction process in a table. (c) How many rounds does it take for 95% of the total contraction to occur? (d) Explain why the actual contraction will be smaller than the theoretical maximum.

Solution

(a) Money multiplier $= 1/0.10 = 10$. Required bond sale = 400/10 = \text{HK}\40$ billion.

(b) | Round | Deposits | Reserves | Loans | |---|---|---|---| | 0 | -40 | -40 | 0 | | 1 | 0 | -36 | -36 | | 2 | -36 | -32.4 | -32.4 | | 3 | -32.4 | -29.16 | -29.16 |

Total after 3 rounds: Deposits reduced by $40 + 36 + 32.4 = 108.4$ billion (of 400 total).

(c) After $n$ rounds, the cumulative contraction $= 40 \times (1 + 0.9 + 0.9^2 + ... + 0.9^{n-1}) = 40 \times \frac{1 - 0.9^n}{1 - 0.9} = 400 \times (1 - 0.9^n)$.

For 95%: $0.9^n = 0.05$. $n = \ln(0.05)/\ln(0.9) = -2.996/-0.1054 = 28.4$ rounds.

It takes approximately 29 rounds for 95% of the contraction to occur.

(d) The actual contraction will be smaller because: (i) banks may hold excess reserves (especially during uncertain times); (ii) the public may hold more cash (currency drain), reducing the deposit multiplier; (iii) some borrowers may not redeposit loans into the banking system; (iv) banks may be unwilling to reduce lending if loan demand is strong (they may sell other assets instead).

If you get this wrong, revise: Open Market Operations

Problem 14: Inflation Targeting and Central Bank Credibility

A central bank has an inflation target of 2% with a tolerance band of $\pm 1\%$. Actual inflation has been 5% for the past two years. The public expects inflation to be 6% next year. The Phillips curve is $\pi = \pi^e - 0.5(u - 5) + s$, where $s$ is a supply shock (0 this year).

(a) If the central bank wants to reduce inflation to 2%, calculate the required unemployment rate using the Phillips curve. (b) Calculate the sacrifice ratio (the cumulative unemployment cost of reducing inflation by 1 percentage point) if each percentage point of disinflation requires the unemployment rate to exceed the natural rate by 2 percentage points for one year. (c) Explain how central bank credibility can reduce the sacrifice ratio. (d) Evaluate the advantages and disadvantages of inflation targeting compared to exchange rate targeting for Hong Kong.

Solution

(a) Target $\pi = 2\%$. With $\pi^e = 6\%$ and $s = 0$: $2 = 6 - 0.5(u - 5)$. $0.5(u - 5) = 4$. $u - 5 = 8$. $u = 13\%$.

The central bank must engineer unemployment of 13% (8 percentage points above the natural rate of 5%) for one year to reduce inflation to 2%. This is an extremely high cost.

(b) Sacrifice ratio: reducing inflation from 5% to 2% requires a 3 percentage point reduction. If each 1pp reduction costs 2 percentage-point-years of excess unemployment: sacrifice ratio $= 2 \times 3 = 6$ percentage-point-years.

Total cost $= 6$ percentage-point-years. If the labour force is 4 million, this represents $0.06 \times 4\,000\,000 \times 1 = 240\,000$ person-years of unemployment.

(c) If the central bank is credible (the public believes it will achieve its target), $\pi^e$ falls. If $\pi^e = 2\%$ (instead of 6%): $2 = 2 - 0.5(u - 5)$. $u = 5\%$. No excess unemployment is needed! Credibility eliminates the sacrifice ratio entirely.

In practice, credibility is built through: (i) a track record of meeting targets, (ii) central bank independence, (iii) transparent communication (forward guidance), and (iv) institutional commitment (legislated mandates).

(d) Inflation targeting vs exchange rate targeting for Hong Kong:

Exchange rate targeting (current system -- Currency Board):

• Advantages: provides clear nominal anchor; eliminates exchange rate uncertainty for trade; constrains monetary policy to be disciplined; has worked well for 40 years.
• Disadvantages: no independent monetary policy; imports US monetary conditions (which may be inappropriate for HK); cannot respond to domestic shocks; requires large reserve holdings.

Inflation targeting (hypothetical):

• Advantages: allows independent monetary policy; central bank can respond to domestic inflation and output gaps; more flexible exchange rate could absorb external shocks.
• Disadvantages: loss of exchange rate stability would increase transaction costs for trade (Hong Kong's trade-to-GDP ratio > 300%); requires a track record of central bank credibility (which the HKMA has not built in this domain); could trigger capital flight and a sharp depreciation during the transition.

Conclusion: For Hong Kong, the benefits of exchange rate stability (critical for an international financial centre and trade hub) outweigh the benefits of monetary independence. The Currency Board should be maintained, with fiscal policy and macroprudential tools used for domestic stabilisation.

If you get this wrong, revise: Inflation Targeting

Problem 15: Financial Intermediation and Economic Development

Country Y has an underdeveloped financial system: only 20% of the population has bank accounts, the stock market capitalisation is 5% of GDP, and most lending is to the government rather than the private sector. Country Z has a developed financial system: 90% bank account coverage, stock market capitalisation of 120% of GDP, and active venture capital and corporate bond markets.

(a) Explain four channels through which financial development promotes economic growth. (b) If Country Y's savings rate is 15% of GDP and Country Z's is 30%, and both have the same production function $Y = K^{0.3}L^{0.7}$, calculate the steady-state GDP per capita ratio. (c) Explain why financial development may have diminishing returns at very high levels (financialisation risks). (d) Suggest three specific policies Country Y should implement to develop its financial system.

Solution

(a) Four channels:

1. Capital mobilisation and allocation: Financial intermediaries (banks, stock markets) pool savings from many small savers and allocate them to the most productive investments. Without financial markets, savings remain idle or are invested in low-return activities (e.g., gold, real estate speculation).
2. Risk management: Financial markets allow risk to be diversified (portfolio diversification, insurance, hedging). This enables firms to undertake risky but high-return investments (innovation, R&D) that they would not undertake without risk-sharing mechanisms.
3. Information production: Banks and credit rating agencies produce information about borrowers' creditworthiness, reducing adverse selection and moral hazard. This lowers the cost of capital and improves the efficiency of lending.
4. Liquidity provision: Financial markets allow savers to convert illiquid assets (long-term investments) into liquid claims (bank deposits, tradable securities). This encourages saving by reducing the liquidity risk of long-term investment.

(b) In the Solow model, steady-state capital per worker is proportional to $(s/n)^{1/(1-\alpha)}$, where $s$ is the saving rate, $n$ is the population growth rate, and $\alpha = 0.3$.

Steady-state $k^* \propto s^{1/0.7} = s^{1.429}$.

GDP per capita ratio $= (s_Z / s_Y)^{1.429} = (30/15)^{1.429} = 2^{1.429} = 2.70$.

Country Z's GDP per capita is approximately 2.7 times Country Y's, purely due to the higher saving rate enabled by financial development.

(c) Financialisation risks: At very high levels of financial development, the financial sector may grow to a size that is disproportionate to the real economy. Risks include: (i) resources (especially talent) flowing to finance from more productive sectors (engineering, science); (ii) excessive leverage and asset price bubbles (as in the 2008 financial crisis); (iii) rent-seeking through financial engineering rather than productive investment; (iv) increased systemic risk from complex, interconnected financial products. The marginal benefit of additional financial development diminishes and may eventually turn negative.

(d) Policies for Country Y:

1. Expand financial inclusion: Use mobile banking technology to reach unbanked populations. Implement simplified KYC (know-your-customer) procedures and microfinance products for low-income households.
2. Develop capital markets: Create a securities regulator, establish disclosure requirements, and introduce corporate bond and equity markets. Start with government bonds to establish a yield curve, then gradually introduce corporate securities.
3. Strengthen legal infrastructure: Enforce property rights, contract law, and creditor rights. Weak legal enforcement discourages lending because lenders cannot recover loans from defaulting borrowers. Establish bankruptcy laws that balance debtor protection with creditor rights.
4. Promote competition: Reduce barriers to entry for foreign banks (which bring expertise and technology). Encourage fintech innovation (digital payments, peer-to-peer lending, robo-advisors) to challenge incumbents.

If you get this wrong, revise: Financial Development