Monetary Policy: formula sheet

Key formulas

Money multiplier (simple)

Money multiplier = 1 ÷ reserve requirement

Assumes banks hold no excess reserves and the public holds no cash. Use the decimal form of the ratio.

Change in money supply

Δ Money supply = new reserves × money multiplier

Use the new excess reserves injected into the system as the starting amount.

Excess reserves

Excess reserves = deposits − required reserves

Required reserves = deposits × reserve requirement. Only excess reserves can be lent.

Equation of exchange

M × V = P × Y

V is velocity. Quantity theory assumes V and Y are stable, so P moves with M.

Functions of money

Medium of exchange; unit of account; store of value

Know which function a scenario describes.

Central bank objective

Price stability = low, stable inflation (often a target near 2%)

Typical primary objective. Secondary goals can include employment, growth, financial stability and exchange rate stability.

Independence

Independence has two dimensions: operational and target. Many banks have operational independence only.

Target independence is less common. In many cases the government sets the target and the bank has operational independence only.

Credibility channel

Independence + transparency → credibility → anchored inflation expectations

A credible bank can control inflation with smaller changes in policy rates.

Inflation target band

Target = point target ± tolerance band (e.g., 2% ± 1%)

Some banks use a point target, others use a range. Know the difference.

Fisher effect (approximation)

nominal rate ≈ real rate + expected inflation

Use when rates are small. Rearrange to find the real rate: real ≈ nominal − expected inflation.

Fisher effect (exact)

(1 + nominal) = (1 + real) × (1 + expected inflation)

Use when the question asks for an exact value or when rates are high.

Simple money multiplier

money multiplier = 1 ÷ reserve requirement

Assumes banks hold no excess reserves and no cash leaks out of the banking system.

Direction of OMO and reserve changes

Buy securities → reserves ↑ → rates ↓. Sell securities → reserves ↓ → rates ↑. Reserve requirement ↑ → lending capacity ↓.

Know these directions without hesitation.

Transmission chain

Policy rate → short-term rates → bank lending, asset prices, exchange rate, expectations → demand → output and inflation

Policy works with a lag.

Neutral nominal policy rate

Neutral rate = real trend rate of growth + inflation target

Use the central bank's target inflation, not current inflation, unless the question says otherwise.

Stance rule

Policy rate < neutral: expansionary. Policy rate > neutral: contractionary. Policy rate = neutral: neutral.

Compare levels, not the direction of the latest change.

Real policy rate

Real policy rate ≈ policy rate − expected inflation

Compare with the real trend rate to judge stance in real terms.

Taylor rule

i* = r_neutral + π + 0.5 × (π − π*) + 0.5 × (y − y*)

This is the standard textbook form, not the curriculum's neutral-rate formula. i* is the target nominal policy rate, r_neutral is the real neutral rate (approximately the real trend growth rate), so the nominal neutral rate is r_neutral + π*. π is current inflation, π* is target inflation, and y − y* is the output gap in percent. Weights of 0.5 are the common textbook values. Use the form and weights given in the question.

Zero lower bound idea

Policy rate ≈ 0 → conventional rate cuts lose power

Rates can go slightly negative in some economies, so the floor is not always exactly zero.

QE effect on bonds

Central bank bond purchases → bond prices ↑ → long-term yields ↓

Prices and yields move in opposite directions.

Policy mix: expansionary fiscal + expansionary monetary

Output ↑; interest rates ambiguous (fiscal raises them, monetary lowers them); inflation pressure ↑

Effects on output are reinforced when both point the same way. The effect on interest rates depends on which force is stronger.

Policy mix: tight fiscal + loose monetary

Output effect indeterminate (depends on relative strength); interest rates ↓; private investment favoured

Rates fall, so the mix tends to favour private-sector spending over government spending. The net effect on output depends on which policy is stronger.

Policy mix: loose fiscal + tight monetary

Output effect mixed; interest rates ↑; government share of demand ↑

Higher rates can crowd out private investment.

Quick revision

• Money functions: medium of exchange, unit of account, store of value.
• Money multiplier = 1 ÷ reserve requirement; with a 10% requirement it is 10.
• Banks create money by lending out deposits beyond required reserves.
• Central bank goals usually include price stability; many also target growth and employment.
• Many central banks target a low, positive inflation rate rather than zero.
• Tools: policy rate, reserve requirement, open market operations, and communication.
• Buying securities adds reserves and eases policy; selling securities drains reserves and tightens policy.
• A rate cut tends to lower borrowing costs, raise asset prices, weaken the currency and lift inflation.
• Neutral rate = real trend rate of economic growth + target inflation rate.
• Policy rate above neutral is contractionary; below neutral is expansionary.
• Unconventional tools include quantitative easing, forward guidance and negative policy rates.
• Limits: policy lags, weak transmission, and a liquidity trap when rates near zero fail to lift spending.

Common mistakes

• Multiplying by the reserve requirement instead of dividing 1 by it. Fix: A smaller reserve ratio must give a bigger multiplier. Use 1 ÷ ratio and sanity-check that result.
• Applying the multiplier to total deposits rather than new reserves. Fix: Apply it to the new reserves or excess reserves injected, not to the whole existing deposit base.
• Treating a central bank like a large commercial bank that lends to the public and seeks profit. Fix: Remember the central bank serves banks and government, issues currency and targets public goals, not profit.
• Confusing operational independence with target independence. Fix: Operational = chooses tools. Target = sets the goal. Target independence is the less common of the two.
• Saying a central bank sale of securities increases reserves. Fix: When the central bank sells, banks pay with reserves, so reserves fall and rates rise.
• Treating a lower reserve requirement as contractionary. Fix: A lower requirement frees funds to lend, so it is expansionary. Think of the multiplier 1 ÷ reserve ratio rising.
• Using current inflation instead of the inflation target in the neutral rate. Fix: Neutral rate uses the target. Current inflation appears in the Taylor rule gap.
• Calling policy expansionary because the bank just cut rates. Fix: Compare the rate level with neutral. A cut from a high level may still leave policy contractionary.
• Saying QE lowers the short-term policy rate directly Fix: QE works mainly on long-term yields by buying bonds when the policy rate is already near its floor.
• Thinking bond purchases raise yields Fix: More demand raises bond prices, and higher prices mean lower yields.

Exam tips

• Questions often give a reserve ratio and a deposit. Compute the multiplier first, then check which base to use.
• Expect conceptual items asking which function of money a situation illustrates. Match the behavior to the function.
• Remember that the simple multiplier is a maximum. Options mentioning leakages usually point to a smaller real multiplier.
• For equation of exchange items, use growth rates and keep track of the sign of each term.
• With no penalty for wrong answers, never leave a question blank. Eliminate the option that reverses the direction first.
• Questions are often definitional. Learn the six roles and the one-line meaning of each.
• Expect a comparison of inflation targeting versus exchange rate targeting. Link each to its policy trade-off.
• Watch wording on independence: operational versus target.