Recent macroeconomic history: formula sheet

Key formulas

Gold parity of the dollar

Official price = $35 per ounce of gold

The anchor of the system. The US promised to convert dollars held by foreign central banks into gold at this price.

Par value and band

Allowed range = par value ± 1%

Members pegged to the dollar and kept the market rate within this band. Narrow band is the usual figure; state it as the typical rule.

Implied gold price of a currency

Gold price in local currency = $35 × (local currency units per $1)

Use it to turn a dollar peg into an implied gold price per ounce.

Defending a peg

Deficit at the peg → excess supply of the currency → central bank buys it using foreign reserves

If reserves run low, the country must borrow from the IMF, raise interest rates, cut demand or devalue.

Triffin dilemma

More dollars for world liquidity ⇒ larger US deficit ⇒ weaker confidence in gold convertibility

Liquidity and confidence cannot both be met in the long run.

Stagflation condition

Stagflation = inflation rising (or high) + output growth falling (or negative) + unemployment rising

All three features must appear together. High inflation alone is not stagflation.

Supply shock in AD-AS

Higher input costs → SRAS shifts left → price level ↑, real GDP ↓

Aggregate demand does not shift in the basic story. Draw only the SRAS shift.

Expectations-augmented Phillips curve

π = πᵉ − β(u − uₙ)

π is actual inflation, πᵉ is expected inflation, u is unemployment, uₙ is the natural rate, β > 0. Higher πᵉ shifts the short-run curve up.

Real wage

Real wage = nominal wage ÷ price level

Rising prices cut real wages unless nominal wages rise, which fuels the wage-price spiral.

Equation of exchange

M × V = P × T

M is money supply, V is velocity of circulation, P is the price level and T is the volume of transactions (often replaced by real output Y). It is an identity. It becomes the quantity theory only if V and T are assumed stable.

Quantity theory (growth form)

% change in M + % change in V ≈ % change in P + % change in Y

If V is stable and Y grows at its trend rate, inflation ≈ money growth minus real growth. This is an approximation.

Expectations-augmented Phillips curve

π = πe + f(U − Un)

Inflation π depends on expected inflation πe and on the gap between actual unemployment U and the natural rate Un. At U = Un, inflation equals expected inflation, so the long-run curve is vertical.

Inflation rate

Inflation rate (%) = (P₁ − P₀) ÷ P₀ × 100

P₀ is the price index in the base period and P₁ in the later period. Use this to compare actual inflation with the target.

Real interest rate (approximate)

Real rate ≈ nominal rate − expected inflation

Central banks aim at the real rate. The exact form is (1 + nominal) ÷ (1 + inflation) − 1.

Taylor rule (one common form)

i = r* + π + 0.5(π − π*) + 0.5(y gap)

i is the policy rate, r* the neutral real rate, π inflation, π* the target and y gap the output gap in %. It is a guide to how rates respond, not a rule central banks follow exactly. Coefficients vary by version.

Balance of payments identity

Current account + Capital and financial account + Change in reserves (with sign) = 0

A current account deficit must be financed by net capital inflow or by running down reserves. Ignoring errors and omissions.

Current account

CA = (X − M) + net income + net transfers

Trade deficit is only one part. In India, remittances are a large positive transfer.

Real interest rate (approximate)

r ≈ i − π

With deflation, π is negative, so real rate can be positive even when nominal rate i is zero. This is why Japan's zero rates were still tight.

Liquidity trap

Nominal interest rate i ≈ 0, so monetary policy cannot cut further

Money demand becomes very elastic at the lower bound. Condition, not an always-true rule.

Foreign currency debt in local terms

Debt (local) = Debt (USD) × Exchange rate (local per USD)

A fall in the local currency raises the local value of the debt.

Import cover of reserves

Import cover (months) = Reserves ÷ (Annual imports ÷ 12)

A common vulnerability measure.

Leverage ratio

Leverage = Total assets ÷ Equity

Higher leverage means a small fall in asset value can wipe out equity. For example, leverage of 30 means a fall of about 3.3% in assets erases equity.

Equity wipe-out point

Fall in assets that eliminates equity = 1 ÷ Leverage

Use it to show why highly geared banks were fragile.

Causal chain

Easy credit → subprime lending → securitisation → house price fall → defaults → asset losses → credit freeze → recession

A structure for any essay. Add the Lehman event and policy response.

Simple spending multiplier

k = 1 ÷ (1 − MPC × (1 − t) + MPM), which simplifies to k = 1 ÷ (1 − MPC) when there are no taxes or imports

Here MPC is the marginal propensity to consume out of disposable income, t is the tax rate on income, and MPM is the marginal propensity to import (the share of each extra rupee of income spent on imports). Use the simplified form only if the question ignores taxes and imports (t = 0 and MPM = 0). With taxes and imports, the multiplier is smaller. Austerity debates turn on its size.

Change in output from a spending change

ΔY = k × ΔG

A cut in government spending (ΔG negative) lowers output by a multiple. Taxes work through MPC × ΔT, with a smaller effect than spending.

Bond price and yield

Price = Σ C ÷ (1 + y)^t + F ÷ (1 + y)^n

Price and yield move in opposite directions. QE buying raises prices and lowers yields.

Debt-to-GDP ratio

Debt ratio = Public debt ÷ GDP

It can rise even when debt is cut, if GDP falls by more in proportion.

Inflation rate

Inflation rate = (P₁ − P₀) ÷ P₀ × 100%

P is a price index such as the CPI. P₀ is the earlier period and P₁ the later period.

Real interest rate (approximate)

Real rate ≈ nominal rate − expected inflation

Exact form: (1 + real) = (1 + nominal) ÷ (1 + inflation). The approximation works for small rates.

Real GDP growth (approximate)

Real growth ≈ nominal GDP growth − inflation

Use the exact form (1 + g real) = (1 + g nominal) ÷ (1 + inflation) for precise answers.

Fiscal deficit

Budget deficit = government spending − government revenue

Pandemic support raised spending and cut revenue, so deficits widened.

Quick revision

• Bretton Woods: post-war system of fixed but adjustable exchange rates tied to the US dollar, with the dollar linked to gold; it broke down in the early 1970s.
• Stagflation: high inflation together with high unemployment and weak growth; it is hard to explain with a simple demand-side view.
• Oil shocks of the 1970s were supply shocks that raised costs and prices and cut output.
• Monetarism: inflation is mainly caused by excessive growth of the money supply, so control money growth.
• The neoliberal turn favoured markets, deregulation, privatisation and lower inflation as the main policy goal.
• The Great Moderation: a period of low and stable inflation and steadier growth, often linked to inflation targeting and credible central banks.
• Inflation targeting: the central bank announces a numerical inflation target and adjusts interest rates to meet it.
• 1990s crises showed the risks of fixed exchange rates, short-term foreign borrowing and weak banks.
• 2007-08 crisis: a collapse in housing and mortgage-linked assets spread through highly leveraged banks and caused a global credit freeze.
• QE: the central bank buys assets to lower long-term yields and add liquidity when the policy rate is near zero.
• Austerity means cutting government spending or raising taxes to reduce deficits; critics argue it can slow recovery.
• COVID-19 combined demand collapse, supply disruption and large fiscal and monetary support, followed by an inflation surge and rate rises.

Common mistakes

• Saying the IMF and World Bank do the same job. Fix: IMF: monetary stability, exchange rate rules, short-term balance of payments support. World Bank: long-term lending for reconstruction and development.
• Describing the system as a pure gold standard with every currency tied to gold. Fix: Only the dollar was linked to gold. Other currencies were pegged to the dollar. It was a gold-exchange standard.
• Drawing the oil shock as a rightward shift of aggregate demand. Fix: An oil shock is a cost shock. Shift SRAS left. Prices rise but output falls.
• Saying oil shocks were the only cause of stagflation. Fix: Mention amplifiers too: wage indexation and bargaining, rising expectations and earlier loose policy.
• Saying monetarists believe money supply never affects output. Fix: Say money growth can affect output briefly, but in the long run it mainly affects prices.
• Treating MV = PT as proof that money causes inflation. Fix: Remember it is an identity. It supports the causal claim only if V and T are stable.
• Saying the Great Moderation was caused only by inflation targeting. Fix: Always list policy, good luck and structural change, and say economists disagree on the weights.
• Dating the Great Moderation to the 1970s or after 2008. Fix: Remember: mid-1980s to 2007, between the 1970s stagflation and the crisis.
• Saying Japan's lost decade was caused by high interest rates throughout. Fix: Say the bubble burst, balance sheets were damaged, and rates then fell close to zero, creating a liquidity trap.
• Treating the Asian crisis as only a current account problem. Fix: Stress the capital account: short-term dollar borrowing, currency mismatch and sudden capital flight.

Exam tips

• Write the roles of the IMF and World Bank in separate sentences. Examiners award marks for each role.
• For collapse questions, aim for three or four distinct causes and name the Triffin dilemma. A one-cause answer loses marks.
• In calculations, state the par value, the band and the direction of central bank action. Show the 1% step explicitly.
• Link the topic to the Keynesian consensus and to the 1970s stagflation. Examiners reward answers that place events in sequence.
• In multiple-choice questions, watch for options that call the system a pure gold standard or a freely floating system. Both are wrong.
• Always draw and label the SRAS shift. Examiners reward the correct diagram and its reading.
• Use the words 'supply shock', 'cost-push' and 'expectations'. These are the marking terms.
• Give a balanced answer: oil shocks as the trigger, other factors as amplifiers.