A Level Economics (A2) formulas and key terms

The price system and the microeconomy

Utility

• Total utility (TU): total satisfaction from all units consumed.
• Marginal utility (MU) = change in total utility ÷ change in quantity.
• Diminishing marginal utility: MU falls as more units of a good are consumed.
• TU is at its maximum when MU = 0. If MU is negative, TU falls.
• Equi-marginal principle: MU of X ÷ price of X = MU of Y ÷ price of Y (MU_X/P_X = MU_Y/P_Y), with all income spent.
• A consumer buys a good up to the unit where its marginal utility, valued in money, equals its price.
• Limitations: utility cannot be measured in units, and consumers are not always rational (habit, impulse, poor information).

Indifference curves and budget lines

• Slope of the budget line = price of X ÷ price of Y (X on the horizontal axis).
• Intercepts of the budget line: income ÷ price of X, and income ÷ price of Y.
• A change in income shifts the budget line parallel. A change in one price pivots it about the other good’s intercept.
• At the best choice: marginal rate of substitution = price of X ÷ price of Y.
• Substitution effect: a fall in price always raises the quantity demanded.
• Income effect of a price fall: raises quantity for a normal good, lowers it for an inferior good.
• Giffen good: an inferior good whose income effect is larger than its substitution effect, so a price fall lowers the quantity demanded.

Efficiency and market failure

• Productive efficiency: production at the lowest point of the average total cost curve, where MC = ATC. For an economy: any point on the production possibility curve.
• Allocative efficiency: price = marginal cost (P = MC).
• Pareto optimality: no one can be made better off without making someone else worse off.
• Dynamic efficiency: lower costs and better products over time through investment, research and innovation.
• Market failure: the free market fails to allocate resources efficiently.
• Reasons for market failure: externalities, public goods, merit and demerit goods, information failure, market power (monopoly), immobility of factors of production.

Private costs and benefits, externalities and social costs and benefits

• Social cost = private cost + external cost (MSC = MPC + MEC).
• Social benefit = private benefit + external benefit (MSB = MPB + MEB).
• Free market output: MPB = MPC. Socially optimal output: MSB = MSC.
• Negative production externality: MSC is above MPC, so the good is overproduced. Negative consumption externality: MSB is below MPB, so it is overconsumed.
• Positive production externality: MSC is below MPC. Positive consumption externality: MSB is above MPB. The good is underproduced or underconsumed.
• Deadweight welfare loss: the triangle between MSB and MSC, from the market output to the social optimum. Area = ½ × base × height.
• Cost-benefit analysis: go ahead if total social benefit is greater than total social cost.

Types of cost, revenue and profit, short-run and long-run production

• Average product = total product ÷ number of workers. Marginal product = change in total product ÷ change in workers.
• TC = TFC + TVC. ATC = TC ÷ output = AFC + AVC. MC = change in TC ÷ change in output.
• AFC always falls as output rises. MC cuts AVC and ATC at their lowest points.
• Returns to scale: all inputs rise by x%. Output rises by more than x% (increasing), by x% (constant) or by less than x% (decreasing).
• Internal economies or diseconomies of scale: a movement along the LRAC curve as the firm grows. External ones: the whole LRAC curve shifts as the industry grows.
• TR = price × quantity. AR = TR ÷ quantity = price. MR = change in TR ÷ change in quantity.
• Supernormal profit: TR is greater than TC. Normal profit: TR = TC. Subnormal profit (a loss): TR is less than TC. Profit = (AR − ATC) × quantity.

Different market structures

• Perfect competition: P = AR = MR (horizontal demand). In the long run P = MC = lowest ATC: normal profit, allocative and productive efficiency.
• Monopoly: AR slopes down and MR lies below it. Output is lower and price higher than in perfect competition, with P above MC. X-inefficiency: costs above the lowest possible level.
• Monopolistic competition in the long run: AR touches ATC (normal profit), but P is above MC and there is excess capacity.
• Shutdown: in the short run if price is below AVC. In the long run if price is below ATC.
• A perfectly competitive firm’s short-run supply curve is its MC curve above AVC.
• Natural monopoly: economies of scale are so large that one firm can supply the whole market at the lowest average cost.
• n-firm concentration ratio = total market share of the n largest firms (%).

Growth and survival of firms

• Horizontal integration: firms at the same stage of the same industry. Gains: larger market share and economies of scale.
• Vertical integration backwards: joining with a supplier. Forwards: joining with a firm nearer the customer, such as a retailer.
• Conglomerate integration: firms in unrelated industries. Main gain: spreading risk.
• Conditions for an effective cartel: few firms, similar products and costs, high barriers to entry, inelastic demand, output that is easy to check.
• Each cartel member gains by selling more than its quota at the high price, so cartels tend to break down.
• Consequences of a cartel: higher prices, lower output and less consumer surplus.
• Principal-agent problem: shareholders (principals) want profit, but managers (agents) may follow their own aims such as sales, pay or status. Profit-related pay and share schemes reduce it.

Differing objectives and policies of firms

• Profit maximisation: MC = MR, with MC rising. Revenue maximisation: MR = 0. Sales maximisation: the largest output where AR = AC (normal profit).
• First degree: each buyer pays the most they are willing to pay. Second degree: price depends on the quantity bought. Third degree: different prices for different groups of buyers.
• Conditions for price discrimination: market power, separate markets with different price elasticities, no resale between them.
• With third-degree discrimination the higher price is set in the market with the less elastic demand.
• Limit pricing: a price low enough to deter entry. Predatory pricing: a price below cost to drive rivals out. Price leadership: other firms follow one firm’s price changes.
• Elastic demand: a price cut raises total revenue and MR is positive. Inelastic demand: a price cut lowers total revenue and MR is negative. Total revenue is highest where elasticity is 1.
• Kinked demand curve: MR has a vertical gap at the kink. If MC shifts within the gap, price and output do not change.

Government microeconomic intervention

Government policies to achieve efficient resource allocation and correct market failure

• Specific tax: a fixed amount per unit, so supply shifts up parallel. Ad valorem tax: a percentage of price, so supply pivots and the gap widens as price rises.
• Ideal tax per unit = marginal external cost at the socially optimal output. Ideal subsidy per unit = marginal external benefit.
• A subsidy shifts supply to the right: price falls and quantity rises. Cost to the government = subsidy per unit × new quantity.
• Maximum price below equilibrium: shortage. Minimum price above equilibrium: surplus.
• Tradable pollution permits: total pollution is fixed. Firms that can cut pollution cheaply do so and sell permits to firms for which it is costly.
• Privatisation: selling state-owned firms to the private sector. Nationalisation: the opposite. Deregulation: removing rules that restrict competition.
• Causes of government failure: poor information, unintended consequences, administrative costs, political aims, regulatory capture.

Equity and redistribution of income and wealth

• Horizontal equity: people in the same circumstances are treated the same. Vertical equity: people with more ability to pay contribute more.
• Absolute poverty: income too low to buy basic needs such as food, clothing and shelter.
• Relative poverty: income below a set share of the average, for example below 60% of median income.
• Effective marginal tax rate = (extra tax paid + benefits lost) ÷ extra income × 100.
• Means-tested benefits: paid only to those with low income. They are targeted and cheaper, but can cause a poverty trap and some people do not claim.
• Universal benefits: paid to everyone in a group whatever their income. Simple and no poverty trap, but costly.
• Negative income tax: people below a set income receive a payment from the state. Universal basic income: a regular payment to every citizen with no conditions.

Labour market forces and government intervention

• Marginal revenue product (MRP) = marginal product × marginal revenue. In a perfectly competitive product market, MRP = marginal product × price.
• A firm hires workers up to the point where MRP = the marginal cost of labour (the wage, in a competitive labour market).
• A change in the wage causes a movement along the demand curve. A change in productivity or product price shifts it.
• A wage set above a competitive equilibrium raises the supply of labour and cuts the quantity demanded, giving unemployment.
• Monopsony: hires where the marginal cost of labour = MRP and pays the wage on the supply curve at that employment. A minimum wage can raise both the wage and employment.
• Transfer earnings: the minimum payment needed to keep a factor in its present use. Economic rent: any payment above transfer earnings.
• The more inelastic the supply of labour, the larger the share of earnings that is economic rent.

The macroeconomy

The circular flow of income

• Multiplier (k) = change in national income ÷ change in injection.
• Closed economy, no government: k = 1 ÷ mps = 1 ÷ (1 − mpc). With government: k = 1 ÷ (mps + mrt). Open economy with government: k = 1 ÷ (mps + mrt + mpm).
• Average propensity = total ÷ income (apc = C ÷ Y). Marginal propensity = change ÷ change in income (mpc = ΔC ÷ ΔY). The same pattern gives aps, mps, apm, mpm, art and mrt.
• Consumption function: C = a + bY. a is autonomous consumption and bY is induced consumption (b = mpc). Savings function: S = −a + (1 − b)Y.
• Accelerator: net investment = capital-output ratio × change in output. It is induced investment.
• Deflationary gap: aggregate expenditure is below the level needed for full employment income. Inflationary gap: it is above.
• Change in injection needed to close a gap = change in income needed ÷ multiplier.

Economic growth and sustainability

• Output gap = actual output − potential output; often given as a percentage of potential output.
• Negative output gap: actual below potential, so spare capacity and cyclical unemployment. Positive output gap: actual above potential, so inflationary pressure.
• Recession: real GDP falls for two consecutive quarters. Slower positive growth is not a recession.
• Automatic stabilisers: tax revenue and welfare spending change with the cycle without any new government decision, so they reduce the size of booms and recessions.
• Accelerator: a change in the growth of output or consumer demand causes a larger proportional change in investment.
• Demand-side policies raise actual growth; supply-side policies (education, training, investment, infrastructure) raise potential growth.
• A renewable resource is used sustainably only if the amount taken each year is no more than the amount that regenerates.

Employment and unemployment

• Unemployment rate = unemployed ÷ labour force × 100. Labour force = employed + unemployed.
• Natural rate of unemployment: the rate when the labour market is in equilibrium and inflation is stable; it consists of frictional and structural unemployment.
• Disequilibrium unemployment = workers willing to accept jobs at the current real wage − workers demanded by firms.
• Voluntary unemployment: a person chooses not to accept a job at the current wage. Involuntary unemployment: a person is willing to work at the current wage but cannot find a job.
• Occupational mobility: ability to change job type (helped by training). Geographical mobility: ability to move to another area (limited by housing costs, family ties, lack of information).
• Unemployment above the natural rate: use demand-side policies. Unemployment at the natural rate: use supply-side policies, because extra demand only raises inflation.
• The natural rate falls with better training, better job information, lower benefits relative to wages and greater labour mobility.

Money and banking

• Quantity theory: money supply × velocity of circulation = price level × volume of transactions (MV = PT). If V and T are constant, a rise in M causes a proportional rise in P.
• Bank credit multiplier = 1 ÷ reserve ratio. Maximum total deposits = reserves × credit multiplier.
• Reserve ratio = liquid reserves ÷ deposits. Capital ratio = a bank's own capital ÷ its (risk-weighted) assets, mainly loans.
• Bank objectives conflict: liquid assets (cash, bills) are safe but earn little; loans earn more but are less liquid and more risky.
• Money supply rises with more bank lending, government borrowing from the central bank or commercial banks, quantitative easing (the central bank creates money to buy bonds) and a balance of payments surplus.
• Liquidity preference: transactions and precautionary demand depend on income; speculative demand is inversely related to the interest rate. In a liquidity trap, extra money is simply held and the interest rate does not fall.
• Loanable funds: the interest rate is set where the supply of loanable funds (saving) equals the demand for loanable funds (borrowing for investment and by government).

Government macroeconomic intervention

Government macroeconomic policy objectives

• Price stability: a low, stable inflation target (often around 2%). A little inflation allows real wages to adjust and keeps the economy away from deflation.
• Unemployment: low, close to the natural rate, not zero.
• Growth: a steady, sustainable rise in real GDP in line with the growth of potential output.
• Balance of payments: a sustainable current account; a large persistent deficit must be financed by borrowing or by selling assets.
• Redistribution: a lower Gini coefficient shows income is more equally shared.
• Development is wider than growth: it includes health, education and living standards, for example a rising HDI.
• Sustainability: targets that protect resources for future generations, such as limits on carbon emissions.

Links between macroeconomic problems

• Change in internal value of money (%) = (old price index ÷ new price index − 1) × 100.
• Relatively high inflation: floating rate, the currency depreciates; fixed rate, the current account worsens.
• Depreciation raises import prices (cost-push) and net exports (demand-pull), so it tends to raise inflation.
• Rise in imports = income elasticity of demand for imports × % rise in income × original imports.
• Traditional Phillips curve: an inverse relationship between the unemployment rate and the rate of inflation (originally money wage inflation).
• Expectations-augmented: each short-run Phillips curve is drawn for one expected rate of inflation; higher expected inflation shifts it upwards.
• The long-run Phillips curve is vertical at the natural rate of unemployment. Holding unemployment below it needs ever-accelerating inflation.

Effectiveness of policy options

• Tax revenue = tax rate × taxable income. On the Laffer curve, revenue is zero at 0% and at 100% and is highest at a rate in between.
• Above the revenue-maximising rate, a tax cut raises revenue; below it, a tax cut lowers revenue.
• Market-based supply-side policies: lower direct taxes, lower benefits, deregulation, privatisation. Interventionist: state spending on education, training, infrastructure and research.
• Crowding out: government borrowing raises interest rates and reduces private investment, so fiscal expansion has less effect.
• Higher interest rates under a floating rate attract hot money, the currency appreciates, and exports and the current account suffer.
• A fall in the exchange rate works only if the price elasticities of demand for exports and imports add up to more than 1 and there is spare capacity.
• Causes of government failure: inaccurate data, time lags (recognition, decision, effect), political pressure before elections, and unintended effects on incentives.

International economic issues

Policies to correct balance of payments disequilibrium

• Current account balance = balance of trade in goods + balance of trade in services + net primary income + net secondary income.
• Primary income: profits, interest, dividends and wages earned across borders. Secondary income: transfers with nothing given in return, such as workers' remittances and aid grants.
• Financial account: foreign direct investment, portfolio investment (shares and bonds), other investment (loans, bank deposits) and reserve assets.
• Current account + capital account + financial account + net errors and omissions = 0.
• Expenditure-reducing: higher taxes, lower government spending, higher interest rates. They cut imports by cutting aggregate demand, so output and jobs also fall.
• Expenditure-switching: devaluation or depreciation, tariffs, quotas, export subsidies. They change relative prices.
• Supply-side policies improve competitiveness and the current account, but only in the long run.

Exchange rates

• Real exchange rate = nominal exchange rate × (domestic price level ÷ foreign price level).
• Trade-weighted index = sum of (each partner's trade weight × the exchange rate index against that partner).
• Fixed rate with excess supply of the currency: the central bank buys its own currency with foreign reserves or raises interest rates.
• Devaluation: an official lowering of a fixed rate. Depreciation: a fall in a floating rate caused by market forces. Revaluation and appreciation are the opposites.
• A floating currency appreciates when demand for it rises (more exports, higher interest rates, inward investment) or its supply falls.
• Marshall-Lerner condition: a depreciation improves the balance of trade only if PED for exports + PED for imports is greater than 1 (ignoring the minus signs).
• J curve: after a depreciation the trade balance first worsens, because demand is inelastic in the short run, and later improves as buyers adjust.

Economic development

• GNI = GDP + net primary income from abroad. NNI = GNI − capital consumption (depreciation).
• Real GDP per head growth ≈ nominal GDP growth − inflation − population growth.
• PPP exchange rate = cost of a basket of goods at home ÷ cost of the same basket in the US, in each country's own currency.
• HDI (0 to 1) combines life expectancy at birth, education (mean and expected years of schooling) and GNI per head at PPP.
• MEW adjusts national income: adds the value of leisure and unpaid work, subtracts 'regrettables' such as commuting and defence, and environmental damage.
• MPI = proportion of people who are multidimensionally poor × average intensity of their deprivation.
• Kuznets curve: as income per head rises, inequality first rises and then falls (an inverted U shape).

Characteristics of countries at different levels of development

• Birth rate and death rate: live births and deaths per 1,000 of the population per year.
• Infant mortality rate: deaths of children under one year old per 1,000 live births per year.
• Natural increase = birth rate − death rate. Population growth = natural increase + net migration (immigration − emigration).
• Below the optimum population, a rise in population raises output per head; above it, output per head falls.
• Gini coefficient = area between the line of equality and the Lorenz curve ÷ total area under the line of equality (A ÷ (A + B)).
• Gini = 0 is perfect equality; Gini = 1 is perfect inequality. A Lorenz curve further from the 45° line means more inequality.
• Dependence on a few primary exports brings unstable export earnings and a risk of falling terms of trade.

Relationship between countries at different levels of development

• Tied aid: the recipient must spend it on goods and services from the donor country, or on a named project.
• Terms of trade index = index of export prices ÷ index of import prices × 100.
• MNC: a firm that owns or controls production in more than one country. FDI: investment that sets up or buys a lasting controlling interest in a business abroad.
• FDI inflow: a credit in the host's financial account. Profits sent home later: a debit in primary income on the host's current account.
• Transfer pricing: an MNC sets prices between its own subsidiaries so that profit appears in low-tax countries.
• If debt is in foreign currency, a depreciation raises its cost in local currency. Debt servicing uses export earnings that could have paid for imports, schools and health.
• IMF: short-term loans to countries with balance of payments problems, usually with conditions, and support for exchange rate stability. World Bank: long-term loans and grants for development projects and poverty reduction.

Globalisation

• Free trade area: no trade barriers between members; each member keeps its own barriers against non-members.
• Customs union: a free trade area plus a common external tariff on imports from non-members.
• Monetary union: members share a single currency, a single central bank and one interest rate.
• Full economic union: a single market and currency with common fiscal and other economic policies set centrally.
• A free trade area needs rules of origin, to stop imports entering through the member with the lowest tariff.
• Trade creation moves production to a lower-cost source and raises efficiency; trade diversion moves it to a higher-cost source and lowers efficiency.
• To compare sources, use price including tariff = cost × (1 + tariff rate); members pay no tariff.