Relationship between the government and the individual firm: formula sheet

Key formulas

Allocative efficiency condition

P = MC

Price equals marginal cost. Monopoly output usually has P > MC, which is the efficiency case for regulation.

Public good test

Non-excludable AND non-rival

Both features must hold for a pure public good. If only one holds, it is a quasi-public or common resource.

Externality and social cost

MSC = MPC + MEC (negative externality); MSB = MPB + MEB (positive externality)

Social optimum is where MSB = MSC. Market output is too high with negative externalities and too low with positive ones.

Government budget balance

Budget balance = Government revenue − Government spending

A negative value is a deficit. It is a basic measure of fiscal stance.

Social cost

Marginal social cost (MSC) = marginal private cost (MPC) + marginal external cost (MEC)

Use for negative production externalities. The efficient output is where MSC = MSB.

Social benefit

Marginal social benefit (MSB) = marginal private benefit (MPB) + marginal external benefit (MEB)

Use for positive externalities. Market output is where MPB = MPC, which is below the social optimum.

Efficiency condition

Socially efficient output: MSB = MSC

Market failure exists when the market output does not satisfy this.

Corrective (Pigouvian) tax

Tax per unit = marginal external cost at the efficient output

This makes the firm face the full social cost. A subsidy per unit equal to marginal external benefit is the matching fix for positive externalities.

Public good test

Non-excludable AND non-rival

Both conditions are needed for a pure public good. Goods failing one test are quasi-public goods.

Price cap (RPI − X)

Allowed average price change = RPI inflation − X

X is the required efficiency gain. A higher X forces prices down in real terms. Use CPI − X if the question names CPI.

Price cap with pass-through (RPI − X + K)

Allowed price change = RPI − X + K

K adjusts for items such as new investment or quality targets. Only use it if the question mentions it.

Rate-of-return limit

Allowed profit = allowed rate of return × capital base

Weak incentive to cut costs because higher costs can justify higher allowed revenue.

Profit-maximising monopoly

MR = MC, then price from the demand curve

Unregulated monopoly price exceeds MC, which causes deadweight loss.

Efficient regulated price

P = MC (allocative efficiency)

For a natural monopoly with falling average cost, MC lies below AC, so P = MC creates a loss and may need a subsidy.

Fair-return price

P = AC

A common compromise: the firm breaks even with normal profit, with some deadweight loss remaining.

Per-unit tax: new supply curve

If original supply is P = a + bQ, new supply is P = a + t + bQ

t is the tax per unit. The curve shifts up by t. Parallel shift for a per-unit tax.

Price received by the seller

Pseller = Pbuyer − t

At the new equilibrium, the buyer's price is higher than before. The seller keeps less than the buyer pays.

Consumer burden of a tax

Consumer burden per unit = Pbuyer(after) − P(before)

Producer burden per unit = P(before) − Pseller(after). The two burdens add up to t.

Incidence split (elasticities)

Consumer share ÷ Producer share = |Es| ÷ |Ed|

Es is price elasticity of supply, Ed is price elasticity of demand, at the equilibrium. This is a standard approximation for small taxes. Less elastic side bears more. In slope terms for linear curves, the consumer share of t is B ÷ (B + D), where B is the demand slope and D is the supply slope.

Government tax revenue

Revenue = t × Q(after tax)

Use the new quantity, not the old one.

Per-unit subsidy

New supply: P = a − s + bQ. Subsidy cost = s × Q(after)

s is the subsidy per unit. Price paid by buyer falls. Price received by seller = buyer's price + s.

Deadweight loss (linear curves)

DWL = ½ × t × (Q(before) − Q(after))

Valid for linear demand and supply curves, for any size of tax. It is the area of the triangle between the curves. In the worked example, DWL = ½ × 8 × (20 − 18) = ₹8.

Aggregate demand

AD = C + I + G + (X − M)

Fiscal policy acts on G and, through taxes, on C and I. Monetary policy acts mainly on C and I, and on X − M through the exchange rate.

Budget balance

Budget balance = Government revenue − Government spending

A negative value is a deficit. A deficit financed by borrowing can raise interest rates.

Real interest rate (approximate)

Real rate ≈ Nominal rate − Inflation rate

Firms and savers respond to the real rate. This is an approximation that works for small rates.

Exchange rate effect on price

Rupee price of an import = Foreign price × Exchange rate (₹ per unit of foreign currency)

If the rupee depreciates, the rate rises and imports cost more in rupees.

Direction rules

Lower interest rates or lower taxes → higher AD; higher rates or higher taxes → lower AD

These are general tendencies, with lags. Effects depend on confidence, existing debt and spare capacity.

Quick revision

• Governments intervene to improve efficiency, promote equity and keep the economy stable.
• A negative externality means social cost is higher than private cost, so the market produces too much.
• A positive externality means social benefit is higher than private benefit, so the market produces too little.
• A tax on a negative externality aims to make the firm bear the full social cost.
• Public goods are non-excludable and non-rival, so free riding leads to under-provision by the market.
• Competition policy targets abuse of market power, cartels and harmful mergers.
• Price controls such as a ceiling below equilibrium cause shortages.
• A per-unit tax shifts the supply curve up. The burden falls more on the less elastic side.
• A subsidy lowers a firm's costs and shifts supply down, raising output and lowering price.
• Fiscal policy uses government spending and tax. Monetary policy uses interest rates and money supply.
• Higher interest rates raise a firm's borrowing cost and usually reduce investment.
• Always end a written answer by stating the effect on the firm: cost, price, output or profit.

Common mistakes

• Calling every public service a public good. Fix: Apply both tests. Education and healthcare are often government-provided but are rival and excludable, so they are not pure public goods.
• Treating inequality as a market failure. Fix: Keep them apart. Market failure is about inefficiency. Equity is about fairness and is a value judgement.
• Treating any harmful effect as a negative externality. Fix: Ask who pays. If the buyer and seller bear the cost themselves, it is not an externality.
• Saying a public good is one provided by the government. Fix: Define it by non-excludability and non-rivalry. Government provision is a response, not the definition.
• Treating privatisation and deregulation as the same thing. Fix: Privatisation changes ownership. Deregulation removes rules or entry barriers. Say which one a policy does.
• Saying a price cap fixes the price at a set level. Fix: An RPI − X cap limits the rate of price increase for a regulated basket. It is linked to inflation and an efficiency target.
• Shifting the supply curve by the wrong amount or in the wrong direction. Fix: A per-unit tax adds t to the price at every quantity, so the curve moves up by t. A subsidy subtracts s. Check the direction against what should happen to quantity.
• Saying consumers pay the whole tax because the firm passes it on. Fix: Compute the rise in the buyer's price and compare it with t. It is usually less than t unless demand is perfectly inelastic or supply is perfectly elastic.
• Mixing up fiscal and monetary policy. Fix: Fiscal means government spending and taxes. Monetary means the central bank, interest rates and money supply.
• Saying a rate cut always raises demand. Fix: Say it tends to raise demand. Weak confidence, high existing debt or lags can limit the effect.

Exam tips

• Start answers by naming the type of failure. Examiners award marks for the correct term.
• Always include one evaluation point on government failure for 'discuss' or 'assess' questions.
• In multiple-choice questions on public goods, check both non-excludability and non-rivalry before choosing.
• Link each macroeconomic objective to a policy tool. Do not just list the objectives.
• Show working for any externality calculation: write MSC = MPC + MEC before substituting.
• Define terms precisely in one line first. Examiners award marks for correct definitions of externality, public good and free rider.
• Use the MPC, MSC, MPB and MSB language in written answers and say which curve is above which.
• Always pair the failure with a matching remedy, then add one evaluation point on its limits.