Which pair of properties together defines a pure public good?

Non-rivalry in consumption and non-excludability of non-payers

Rivalry in consumption together with the excludability of non-paying users

Rivalry in consumption and non-excludability of non-payers

Non-rivalry in consumption and non-excludability of non-payers

Non-rivalry in consumption and excludability of non-payers

A factory's production imposes pollution costs on nearby residents that it does not pay for. In an unregulated market, how does its output compare with the socially efficient level, and what is the textbook remedy?

Output is above the efficient level, and a Pigouvian tax equal to the marginal external cost would restore efficiency

Output is below the efficient level, and a Pigouvian subsidy for each unit produced would restore efficiency

Output is above the efficient level, and a Pigouvian tax equal to the marginal external cost would restore efficiency

Output is exactly at the efficient level, because the market already prices the pollution in, so no remedy is needed

Output is above the efficient level, and a flat per-unit production subsidy paid to the firm would restore efficiency

The Coase theorem states that private parties will bargain to the efficient outcome for an externality provided which condition holds?

Property rights are clearly assigned and transaction costs are negligible

The government has already imposed a tax equal to the marginal external cost

The right to pollute has been assigned specifically to the polluter rather than to the victims

A very large number of affected parties must bargain together at once

Property rights are clearly assigned and transaction costs are negligible

The rule for the efficient quantity of a pure public good differs from the rule for a private good. Which statement states the public-good rule correctly?

The sum of individuals' marginal rates of substitution equals the marginal rate of transformation, with demand curves added vertically

Each individual's marginal rate of substitution equals the marginal rate of transformation, with demand curves added horizontally

Marginal revenue equals marginal cost for the single public supplier of the good, with the price set by the supplier

The marginal external benefit is driven to zero by an appropriately chosen corrective subsidy

Which of the following statements about public goods, externalities and the Coase theorem are correct?

A pure public good is non-rival and non-excludable, which is why a competitive market tends to under-provide it

With zero transaction costs and clear property rights, Coasean bargaining reaches the efficient outcome whichever party holds the right

A pure public good is non-rival and non-excludable, which is why a competitive market tends to under-provide it

A negative production externality means the marginal social cost lies below the marginal private cost

With zero transaction costs and clear property rights, Coasean bargaining reaches the efficient outcome whichever party holds the right

Because the atmosphere cannot be fenced off, clean air behaves like a private good that markets supply efficiently

A health insurer finds that, once people are insured, they visit doctors more often and take fewer precautions than before. This behaviour is best described as:

Moral hazard, because it is a hidden change in behaviour after the contract is in force

Adverse selection, because the sicker people were the ones most likely to buy the policy in the first place

A separating signalling equilibrium deliberately engineered by the insurer

Moral hazard, because it is a hidden change in behaviour after the contract is in force

A Pigouvian externality that the insured impose on uninvolved third parties

Which of the following statements about information problems and market regulation are correct?

Adverse selection arises from hidden information before a contract, as when high-risk buyers are keenest to insure

In a natural monopoly, average cost falls over the relevant range, so a single firm supplies the market most cheaply

Costly signalling, such as a credible warranty, can help separate good types from bad under asymmetric information

Adverse selection arises from hidden information before a contract, as when high-risk buyers are keenest to insure

A successful cartel that raises price toward the monopoly level increases consumer surplus

In a natural monopoly, average cost falls over the relevant range, so a single firm supplies the market most cheaply

Costly signalling, such as a credible warranty, can help separate good types from bad under asymmetric information

Which one of the following is an indirect tax?

A value-added tax such as GST charged on a restaurant bill

Personal income tax deducted from a salary

A value-added tax such as GST charged on a restaurant bill

Corporate income tax levied on a company's profits

Capital gains tax charged on the sale of an asset by the owner who holds it

A tax is said to be regressive when:

The average tax rate falls as income rises

The average tax rate rises as income rises

The marginal tax rate equals the average tax rate at every income level

The total amount of tax paid falls as income rises

The average tax rate falls as income rises

A per-unit tax on a good can be collected either from sellers or from buyers. Standard incidence theory predicts that:

The split of the burden between buyers and sellers is the same either way, set only by relative elasticities

Buyers bear more of the burden when the tax is legally collected from buyers

Sellers bear more of the burden when the tax is legally collected from sellers

The split of the burden between buyers and sellers is the same either way, set only by relative elasticities

Whichever side is named as legally liable for the tax always ends up bearing the entire economic burden by itself

Which of the following statements about the effects of taxation are correct?

The more inelastic side of the market bears the larger share of a per-unit tax

The deadweight loss of a tax rises more than proportionately as the tax rate increases

A lump-sum tax creates no deadweight loss because it does not alter any decision at the margin

The statutory side on which a tax is levied determines who ultimately bears its economic burden

The more inelastic side of the market bears the larger share of a per-unit tax

The deadweight loss of a tax rises more than proportionately as the tax rate increases

A lump-sum tax creates no deadweight loss because it does not alter any decision at the margin

Two public projects have the same upfront cost and the same total undiscounted benefits, but Project One delivers most of its benefits in early years while Project Two delivers most of them in later years. Raising the social discount rate will:

Favour Project One relative to Project Two, because more distant benefits are discounted more heavily

Favour Project Two relative to Project One, because later benefits gain in present value when the rate rises

Leave the ranking unchanged, since the total undiscounted benefits of the two projects are equal

Raise the net present value of both projects by the same proportion, because every benefit gains value together

Which of the following statements about the budget, public debt and project appraisal are correct?

In the simple Keynesian model the balanced-budget multiplier equals one

On cost-benefit grounds a public project should be accepted when its net present value is positive

Public debt is more likely to be sustainable when the growth rate of the economy exceeds the real interest rate on the debt

In the simple Keynesian model the balanced-budget multiplier equals one

On cost-benefit grounds a public project should be accepted when its net present value is positive

Public debt is more likely to be sustainable when the growth rate of the economy exceeds the real interest rate on the debt

The tax multiplier is larger in absolute size than the government-spending multiplier

Public Economics: Market Failure, Taxation, the Budget and Project Appraisal

This chapter answers Section XH1.5 of the Humanities and Social Sciences (XH) paper, "Public Economics": "Market Failure and Remedial Measures: Asymmetric Information, Public Goods, Externality, Regulation of Market, Public Revenue: Tax & Non-Tax Revenue, Direct & Indirect Taxes, Progressive and non-Progressive Taxation, Incidence and Effects of Taxation, Public expenditure, Public Debt and its management, Public Budget and Budget Multiplier, Fiscal Policy and its implications, Environment as a Public Good, Coase Theorem, Cost-Benefit Analysis." Public Economics is Section XH1.5 of XH1 Economics, one of the six optional sections of the paper, chosen at the time of application. The chapter teaches why competitive markets fail, the correct remedy for each kind of failure, how a government raises and spends revenue, who really bears a tax, and how a public project is appraised. The numericals are tax-incidence shares, deadweight loss, the budget multipliers and net present value.

1. Market failure and its four sources

Market failure is a situation in which a free market, left to itself, does not allocate resources Pareto-efficiently, so total surplus is not maximised. The First Fundamental Theorem of Welfare Economics promises efficiency only under strong conditions: complete competitive markets, price-taking behaviour, no externalities, full information, and well-defined property rights. A market fails exactly when one of these breaks. There are four canonical sources, and the examiner rewards matching each failure to its own remedy rather than reaching for the same cure every time.

Market power — a monopoly or cartel prices above marginal cost, so output is too low and a deadweight loss appears. Remedy: competition policy and regulation.
Externalities — a cost or benefit falling on a third party is left out of the price. Remedy: Pigouvian taxes or subsidies, or Coasean bargaining.
Public goods — non-rival, non-excludable goods that the market under-provides because of free-riding. Remedy: public provision funded by taxation.
Asymmetric information — one side of a deal knows more than the other, producing adverse selection and moral hazard. Remedy: signalling, screening, disclosure rules.

⚠️ Inefficiency is not the same as inequity

Market failure is strictly about lost efficiency. A perfectly competitive market can be fully efficient yet leave some people very poor; that is a distributional concern calling for redistribution, not a market failure. Conversely, a genuine market failure means the economy could make someone better off without making anyone worse off and is not doing so. Keep the efficiency question and the fairness question apart.

2. Public goods, externalities, Coase and the environment

A pure public good has two properties: it is non-rival (one person's use does not reduce what is left for others) and non-excludable (non-payers cannot be shut out). National defence and a lighthouse are the standard examples. Non-excludability creates the free-rider problem: each person hopes others will pay, so the market under-provides. The efficient quantity obeys the Samuelson condition, the sum of individuals' marginal rates of substitution equal to the marginal rate of transformation (ΣMRS = MRT). Because everyone consumes the same quantity jointly, individual demand curves are added vertically, in contrast with the horizontal summation used for private goods.

An externality is a cost or benefit falling on someone outside the transaction. With a negative externality such as pollution, the marginal social cost exceeds the marginal private cost (MSC > MPC), so the market over-produces. The textbook remedy is a Pigouvian tax set equal to the marginal external cost at the efficient output, which raises private cost to social cost. With a positive externality such as vaccination or education, marginal social benefit exceeds marginal private benefit, the market under-produces, and the remedy is a Pigouvian subsidy.

🎯 Coase theorem and the environment as a public good

The Coase theorem says that if property rights are clearly assigned and transaction (bargaining) costs are negligible, the parties will bargain their way to the efficient outcome regardless of who initially holds the right; the assignment changes only who pays whom, not the efficient quantity. It breaks down when parties are many, information is poor, or bargaining is costly, which is why a Pigouvian tax or regulation is often used instead. Clean air is a public good (non-rival and non-excludable), and pollution is the classic negative externality and a tragedy of the commons, so environmental policy uses exactly these tools: emission taxes, tradable permits (cap-and-trade), and Coasean bargaining where few parties are involved.

3. Asymmetric information and the regulation of markets

When one side of a market knows more than the other, two distinct problems arise, separated by timing. Adverse selection is hidden information before the deal: in Akerlof's market for lemons, buyers cannot tell good used cars from bad, offer only an average price, good cars withdraw, and quality collapses; in insurance, the highest-risk people are the keenest to buy. Moral hazard is a hidden action after the deal: once insured, people take more risk or less care. Remedies for adverse selection are signalling (Spence: the better type takes a costly, credible action such as a degree or a warranty) and screening (the uninformed side designs choices that separate the types). Remedies for moral hazard are deductibles, co-payments, monitoring and incentive contracts.

Regulation of the market addresses market power. Firms may collude, forming a cartel that restricts output and raises price toward the monopoly level, transferring surplus from consumers to producers and creating deadweight loss; competition (antitrust) law therefore prohibits cartels and the abuse of a dominant position. A natural monopoly has a falling average cost over the whole relevant range (water, electricity networks), so a single firm is cheapest, but it would exploit its position; regulators respond with price caps or rate-of-return rules. Marginal-cost pricing is efficient but makes a loss here (because marginal cost lies below average cost), so average-cost pricing is used to let the firm break even.

⚠️ Adverse selection versus moral hazard: use the clock

The quickest way to tell them apart is when the problem bites. If the trouble is who chooses to enter the contract (bad risks are over-represented), it is adverse selection, settled before the ink dries. If the trouble is how someone behaves once the contract is in force, it is moral hazard. A question that describes a change in behaviour after a policy is bought is moral hazard, however much it sounds like "selection".

4. Public revenue and the structure of taxation

Public revenue divides into tax and non-tax revenue. A tax is a compulsory payment with no direct quid pro quo: the taxpayer cannot claim a specific service in return. Non-tax revenue includes fees, fines, interest receipts, dividends and profits of public enterprises, and grants. Taxes split again into direct and indirect. A direct tax is levied on income or wealth and is meant to be borne by the person who pays it (income tax, corporate tax). An indirect tax is levied on goods and services and is readily shifted down the chain to the final buyer (a value-added tax such as GST, customs and excise duties).

Taxes are classified by how the average tax rate moves with income. A progressive tax has an average rate that rises with income (a slab income tax); a proportional (flat) tax has a constant average rate; a regressive tax has an average rate that falls as income rises. Indirect taxes tend to be regressive, because a poorer household spends a larger fraction of its income on taxed goods. The marginal rate (tax on the next rupee) differs from the average rate (tax as a share of total income); under a progressive schedule the marginal rate lies above the average. Adam Smith's four canons of taxation are equity, certainty, convenience and economy, and a good tax also balances the benefit principle against the ability-to-pay principle.

How the average rate behaves under each kind of tax
Type	Average rate as income rises	Typical example
Progressive	Rises	Slab-based personal income tax
Proportional	Constant	A flat-rate tax on all income
Regressive	Falls	Many indirect taxes on necessities

5. Tax incidence and the effects of taxation

Statutory (legal) incidence is who the law requires to hand over the tax; economic incidence is who actually ends up poorer. They are usually different, because a tax is shifted forward to buyers through a higher price or backward to suppliers through a lower one. The central result is that incidence depends on relative elasticities, not on which side the law names. The more inelastic side cannot escape and bears the larger share. For a per-unit tax, the share borne by consumers is Es/(Es + Ed) and the share borne by producers is Ed/(Es + Ed), where Ed is the magnitude of the price elasticity of demand and Es the elasticity of supply.

Taxation also has an efficiency cost. A tax drives a wedge between the price the buyer pays and the price the seller receives, cuts the quantity traded below the efficient level, and so destroys surplus beyond the revenue collected: this is the excess burden or deadweight loss. It is approximated by the triangle ½ × t × ΔQ, and it rises roughly with the square of the tax rate and with the elasticities, so a small tax is cheap and a large one disproportionately costly. The Ramsey rule follows: to raise a given revenue with least deadweight loss, tax inelastic goods more heavily. A lump-sum tax (a fixed amount independent of behaviour) causes no deadweight loss because it leaves every margin untouched, but it is widely seen as inequitable and is rarely used.

🎯 Why the legal side does not matter

Picture the demand and supply curves. A per-unit tax opens a vertical gap of exactly t between them, and the new quantity is where that gap closes. The size of the gap, and hence the new quantity and the two prices, is the same whether the tax is written as a charge on buyers (shifting demand down) or on sellers (shifting supply up). The algebra is symmetric, so the burden split is a fact about elasticities, and a question that keys on the collecting side is testing whether you know this.

6. Public expenditure, debt, the budget multiplier and cost-benefit analysis

Public expenditure tends to grow with development: Wagner's law holds that the public sector expands as income rises, and the Peacock-Wiseman displacement effect notes that spending ratchets up during crises and does not fully return. Spending is classified as revenue (recurring, such as salaries and interest) versus capital (asset-creating, such as roads). Public debt may be internal (owed to residents) or external (owed abroad); its management means arranging the maturity profile, rolling over maturing stock, and keeping the burden sustainable. A simple sustainability guide: the debt-to-GDP ratio is easier to hold in check when the economy's growth rate exceeds the interest rate on the debt and the primary balance is manageable.

In the simple Keynesian model the budget moves income through multipliers. The government-spending multiplier is 1/(1 − MPC); the tax multiplier is −MPC/(1 − MPC), smaller in magnitude because a tax cut first leaks into saving. The striking result is the balanced-budget multiplier of one (Haavelmo): if government raises spending and lump-sum taxes by the same amount, income rises by exactly that amount, because the spending injection is larger than the tax leakage. Fiscal policy uses these: expansionary (more spending or lower taxes) to fight a recession, contractionary to cool an overheating economy, with automatic stabilisers working in the background. The main caveat is crowding out, where government borrowing raises interest rates and squeezes private investment.

🧠 Cost-benefit analysis: discount, then decide

A public project is appraised by net present value: NPV = Σ (Bt − Ct)/(1 + r)^t, summing discounted benefits minus costs over the project's life. Accept a project when NPV > 0, and prefer the higher-NPV project when choosing among several. Two points carry marks: a higher social discount rate shrinks distant benefits more, so it hurts long-horizon projects; and distorted markets call for shadow prices (true opportunity costs) rather than observed prices, with a sensitivity analysis to see how the verdict changes as r and key inputs vary.

Key takeaways

Market failure is lost efficiency, and it comes in four forms — market power, externalities, public goods and asymmetric information — each with its own remedy. It is not the same as an unfair distribution, which is a separate, equity question.
A pure public good is non-rival and non-excludable and is under-provided by free-riding; its efficient level is ΣMRS = MRT (vertical summation). A negative externality means MSC > MPC and overproduction, corrected by a Pigouvian tax; the Coase theorem reaches efficiency by bargaining when rights are clear and transaction costs are low.
Asymmetric information gives adverse selection (hidden information before the deal) and moral hazard (hidden action after it); the cures are signalling and screening, and deductibles and monitoring respectively. Cartels and natural monopolies justify competition law and price regulation.
Taxes are direct (on income/wealth, borne by the payer) or indirect (on goods, shiftable); progressive, proportional or regressive by how the average rate moves with income. Tax incidence depends on relative elasticities, not on the legal side: the inelastic side bears more, with consumer share Es/(Es + Ed).
A tax creates deadweight loss (½ × t × ΔQ), rising with the square of the rate, so tax inelastic goods (Ramsey); a lump-sum tax has none. The spending multiplier is 1/(1 − MPC), the tax multiplier −MPC/(1 − MPC), and the balanced-budget multiplier is one.
A public project is accepted when its net present value Σ (Bt − Ct)/(1 + r)^t is positive; a higher discount rate penalises distant benefits, and distorted markets require shadow prices and sensitivity analysis.

Practice questions (17)

Attempt each one before opening the answer. Every explanation names the tempting wrong option as well as the right one, because that is where marks are lost.

Which pair of properties together defines a pure public good?
1. Rivalry in consumption together with the excludability of non-paying users
2. Rivalry in consumption and non-excludability of non-payers
3. Non-rivalry in consumption and non-excludability of non-payers
4. Non-rivalry in consumption and excludability of non-payers
Show answer
Answer: C — Non-rivalry in consumption and non-excludability of non-payers
A pure public good is both non-rival and non-excludable, which is why free-riding makes the market under-provide it. The combination of non-rivalry with excludability describes a club good (like a toll road), and rivalry with non-excludability describes a common resource (like an open fishery), so both of those pairs are genuine categories but not a pure public good.
A factory's production imposes pollution costs on nearby residents that it does not pay for. In an unregulated market, how does its output compare with the socially efficient level, and what is the textbook remedy?
1. Output is below the efficient level, and a Pigouvian subsidy for each unit produced would restore efficiency
2. Output is above the efficient level, and a Pigouvian tax equal to the marginal external cost would restore efficiency
3. Output is exactly at the efficient level, because the market already prices the pollution in, so no remedy is needed
4. Output is above the efficient level, and a flat per-unit production subsidy paid to the firm would restore efficiency
Show answer
Answer: B — Output is above the efficient level, and a Pigouvian tax equal to the marginal external cost would restore efficiency
A negative externality means marginal social cost exceeds marginal private cost, so the firm overproduces; a Pigouvian tax equal to the marginal external cost at the efficient output lifts private cost to social cost. The subsidy-and-underproduction answer is the correct description of a positive externality, not this one, and a production subsidy here would worsen the overproduction.
The Coase theorem states that private parties will bargain to the efficient outcome for an externality provided which condition holds?
1. The government has already imposed a tax equal to the marginal external cost
2. The right to pollute has been assigned specifically to the polluter rather than to the victims
3. A very large number of affected parties must bargain together at once
4. Property rights are clearly assigned and transaction costs are negligible
Show answer
Answer: D — Property rights are clearly assigned and transaction costs are negligible
Coase requires well-defined property rights and near-zero transaction costs; then bargaining reaches efficiency and only the distribution depends on who holds the right. Assigning the right to one side does not by itself guarantee efficiency, and a large number of parties raises transaction costs and is exactly the situation in which the theorem breaks down and a tax or regulation is used instead.
The rule for the efficient quantity of a pure public good differs from the rule for a private good. Which statement states the public-good rule correctly?
1. The sum of individuals' marginal rates of substitution equals the marginal rate of transformation, with demand curves added vertically
2. Each individual's marginal rate of substitution equals the marginal rate of transformation, with demand curves added horizontally
3. Marginal revenue equals marginal cost for the single public supplier of the good, with the price set by the supplier
4. The marginal external benefit is driven to zero by an appropriately chosen corrective subsidy
Show answer
Answer: A — The sum of individuals' marginal rates of substitution equals the marginal rate of transformation, with demand curves added vertically
The Samuelson condition is ΣMRS = MRT: because all consumers enjoy the same single quantity of a public good jointly, their marginal valuations are summed vertically. The private-good rule, each consumer's MRS equal to the MRT with horizontal summation, is the tempting wrong answer because it is the familiar case, but it applies when each person can buy a different quantity at a common price.
Which of the following statements about public goods, externalities and the Coase theorem are correct?
1. A pure public good is non-rival and non-excludable, which is why a competitive market tends to under-provide it
2. A negative production externality means the marginal social cost lies below the marginal private cost
3. With zero transaction costs and clear property rights, Coasean bargaining reaches the efficient outcome whichever party holds the right
4. Because the atmosphere cannot be fenced off, clean air behaves like a private good that markets supply efficiently
Show answer
Answer: A — A pure public good is non-rival and non-excludable, which is why a competitive market tends to under-provide it; C — With zero transaction costs and clear property rights, Coasean bargaining reaches the efficient outcome whichever party holds the right
Non-rivalry plus non-excludability is exactly what causes free-riding and under-provision, and under the Coase conditions the efficient quantity is reached regardless of the initial right (only distribution changes). A negative externality means social cost is above, not below, private cost. Clean air is non-excludable and so is a public good, the opposite of a private good the market supplies efficiently.
A health insurer finds that, once people are insured, they visit doctors more often and take fewer precautions than before. This behaviour is best described as:
1. Adverse selection, because the sicker people were the ones most likely to buy the policy in the first place
2. A separating signalling equilibrium deliberately engineered by the insurer
3. Moral hazard, because it is a hidden change in behaviour after the contract is in force
4. A Pigouvian externality that the insured impose on uninvolved third parties
Show answer
Answer: C — Moral hazard, because it is a hidden change in behaviour after the contract is in force
A change in behaviour after the policy begins is moral hazard, a hidden action. Adverse selection is the tempting alternative because it also involves insurance, but it is about who chooses to buy before the contract (the worse risks selecting in), not about behaviour afterwards. Deductibles and co-payments are the standard cures for moral hazard.
Which of the following statements about information problems and market regulation are correct?
1. Adverse selection arises from hidden information before a contract, as when high-risk buyers are keenest to insure
2. A successful cartel that raises price toward the monopoly level increases consumer surplus
3. In a natural monopoly, average cost falls over the relevant range, so a single firm supplies the market most cheaply
4. Costly signalling, such as a credible warranty, can help separate good types from bad under asymmetric information
Show answer
Answer: A — Adverse selection arises from hidden information before a contract, as when high-risk buyers are keenest to insure; C — In a natural monopoly, average cost falls over the relevant range, so a single firm supplies the market most cheaply; D — Costly signalling, such as a credible warranty, can help separate good types from bad under asymmetric information
Adverse selection is a pre-contract selection of worse risks, natural monopoly rests on a falling average cost over the whole range, and costly credible signals (warranties, degrees) separate types, which are all standard results. A cartel raising price reduces consumer surplus and creates deadweight loss; it does not increase consumer surplus, which is why competition law targets it.
Which one of the following is an indirect tax?
1. Personal income tax deducted from a salary
2. A value-added tax such as GST charged on a restaurant bill
3. Corporate income tax levied on a company's profits
4. Capital gains tax charged on the sale of an asset by the owner who holds it
Show answer
Answer: B — A value-added tax such as GST charged on a restaurant bill
An indirect tax is levied on goods and services and is readily shifted to the final buyer through the price, which a value-added tax like GST is. Income tax, corporate tax and capital gains tax are all direct taxes levied on income or gains and meant to be borne by the person who earns them.
A tax is said to be regressive when:
1. The average tax rate rises as income rises
2. The marginal tax rate equals the average tax rate at every income level
3. The total amount of tax paid falls as income rises
4. The average tax rate falls as income rises
Show answer
Answer: D — The average tax rate falls as income rises
Regressivity is defined by the average rate falling as income rises, even if the absolute tax paid still goes up. A rising average rate is progressive and a constant one (marginal equal to average) is proportional. The claim that total tax falls as income rises is the trap: a regressive tax can still collect more in rupees from a richer person while taking a smaller share of their income.
For a good, the price elasticity of demand is 0.5 in magnitude and the price elasticity of supply is 2. A small per-unit tax is imposed. Using the standard share rule, the percentage of the tax borne by consumers is ____ (give a whole number).
Numerical answer — type the value.
Show answer
Answer: 80
The consumer's share of a per-unit tax is Es / (Es + Ed) = 2 / (2 + 0.5) = 2 / 2.5 = 0.8, that is 80%. The producer's share is Ed / (Es + Ed) = 0.5 / 2.5 = 20%. Demand is the more inelastic side here, so consumers cannot escape and bear the larger part; swapping the roles of Es and Ed in the formula is the usual slip and gives 20.
A per-unit tax of ₹4 is placed on a good and reduces the equilibrium quantity traded by 200 units. Approximating the efficiency cost by the area of the welfare-loss triangle, the deadweight loss (in ₹) is ____.
Numerical answer — type the value.
Show answer
Answer: 400
The deadweight-loss triangle has base equal to the fall in quantity (200 units) and height equal to the tax wedge (₹4), so the loss is ½ × 4 × 200 = ₹400. Forgetting the one-half and computing 4 × 200 = 800 is the common error; the lost surplus is a triangle, not a rectangle, because the wedge grows from zero across the reduced units.
A per-unit tax on a good can be collected either from sellers or from buyers. Standard incidence theory predicts that:
1. Buyers bear more of the burden when the tax is legally collected from buyers
2. Sellers bear more of the burden when the tax is legally collected from sellers
3. The split of the burden between buyers and sellers is the same either way, set only by relative elasticities
4. Whichever side is named as legally liable for the tax always ends up bearing the entire economic burden by itself
Show answer
Answer: C — The split of the burden between buyers and sellers is the same either way, set only by relative elasticities
A per-unit tax opens the same vertical wedge between demand and supply whichever side writes the cheque, so the new quantity and the two prices, and therefore the burden split, are identical; the split depends only on relative elasticities. The idea that the legally liable side bears everything is the classic misconception that this result overturns.
Which of the following statements about the effects of taxation are correct?
1. The statutory side on which a tax is levied determines who ultimately bears its economic burden
2. The more inelastic side of the market bears the larger share of a per-unit tax
3. The deadweight loss of a tax rises more than proportionately as the tax rate increases
4. A lump-sum tax creates no deadweight loss because it does not alter any decision at the margin
Show answer
Answer: B — The more inelastic side of the market bears the larger share of a per-unit tax; C — The deadweight loss of a tax rises more than proportionately as the tax rate increases; D — A lump-sum tax creates no deadweight loss because it does not alter any decision at the margin
Incidence falls more on the inelastic side, deadweight loss grows roughly with the square of the rate, and a lump-sum tax distorts no margin so carries no deadweight loss, all standard. The remaining claim is false: economic incidence is independent of the statutory side and depends on relative elasticities, which is the single most tested point in this topic.
In a simple Keynesian closed economy with marginal propensity to consume 0.8, the government raises both its spending and its lump-sum taxes by ₹500 crore, keeping the budget balanced. The resulting change in equilibrium income (in ₹ crore) is ____.
Numerical answer — type the value.
Show answer
Answer: 500
The spending multiplier is 1/(1 − 0.8) = 5 and the tax multiplier is −0.8/(1 − 0.8) = −4. With ΔG = ΔT = 500, ΔY = 5 × 500 − 4 × 500 = 2500 − 2000 = 500. This is the balanced-budget (Haavelmo) multiplier of exactly one: equal rises in spending and taxes raise income by that same amount because the spending injection outweighs the tax leakage.
A public project costs ₹500 now (end of year 0). It yields benefits of ₹330 at the end of year 1 and ₹363 at the end of year 2, with no other flows. At a discount rate of 10% per year, the net present value (in ₹) is ____.
Numerical answer — type the value.
Show answer
Answer: 100
Discount each benefit to the present: 330/1.1 = 300 and 363/1.21 = 300, so the present value of benefits is 600. Net present value is 600 − 500 = ₹100, which is positive, so the project is worth undertaking. Adding the undiscounted benefits (330 + 363 − 500 = 193) is the common error and ignores the time value of money.
Two public projects have the same upfront cost and the same total undiscounted benefits, but Project One delivers most of its benefits in early years while Project Two delivers most of them in later years. Raising the social discount rate will:
1. Favour Project One relative to Project Two, because more distant benefits are discounted more heavily
2. Favour Project Two relative to Project One, because later benefits gain in present value when the rate rises
3. Leave the ranking unchanged, since the total undiscounted benefits of the two projects are equal
4. Raise the net present value of both projects by the same proportion, because every benefit gains value together
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Answer: A — Favour Project One relative to Project Two, because more distant benefits are discounted more heavily
A higher discount rate shrinks benefits that arrive further in the future by a larger factor, so the early-benefit project loses less of its value and is favoured. Keeping the ranking unchanged ignores timing, which is exactly what discounting captures, and a higher rate lowers present values rather than raising them.
Which of the following statements about the budget, public debt and project appraisal are correct?
1. In the simple Keynesian model the balanced-budget multiplier equals one
2. On cost-benefit grounds a public project should be accepted when its net present value is positive
3. Public debt is more likely to be sustainable when the growth rate of the economy exceeds the real interest rate on the debt
4. The tax multiplier is larger in absolute size than the government-spending multiplier
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Answer: A — In the simple Keynesian model the balanced-budget multiplier equals one; B — On cost-benefit grounds a public project should be accepted when its net present value is positive; C — Public debt is more likely to be sustainable when the growth rate of the economy exceeds the real interest rate on the debt
The balanced-budget multiplier is one, a positive NPV is the accept rule, and debt is easier to sustain when growth outruns the interest rate, all standard. The tax multiplier is smaller in magnitude than the spending multiplier, −MPC/(1 − MPC) against 1/(1 − MPC), because a tax change first leaks partly into saving before affecting spending.