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9708 · 3.1

Reasons for government intervention in markets — practice questions

Practice and worked examples for 9708 Reasons for government intervention in markets. Short previews only — attempt the full question in MarkScheme against the official scheme.

Worked example 1

A chemical factory emits pollution. At the free market output of 100 units, MPC = £8 and MSC = £14. Marginal external cost = £6.

Explain why this is market failure and state the socially optimal output.

Show solution outline

Market failure: Firms produce where MPC = MPB (private optimum) at Q = 100. They ignore the £6 external cost borne by society.

Social cost: MSC = MPC + MEC = £8 + £6 = £14 at this output — exceeds private cost.

Result: Overproduction — 100 units is above the social optimum where MSC = MSB.

Socially optimal output: Where MSC = MSB, which occurs at a lower Q (e.g. 70 units on a standard diagram). The welfare loss triangle lies between Q* and Q_market.

Policy: Indirect tax of £6 per unit (Pigouvian tax) internalises the externality — shifts supply left to the social optimum (→ 3.2).

Worked example 2

The market for flu vaccinations has a Marginal Private Benefit (MPB) of MPB = 100 - Q and a Marginal Private Cost (MPC) of MPC = 20 + Q, where Q is millions of vaccinations. Each vaccination provides a Marginal External Benefit (MEB) of £20 due to herd immunity. Calculate the free market output and the socially optimal output, and determine the per-unit subsidy required to correct the market failure.

Show solution outline

1. Free Market Equilibrium (where MPB = MPC):

  • Set the private benefit equal to the private cost: 100−Q=20+Q100 - Q = 20 + Q
  • Solve for Q: 80=2Q80 = 2Q → Qmarket=40Q_market = 40 million vaccinations.
  • The market price is P=100−40=£60P = 100 - 40 = £60.

2. Socially Optimal Equilibrium (where MSB = MSC):

  • First, find the Marginal Social Benefit (MSB): MSB=MPB+MEBMSB = MPB + MEB
  • MSB=(100−Q)+20=120−QMSB = (100 - Q) + 20 = 120 - Q
  • Assume no production externalities, so MSC=MPC=20+QMSC = MPC = 20 + Q.
  • Set MSB equal to MSC: 120−Q=20+Q120 - Q = 20 + Q
  • Solve for Q: 100=2Q100 = 2Q → Qsocial=50Q_social = 50 million vaccinations.

3. Market Failure and Subsidy:

  • The market under-produces by 10 million units (50m - 40m). This is a market failure due to a positive externality.
  • To correct this, the government can offer a subsidy to internalise the external benefit.
  • The required subsidy per unit is equal to the Marginal External Benefit.
  • Required Subsidy = MEB = £20 per vaccination.
  • This subsidy would increase demand (shifting MPB up to MSB) and lead the market to produce the socially optimal quantity of 50 million.
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