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9708 · 1.6

Classification of goods and services — practice questions

Practice and worked examples for 9708 Classification of goods and services. Short previews only — attempt the full question in MarkScheme against the official scheme.

Worked example 1

Classify each good and explain why the market may fail:

(a) National defence (b) A cinema ticket (c) Flu vaccination (d) Cigarettes

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(a) Public good — non-rival and non-excludable. Free-rider problem → market will not supply; government provides.

(b) Private good — rival and excludable. Market works well; price rations access.

(c) Merit good — rival and excludable but underconsumed because individuals undervalue health benefits to society (positive externality). Market underprovides → subsidies or free provision (→ 3.2).

(d) Demerit good — rival and excludable but overconsumed because smokers ignore health costs to others and themselves (negative externality). Market overproduces → taxation or regulation (→ 3.2).

Worked example 2

The market for a demerit good, sugary drinks, has the following cost and benefit functions (in millions of units, price in ):):

  • Marginal Private Benefit (Demand): P = 80 - Q
  • Marginal Private Cost (Supply): P = 20 + 0.5Q
  • Marginal External Cost from consumption: $15 per unit

(a) Calculate the free market equilibrium price and quantity. (b) Calculate the socially optimal quantity. (c) Calculate the value of the deadweight welfare loss due to overconsumption in the free market. (d) If the government imposes a specific tax to correct the market failure, what would be the tax revenue?

Show solution outline

(a) Free Market Equilibrium (MPB = MPC)

  • Step 1: Set the MPB equation equal to the MPC equation. 80 - Q = 20 + 0.5Q
  • Step 2: Solve for Q (quantity). 60 = 1.5Q Q = 40 million units
  • Step 3: Substitute Q back into the MPB (or MPC) equation to find P (price). P = 80 - 40 = 4040
  • Answer: The free market equilibrium is a quantity of 40 million units at a price of 40.40.

(b) Socially Optimal Quantity (MSB = MSC)

  • Step 1: Calculate the Marginal Social Cost (MSC). MSC = MPC + MEC. MSC = (20 + 0.5Q) + 15 MSC = 35 + 0.5Q
  • Step 2: Assume no external benefits, so MSB = MPB = 80 - Q.
  • Step 3: Set MSB equal to MSC and solve for the socially optimal quantity (Qsoc). 80 - Q = 35 + 0.5Q 45 = 1.5Q Q = 30 million units
  • Answer: The socially optimal quantity is 30 million units.

(c) Deadweight Welfare Loss

  • Step 1: Identify the area of the welfare loss triangle. The base is the overproduction (Qmarket - Qsoc) and the height is the MEC at the market output. Base = 40m - 30m = 10 million units Height = Marginal External Cost = 1515
  • Step 2: Calculate the area of the triangle (0.5 * base * height). Welfare Loss = 0.5 * 10,000,000 * 1515 Welfare Loss = 75,000,00075,000,000
  • Answer: The deadweight welfare loss is $75 million.

(d) Government Tax Revenue

  • Step 1: The optimal corrective tax (Pigouvian tax) is equal to the MEC, which is $15 per unit.
  • Step 2: This tax will shift the supply curve up, causing the market to produce at the socially optimal quantity of 30 million units.
  • Step 3: Calculate total tax revenue (Tax per unit * Qsoc). Tax Revenue = 15∗30,000,00015 * 30,000,000 Tax Revenue = 450,000,000450,000,000
  • Answer: The government would raise $450 million in tax revenue.
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