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Market Failure and Externalities: Question 9

Syllabus 7.4

Structured A2 9 marks

The Anchorage is a bar with an outdoor terrace that hosts amplified live music several nights a week. Customers who visit the terrace enjoy the music, but the noise also carries into nearby apartment blocks, disturbing the sleep and reducing the wellbeing of residents who are not customers of the bar. There is no externality on the cost side, so marginal private cost equals marginal social cost throughout.

The table below shows, at different monthly output levels, the marginal private benefit (MPB) to customers who visit the terrace, the constant marginal external cost (MEC) to nearby residents, the resulting marginal social benefit (MSB), and the marginal private cost (MPC), which equals marginal social cost (MSC).

Output (thousand customer-visits to the terrace per month) MPB ($ per visit) MEC ($ per visit) MSB = MPB − MEC ($ per visit) MPC = MSC ($ per visit)
0 74 16 58 10
1 66 16 50 18
2 58 16 42 26
3 50 16 34 34
4 42 16 26 42
5 34 16 18 50
6 26 16 10 58

(a) Explain, using the concepts of marginal private benefit and marginal social benefit, why the noise from customers on The Anchorage's terrace is a negative externality of consumption. [2]

(b) Using the table, identify the free-market output, where MPB = MPC, and the socially optimal output, where MSB = MSC, and state whether the free market over-consumes or under-consumes terrace visits relative to the socially optimal level. [3]

(c) Calculate the marginal external cost per visit at the free-market output, and use it, together with your answers to part (b), to calculate the deadweight welfare loss that results from customers consuming the free-market quantity of terrace visits rather than the socially optimal quantity. [4]

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Worked solution

Part (a): Why this is a negative externality of consumption

Customers who pay to sit on The Anchorage’s terrace value the live music based on their own marginal private benefit (MPB). The enjoyment they personally get from the evening out. But the amplified noise also carries into nearby apartment blocks, disturbing the sleep and reducing the wellbeing of residents who are not customers and receive no benefit from the music at all.

This means: MSB=MPB−MECMSB = MPB - MEC

where MEC>0MEC > 0 is the marginal external cost (the disturbance suffered by nearby residents. Because customers only take account of their own MPBMPB when deciding whether to visit the terrace, more visits take place than is socially desirable) this uncompensated third-party cost is exactly what defines a negative externality of consumption.

Part (b): Free-market output and socially optimal output

Free-market output: customers choose to visit the terrace up to the point where their own marginal private benefit equals the marginal private cost of a visit, MPB=MPCMPB = MPC. Reading the table, at an output of 4 thousand visits, MPB=42MPB = 42 and MPC=42MPC = 42, both equal $42 per visit. So the free-market output is 4 thousand customer-visits per month.

Socially optimal output: allocative efficiency requires marginal social benefit to equal marginal social cost, MSB=MSCMSB = MSC. At an output of 3 thousand visits, MSB=34MSB = 34 and MSC=34MSC = 34, both equal $34 per visit. So the socially optimal output is 3 thousand customer-visits per month.

Because the free-market output (4 thousand visits) exceeds the socially optimal output (3 thousand visits), the negative externality causes the market to over-consume terrace visits, and produce more noise disturbance, relative to what is socially efficient.

Part (c): External cost and deadweight welfare loss

At the free-market output of 4 thousand visits per month: MEC=MPB−MSB=42−26=16MEC = MPB - MSB = 42 - 26 = 16

So the marginal external cost is $16 per visit at this output (matching the constant MEC column in the table).

Between the socially optimal output (3 thousand visits) and the free-market output (4 thousand visits), the gap between MPCMPC and MSBMSB widens from $0 (at 3 thousand visits, where MSB=MSC=34MSB = MSC = 34) up to $16 per visit (at 4 thousand visits, where MSC−MSB=42−26=16MSC - MSB = 42 - 26 = 16). Since both MSBMSB and MSCMSC change at a constant rate with output, this gap grows in a straight line, so the deadweight welfare loss is the area of a triangle: DWL=12×base×height=12×(4−3)×16=8DWL = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times (4-3) \times 16 = 8

Because output is measured in thousand visits, this deadweight welfare loss of 88 represents $8 thousand ($8,000) per month, the value of resources wasted on visits between the socially optimal and free-market quantities, where the extra external cost to residents exceeds the extra private benefit to customers.

Final answers

  • (a) MSB is lower than MPB because of the uncompensated marginal external cost (the noise disturbance) imposed on nearby residents
  • (b) Free-market output = 4 thousand visits/month; socially optimal output = 3 thousand visits/month; the free market over-consumes terrace visits
  • (c) MEC at the free-market output = $16 per visit; deadweight welfare loss = $8 thousand ($8,000) per month