Bellview Health Clinic offers seasonal flu vaccinations to the public. Because a vaccinated person is less likely to catch and spread flu to others, each vaccination also protects people who are not vaccinated themselves. A benefit that vaccinated individuals do not personally r…

Answer: ((a)) A person who is vaccinated reduces the chance of passing flu on to others, so the marginal social benefit (MSB) of each vaccination, which includes this benefit to third parties, is greater than the marginal private benefit (MPB) that the vaccinated person alone receives - this… ((b)) The free-market output is 3 thousand vaccinations per month, where MPB equals MPC; the socially optimal output is 4 thousand vaccinations per month, where MSB equals MSC; since the free-market output is below the socially optimal output, the free market under-provides vaccinatio… ((c)) At the free-market output of 3 thousand vaccinations, MEB = MSB - MPB = 60 - 40 = $20 per dose; since this gap falls in a straight line from $20 at the free-market output (3 thousand) to $0 at the socially optimal output (4 thousand), the deadweight welfare loss is the triangula…. Part (a): Why this is a positive externality of consumption Bellview Health Clinic's patients pay for a flu vaccination based on the private protection it gives them, being less likely to catch flu themselves. But a vaccinated person is al…

A Level Economics 9708: Positive Externalities and Under-Consumption

Output (thousand vaccinations per month)	MPB ($ per dose)	MEB ($ per dose)	MSB = MPB + MEB ($ per dose)	MPC = MSC ($ per dose)
0	70	20	90	10
1	60	20	80	20
2	50	20	70	30
3	40	20	60	40
4	30	20	50	50
5	20	20	40	60
6	10	20	30	70

Output (thousand vaccinations per month)

MPB ($ per dose)

MEB ($ per dose)

MSB = MPB + MEB ($ per dose)

MPC = MSC ($ per dose)

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

Bellview Health Clinic’s patients pay for a flu vaccination based on the private protection it gives them, being less likely to catch flu themselves. But a vaccinated person is also less likely to pass flu on to other people, including those who are not vaccinated, which reduces flu transmission across the wider population.

This means: $MSB = MPB + MEB$

where $MEB > 0$ is the marginal external benefit (the reduced-transmission benefit enjoyed by everyone else. Because the clinic’s patients only take account of their own $MPB$ when deciding whether to get vaccinated, fewer vaccinations are demanded than is socially desirable) this uncompensated third-party benefit is exactly what defines a positive externality of consumption.

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

Free-market output: individuals choose to be vaccinated up to the point where their own marginal private benefit equals the marginal private cost of a dose, $MPB = MPC$ . Reading the table, at an output of 3 thousand vaccinations, $MPB = 40$ and $MPC = 40$ , both equal $40 per dose. So the free-market output is 3 thousand vaccinations per month.

Socially optimal output: allocative efficiency requires marginal social benefit to equal marginal social cost, $MSB = MSC$ . At an output of 4 thousand vaccinations, $MSB = 50$ and $MSC = 50$ , both equal $50 per dose. So the socially optimal output is 4 thousand vaccinations per month.

Because the free-market output (3 thousand) is below the socially optimal output (4 thousand), the positive externality causes the market to under-provide vaccinations relative to what is socially efficient.

Part (c): External benefit and deadweight welfare loss

At the free-market output of 3 thousand vaccinations per month: $MEB = MSB - MPB = 60 - 40 = 20$

So the marginal external benefit is $20 per dose at this output.

Between the free-market output (3 thousand) and the socially optimal output (4 thousand), the gap between $MSB$ and $MPB$ narrows from $20 per dose (at 3 thousand, where $MSB - MPB = 60 - 40 = 20$ ) down to $0 (at 4 thousand, where $MSB = MPB = 50$ ). Since both $MSB$ and $MPC$ change at a constant rate with output, this gap shrinks in a straight line, so the deadweight welfare loss is the area of a triangle: $DWL = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times (4-3) \times 20 = 10$

Because output is measured in thousand vaccinations, this deadweight welfare loss of $10$ represents $10 thousand ($10,000) per month. The value of the social benefit foregone because too few people are vaccinated between the free-market and socially optimal quantities.

Final answers

(a) MSB exceeds MPB because of the uncompensated marginal external benefit (reduced flu transmission) enjoyed by others
(b) Free-market output = 3 thousand vaccinations/month; socially optimal output = 4 thousand vaccinations/month; the free market under-provides vaccinations
(c) MEB at the free-market output = $20 per dose; deadweight welfare loss = $10 thousand ($10,000) per month