Signature
MSC = MPC + MEC; MSB = MPB + MEB; NB_S = MPB + MEB - MPC - MEC; NB_P = MPB - MPC
| Inputs | Definition | Unit |
|---|---|---|
MPC | Additional cost of one more unit borne directly by the producer or consumer who decides | currency per unit of activity |
MEC | Additional uncompensated cost of one more unit falling on people outside the decision, zero when there is none | currency per unit of activity |
MPB | Additional benefit of one more unit received directly by the producer or consumer who decides | currency per unit of activity |
MEB | Additional uncompensated benefit of one more unit received by people outside the decision, negative for an external cost of consumption | currency per unit of activity |
MSC | Cost to society as a whole of one more unit of the activity | currency per unit of activity |
|---|---|---|
MSB | Benefit to society as a whole of one more unit of the activity | currency per unit of activity |
NB_S | Marginal social benefit minus marginal social cost of one more unit | currency per unit of activity |
NB_P | Marginal private benefit minus marginal private cost of one more unit, the return the decision-maker weighs | currency per unit of activity |
Function
Social marginal cost and benefit function
Adds the marginal effect that an activity has on third parties to the marginal cost or benefit that the decision-maker weighs, giving the marginal social cost or benefit. The efficient quantity is where marginal social benefit equals marginal social cost; a private decision that ignores the external term stops at a different quantity, and a Pigouvian tax or subsidy set at the marginal external effect at the efficient quantity closes the gap.
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Implementations
Excel
Social values and net benefits from four inputs
With the four marginal values in MargPrivCost, MargExtCost, MargPrivBen and MargExtBen, the formulas return marginal social cost, marginal social benefit, net social benefit and net private benefit; the fifth flags a margin at which the private choice goes against the social one.
=MargPrivCost+MargExtCost; =MargPrivBen+MargExtBen; =MargPrivBen+MargExtBen-MargPrivCost-MargExtCost; =MargPrivBen-MargPrivCost; =SIGN(NetSocialBen)<>SIGN(NetPrivateBen)
Assumptions
Marginal values at the current level of activity
Each term is the effect of one more unit at the level of activity being assessed. External effects such as protection from herd immunity change as coverage rises, so the values hold only at that margin, and the comparison does not by itself identify the efficient level of activity.
No double counting within the stated perspective
An effect already counted as a private cost or benefit within the analysis is not added again as an external one. Which effects are external depends on the perspective of the decision being analysed.
Decision-maker bears the private terms in full
The private comparison assumes that the person deciding pays the whole of MPC and receives the whole of MPB, and all four inputs are valued in the same currency and price year. Insurance or existing subsidies change the private terms and are entered first.
Worked examples
Individual declines a vaccination that society values
Using the article's illustrative values, the marginal private benefit of vaccination is 55 units and the marginal external benefit from reduced transmission 20, so marginal social benefit is 75; with no external cost, marginal social cost equals the private cost of 60. Society gains 15 units from one more vaccination, but the individual faces a net loss of 5 and declines. A subsidy of more than 5 units at this margin would reverse the decision.
MPC = 60; MEC = 0; MPB = 55; MEB = 20; MSC = 60; MSB = 75; NB_S = 15; NB_P = -5
Antibiotic course taken although society loses
An illustrative antibiotic course has a marginal private cost of 10 units and a marginal private benefit of 12. Its contribution to resistance is an external cost of consumption of 4 units, entered as a negative marginal external benefit, so marginal social benefit is 8. The individual gains 2 units and takes the course, while society loses 2.
MPC = 10; MEC = 0; MPB = 12; MEB = -4; MSC = 10; MSB = 8; NB_S = -2; NB_P = 2
Common errors
Counting a consumption externality on both sides
Entering the resistance cost of antibiotic use as a positive MEC and also as a negative MEB subtracts it twice. By convention an external effect of consumption is entered once, on the benefit side.
Using an average external effect for a marginal decision
The total transmission benefit of a programme divided by the number vaccinated is an average. The marginal external benefit of the last person vaccinated is usually smaller at high coverage, because herd immunity already protects many of those who remain susceptible.
Reading a positive social return as proof that a subsidy is worth paying
A net social benefit of 15 at one margin shows that one more vaccination is worth having. Whether a subsidy programme is worthwhile also depends on its administrative cost, on how many people would have been vaccinated anyway and on how the external benefit falls as coverage rises.
Sources
Pigou on divergences between private and social net product
Pigou AC. The Economics of Welfare. 4th ed. London: Macmillan; 1932. Part II, Chapter IX, Divergences between marginal social net product and marginal private net product (section 13: the divergence arises from a service or disservice rendered to persons other than the contracting parties, and the State can remove it by extraordinary encouragements or restraints, most obviously bounties and taxes).
Graduate textbook treatment of externalities
Mas-Colell A, Whinston MD, Green JR. Microeconomic Theory. New York: Oxford University Press; 1995. Chapter 11, Externalities and public goods: the gap between private and social marginal benefit and cost and the efficient level of an externality-generating activity.
Herd immunity as an externality in economic evaluation
Brisson M, Edmunds WJ. Economic evaluation of vaccination programs: the impact of herd-immunity. Medical Decision Making. 2003;23(1):76-82. Vaccination reduces disease in those immunised and indirectly protects unvaccinated susceptible people; static models that ignore these herd-immunity externalities omit part of the benefit.
Canonical Identity
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