San José State University
Department of Economics
Thayer Watkins
Silicon Valley
& Tornado Alley

An Economic Welfare Analysis of a Tax
in a Competitive Market Involving
an External Cost

An externality is a cost or benefit imposed upon some party other than the producer or consumer of a product. In the absence of public intervention the supply schedule for the product may only reflect the private costs and a competitive market may establish an output Qpriv and a price Ppriv that do not take into account the externalities involved in the production and consumption of the product. For the present it is assumed that the externality involves only a cost. External costs are part of the overall social costs of the production and the socially optimal level of production is where marginal social costs is equal to marginal social benefit. In the case depicted below there are no external cost or beneftits to the consumption of the product so marginal social benefit is the same as marginal private benefit.

In such a case the private market results in the production and consumption of more than the socially optimal amount; i.e., too much production. It also results in too low of a price. One way of remeding this situation is to impose a tax on the product. The effect of a tax in a competitive market is to shift the supply curve vertically by the amount of the tax. If the tax is exactly equal to the external cost at the socially optimum level of production then the market will establish the socially optimum level of production and price. This results in a higher price and a lower level of production.

The reduction in social benefit to the consumer is the area under the demand curve as shown below in magenta.

At a lower level of production there is a reduced social cost that is given by the area under the marginal social cost curve, as is shown below in green.

Clearly the reduction in social cost is greater than the reduction in social benefits for the consumer. The net gain from imposing the externality tax is shown as the green triangle in the diagram below.

The concept of a tax to impose the externality cost on a producer was developed by the British economist Arthur Pigou. There is an alternate approach to resolving the problems of external cost was developed by the British-American economist Ronald Coase.

The honey bee industry provides an interesting example of positive externalities. Some plants require honey bees for fertilization. But the production of honey requires flower blossoms. Bee keeping creates a positive externality for farmers and orchard growers. On the other hand farmers and orchardists create a positive externality for bee keepers.

According to Pigouvian theory the positive externalities justify the payment of a public subsidy to both the farmer/orchardists and the bee keepers to give them the benefit of the benefit they confer on the other. Ronald Coase however says that the bee keepers and the farmer/orchardists can work out an efficient arrangement without any government involvement.

The big question is whether the bee keepers pay the farmer/orchardists to allow the bee to harvest the nectar from the blossoms in their operations or do the farmer/orchardists pay the bee keepers to bring their bee hives to fertilize their crops? The answer is that it works both ways. For crops that need bees for fertilization the farmers/orchardists pay the bee keepers so much per day to keep their hives in the hives in the fields. For crops that do not need bees for their fertilization but produce high quality nectar for honey, such as citrus groves, the bee keepers pay. So when the bee keepers do not have paying clients for the fertilization services of the bees they find a quality crop to harvest for honey even it they have to pay for the privilidge.

(To be continued.)

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