Pigouvian tax: example.

The figure below shows the market for fertilizer. When fertilizer is applied to lawns, it runs off into neighboring streams and ponds, killing fish and creating an external cost.

If the government imposes a tax equal to the marginal external cost. How much is the tax? What is the equilibrium quantity after the implementation of the tax? What is the price paid by consumers?

To understand this question, you need to recall that when a tax is imposed, it creates "a wedge between the price buyers pay and the price sellers receive”, regardless of whether the tax is imposed on the buyers or the sellers. Therefore, we need to find the quantity where

Price paid by the buyers - Price received by the sellers = Tax,

that is to say, we need to find the quantity where the distance between the demand curve and the supply curve is the same as the amount of tax.

On the other hand, we know that tax imposed by the government is equal to the marginal external cost, and

marginal external cost = marginal social cost (MSC) - marginal private cost (MC),

we just need to find the quantity where the distance between MSC and MC is the same as the distance between the supply curve (the same as MC) and the demand curve (the same as MSB). This occurs at the intersection between MSC and MSB, so the quantity is 4 tons.

If the analysis feels a bit complicated, you can simply remember the conclusion: when the government imposes a tax equal to the marginal external cost, then the quantity would be the efficient quantity, that is, the quantity where MSB = MSC. Taxes that are used to restore efficiency from negative externalities as in this case are called Pigouvian Taxes, named after English economist Arthur Cecil Pigou (1877–1959).