Tax: Effects
The effects of taxation are well known. In the example that follows the good or service is both discrete (no externalities) and with the same elasticity on supply and demand. This is rarely the case. For example, with goods or services with inelastic demand curves (e.g., cigarettes, petrol) most of the tax is paid by the consumer, whereas for those with inelastic supply curves (e.g., seats at an entertainment venue) most of the tax is paid by the supplier.
Despite these necessary abstractions the principles and general outcome apply to all "real world" goods and services.
For any discrete good or service in a free market, consumer and producer surplus is maximised where Q1 meets P1.
When a tax is introduced and additional fee is applied to the producer whenever they provide a good or service or, in the case of transaction taxes, to the consumer when they receive the good. The effect is that the market price increases to P2 and the quantity demanded falls to Q2. Part of the consumer and producer surplus is converted into government revenue.
In addition to any administrative costs in collecting a tax, there is also a loss in social surplus as the net social surplus is reduced as potential trades are reduced. Often called the "deadweight loss" this loss is proportional to square of the tax rate. It means that a small tax on a broad base is more efficient than a large tax on a narrow base, assuming of course that the government wishes to encourage production and distribution of the particular good!
