Perfect competition II: Taxes

Governments will choose to implement taxes to either individuals or firms in order to increase its revenue. When considering taxes to firms, it must be noted that these taxes will increase the price of goods being produced and sold, which translates into a welfare loss. However, a distinction between the loss in consumer and producer surplus must be made. The impact on both surpluses depends on the period analysed.

Short and long run analysis:

In the short run, both consumers and producers will suffer from the tax imposed. A new tax increases the price of goods. Let’s say this tax is imposed to firms, which increase their prices in order to cover their losses. In this case, as shown in the adjacent figure, supply will shift to the left, decreasing the quantity being produced, which increases its prices since demand remains unchanged: the new equilibrium price will be p_D (if the tax was to be imposed to consumers, there would be a shift in demand instead). A corresponds to the amount of the tax paid by consumers, while B is the amount paid by producers. Only consumers actually pay more, but producers are getting less out of the sale. The loss in consumer and producer surplus will depend on the elasticity of the demand curve, as shown in the figures below. The lower the elasticity in absolute terms (left figure), the higher the loss in consumer surplus, and the lower in producer surplus. Higher elasticity (right figure) will have the opposite effect.

In the long run, since the supply curve is completely elastic, the new tax will reduce only consumer surplus. Producer surplus will remain equal to zero, since there are no profits to be made.

Welfare analysis and government’s revenue:

Governments usually increase taxes to increase their revenue, which they use to relocate wealth and increase social welfare. The adjacent figure shows the effects of imposing a new tax on a good. P₀ was the price before the tax was imposed, p_D is the price consumers pay and p_S the price producers receive. Consumer surplus is reduced by B and E, producer surplus decreases by C and F, while government increases its revenue from zero to B and C. Consumers and producers lose B+E+C+F and the tax revenue is B+C, which determines the deadweight loss, the reduction in total surplus: E+F. The deadweight loss depends on the elasticity of both the supply and demand curves: the higher the elasticity in absolute terms, the larger the deadweight loss.

Also, depending on the size of a tax, the tax revenue may be bigger or smaller. In the following figure we see how as the tax increases, the deadweight loss (grey) increases too. 

However, the tax revenue (green) will first increase, and then will start to shrink. This relationship is known as the Laffer curve, shown in the figure below (being t the tax size and T the tax revenue). The Laffer curve might seem as an incredibly useful tool for government intervention. However, it has been widely criticized, mainly because empirical evidence to support it is rarely found, and because even if the relationship was accurate, it’s quite hard to know at which point of the curve a country actually is.

Taxing firms:

There are three main possible ways the government can impose taxes on firms: lump-sum tax, tax on profits and tax on output.

Lump-Sum Tax:

A certain amount of money has to be paid by the firm over a period of time. This kind of tax represents an increase in fixed costs and they consequently treat it as one. It holds the entry of firms in the market as it acts as an entry barrier, and will force some inefficient firms out of the market.

Tax on Profits:

Firms have to pay the government a percentage of their profits. This kind of tax is also considered a fixed cost. Sometimes the application this tax will cause profits to be negative, thus forcing some firms to exit the market.

The effects on total quantity sold and the quantity produced by a given firm of both lump-sum taxes and taxes on profits can be analysed with the following figure:

Tax on Output (or output tax):

In this case, firms pay a certain amount for each unit of output produced. As it has a direct relationship with the output level it is considered an increase in variable costs. The least efficient firms will be forced to exit the market.

The effects on total quantity sold and the quantity produced by a given firm of an output tax can be analysed with the following figure: