Tax and Deadweight Loss

Tax is a major source of revenue for the government. Yet it is also the source of deadweight loss that reduces the size of the economy and surpluses.

When a tax is imposed, both consumer surplus and producer surplus shrink and government tax revenue increases. However, since total surplus (consumer surplus + producer surplus + government tax revenue) after tax is lower than total surplus pretax, a deadweight loss is resulted as losses to buyers and sellers are more than tax revenues of the government. Why is there a deadweight loss? People respond to incentives. When tax is imposed, buyers buy less than they would without tax and sellers sell less than they would without tax, the market shrinks in size and moves away from the equilibrium point.

Another way to understand deadweight loss is that when buyers and sellers' total surplus is less than government tax, they leave the market without making a trade and without government getting tax revenue so deadweight loss is also the total surplus loss.

The price elasticities of supply and demand dictate the size of deadweight loss. When the supply or demand is inelastic, the quantity decreases just a little so deadweight loss is small; when the supply or demand is elastic, the quantity decreases a lot so deadweight loss is large. Think of deadweight loss as the triangle with base as tax and height as change of quantity. Thus, the more elastic the supply or demand or both, the larger the deadweight loss.

When tax increases, deadweight loss also increases. Moreover, when tax doubles, deadweight loss quadruples because both the base (size of tax) and height of the triangle (change of quantity) double. Similarly, when tax decreases, deadweight loss also decreases; and when new tax is a third the size of the old tax, deadweight loss is a ninth of the original.

Government tax revenue is another story. If tax increases when the tax is very small, government revenue does increase but will decrease at a certain point because the too many people leave the market and the tax revenue will be 0 when the tax is too large that no one trades and pays taxes. On the other hand, if tax decreases when the tax is very large, tax revenue increases as more people enter the market but then after a certain point it decreases because the size of tax is too small to compensate the increase of participation. When size of tax is 0, government revenue is surely 0.

This is like a simple maximization of area problem. The maximum area of the rectangle or maximum tax revenue occurs when the area is a square.