Elasticity and the Deadweight Loss

The cost of taxation to society includes the direct cost of revenue paid to government and the cost of administering the tax. This results in a decrease in consumer and producer surplus. This loss of consumer and producer surplus from a tax is known as dead weight loss. This is shown graphically by the welfare loss triangle; a geometric representation of the welfare cost in terms of mis-allocated resources caused by a deviation from supply/demand equilibrium. With a tax, quantity sold declines; therefore the loss in welfare represents a loss for consumers and producers who would have traded without the tax.

Sellers would like to pass the entire tax on to buyers, raising the price by the full amount of the tax, rather than paying any part of it themselves. However, as the price rises, customers respond by purchasing fewer units. Sales decline and sellers must then lower their price toward its pretax level, accepting part of the tax burden themselves in form of a lower price net of tax.

For example, suppose a $1000 tax is levied on used cars and the number of units traded falls from 750 to 500. The imposition of the tax reduced the units traded by 250 units. The loss of the mutual benefit that would have been derived had the tax not eliminated 250 units of exchange imposes a cost on buyers and sellers. This cost is the dead-weight Loss of the tax.

The dead-weight loss generates neither revenue for the government nor gains for any other party (remember trade results in mutual gains for both buyers and sellers). It is a burden imposed on buyers and sellers over and above the cost of the revenue transfered to the government. Thus, it is often referred to as the Excess Burden of Taxation. It is composed of losses to both buyers (the lost consumer surplus), and sellers (the lost producer surplus).

We have seen that elasticities of supply and demand determine how the burden of a tax is distributed between buyer and seller. These elasticities also influence the size of the dead-weight loss caused by the tax because they determine the total reduction in the quantity of exchange. When either demand or supply is relatively inelastic, fewer trades will be eliminated by imposition of the tax, so the resulting dead-weight loss is smaller.

From a policy perspective, the excess burden of a tax system will  be lower if taxes are levied on goods and services for which either demand or supply is highly inelastic.

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