To gain some intuition for why taxes result in deadweight losses, consider an example, Imagine that Joe cleans Jane’s house each week for \$100. The opportunity cost of Joe’s time is \$80 and the value of a clean house to Jane is \$ 120. Thus, Joe and Jane each receive a \$ 20 benefit from their deal. The total surplus of \$40 measures the gains from trade in this particular transaction.

Now suppose that the government levies a \$50 tax on the providers of cleaning services. There is now no price that Jane can pay Joe that will leave both of them better off after paying the tax. The most Jane would be wiling to pay is \$120 but then Joe would be left with only \$70 after paying the tax, which is less than his \$80 opportunity cost. Conversely, for Joe to receive his opportunity cost of \$ 80, Jane would need to pay \$130, which is above the \$120 value she places on a clean house. As a result Jane and Joe cancel their arrangement. Joe goes with out the income and Jane lives in a dirtier house.

The tax has made Joe and Jane worse off by a total of \$40 because they have each lost \$20 of surplus. But note that the government collects no revenue from Joe and Jane because they decide to cancel their arrangement. The \$40 is pure deadweight loss it is a loss to buyers and sellers in a market that is not offset by an increase in government revenue. From this example, we can see the ultimate source of deadweight losses; taxes cause deadweight losses because they prevent buyers and sellers from realizing some of the gains from trade.

The area of Triangle between the supply and demand curves (areas C + E) in figure measures these losses. This conclusion can be seen more easily in Figure by recalling that the demand curve reflects the costs of producers. When the tax raises the price to buyers to PB and lowers the price to sellers to PB the marginal buyers and sellers leave the market, so the quantity sold falls from Q1 to Q2 Yet as the figures shows, the value of the goods to these buyers still exceeds the cost to these sellers. At every quantity between Q1 and Q2 the situation is the same as in our example with Joe and Jane. The gains from trade –the differences between buyers’ value and sellers cost – are less than the tax. As a result these trades do not get made once the tax is imposed. The deadweight loss is the surplus lost because the tax discourages these mutually advantageous trades.

The determinants of the deadweight loss

What determines whether the deadweight loss from a tax is large or small? The answer is the price elasticity’s of supply and demand which measure how much the quantity supplied and quantity demanded respond to changes in the price.

Let’s consider first how the elasticity of supply affects the size of the deadweight loss. In the top two panels of figure the demand curve and the size of the tax are the same. The only difference in the figures is the elasticity of the supply curve. In panel a) the supply curve is relatively inelastic; Quantity supplied responds only slightly ti changes in the price. In panel, b) the supply curve is relatively elastic. Quantity supplied responds substantially to changes in the price. Notice that the deadweight loss, the area of the triangle between the supply and demand curves, is larger when the supply curve is more elastic.

Similarly the bottom two panels of Figure show the elasticity of demands affects the size of the deadweight loss. Here the supply curve and the size of the tax are held constant. In panel c) the demand curve is relatively inelastic and the deadweight loss is small. In panel d) the demand curve is more elastic and the deadweight loss from the tax is larger.

Hence the greater the elasticity of supply and demand, the greater the deadweight loss of tax.