T is the size of the tax and Q is the quantity of goods sold T x Q is the revenue of the gov t Chapter 8 The Costs of Taxation Deadweight Loss of Taxation tax revenue T tax x Q quantity sold How a Tax Affects Welfare o equilibrium price and quantity are found at the intersection of the supply and demands without a tax curves with a tax o consumer surplus is between price and demand A B C o producer surplus is between supply curve and price D E F o tax revenue 0 o price paid by buyers rises to P2 consumer surplus is area A o price received by sellers falls to P3 producer surplus is area F o quantity sold falls to Q2 tax revenue is area B D Changes in Welfare o Consumer surplus falls by B C negative area o Producer surplus falls by D E negative area o Tax revenue rises by B D positive area o When all values are added together the total surplus falls by C E losses to buyers and sellers from a tax exceed the revenue raised by the gov t o Deadweight loss fall in total surplus that results from a market distortion ex Tax Deadweight Losses and the Gains from trade taxes cause deadweight losses because they prevent buyers and sellers from realizing some of the gains from trade fall in surplus C E measures the losses when tax raises the price to buyers to P2 and lowers the price to sellers to P3 marginal buyers and sellers leave he market so Q1 falls to Q2 the gains from trade difference between buyers value and sellers cost are less than the tax as a result these trades are not made once the tax is imposed deadweight loss is the surplus lost because the tax discourages these mutually advantageous trades Determinants of the Deadweight Loss a supply curve is inelastic quantity supplied responds only slightly to changes in price b supply curve is elastic quantity supplied responds substantially to changes in price deadweight loss area of triangle is larger when supply curve is more elastic c demand curve is inelastic deadweight loss is small d demand curve is more elastic deadweight loss is larger the greater the elasticities of supply and demand the greater the deadweight loss of a tax Deadweight Loss and Tax Revenue as taxes Vary a small tax deadweight area is small b c as tax rises deadweight grows larger deadweight loss of a tax rises even more than the size of the tax as the tax grows tax revenue grows until it climaxes then falls c as the tax increases its deadweight loss gets larger d tax revenue first rises with the tax but as tax get larger the market shrinks so much that tax revenue starts to fall
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