When you triple an excise tax, the deadweight loss increases nine-fold

The Financial Times reported a few weeks ago (paywalled):

Turkey has tripled petrol taxes as the government tries to raise money to recoup the cost of huge giveaways ahead of May’s election and fund reconstruction costing up to $100bn after February’s devastating earthquake. 

Taxes on regular petrol were increased about 200 per cent to TL7.53 a litre, with levies on diesel and a series of other petroleum products lifted as well, according to an announcement on Sunday in Turkey’s official gazette. The increase pushed up petrol prices at the pump by about 20 per cent, data from state oil company Turkish Petroleum showed.

My ECONS102 class covered excise taxes (taxes on the sale of goods or services) this week, so it's worth reviewing what happens, first when a tax is introduced, and then when it is tripled in size. Consider the market for petrol, as shown in the diagram below. If the market were left alone, it would operate with a price of P0, and Q0 petrol would be traded. When the excise tax is imposed, we represent that with the new curve S+tax. The price the consumer pays for a petrol increases to PC, but the effective price for the seller decreases to PP (which is the consumer's price PC, minus the amount of the tax paid to the government). The quantity of petrol traded decreases to QT.

However, now think about economic welfare. Consumer surplus is the difference between the amount that consumers are willing to pay (shown by the demand curve), and the amount they actually pay (the price). In the diagram, at the equilibrium price and quantity, consumer surplus is the triangle AEP0. Producer surplus is the difference between the amount the sellers receive (the price), and their costs (shown by the supply curve). In the diagram, at the equilibrium price and quantity, consumer surplus is the triangle P0ED. Total welfare is the sum of the two areas (consumer surplus and producer surplus), and is equal to the triangle AED.

Once the tax is imposed, the consumer surplus decreases to ABPC, while the producer surplus decreases to the area PPFD. The government gains the area of tax revenue, which is the rectangle PCBFPP (this rectangle is the per-unit amount of the tax, multiplied by the quantity of taxed petrol). Total welfare is the sum of all three areas (consumer surplus, producer surplus, and government revenue), or ABFD. Notice that total welfare with the tax is lower than it is without the tax, by the area BEF. That is the deadweight loss of the tax - lost economic welfare as a result of the tax reducing the quantity of petrol traded.

Now, with the tax imposed, consider what happens when the tax is tripled in size. So, instead of S+tax, we have a new curve S+3*tax, as shown in the diagram below. Notice that the distance from G to H is about three times larger than the distance from B to F. As a result, the price the consumer pays for a petrol increases even further to P3C, but the effective price for the seller decreases to P3P (which is the consumer's price P3C, minus the now-larger amount of the tax paid to the government). The quantity of petrol traded decreases to Q3T. The consumer surplus decreases further to AGP3C, while the producer surplus decreases further to the area P3PHD. The government now gains the area of tax revenue equal to P3CGHP3P. Total welfare has decreased further to AGHD, and now the deadweight loss is the much larger area GEH.

How much bigger is the deadweight loss? With the size of the tax tripled, it turns out that the deadweight is nine times larger. To see this, the diagram below splits the new deadweight loss area GEH into nine numbered triangles, each of which is about the same size as the original deadweight loss of BEF.

By tripling the petrol excise tax, the Turkish government may have increased tax revenues, but they have massively increased the loss of total welfare arising from the tax. There are likely to be some offsetting benefits in terms of lower vehicle emissions, cleaner air in Turkish cities, and lower traffic congestion, which are not shown in the diagram above. Perhaps overall the higher tax might increase welfare once those benefits are taken into account? No doubt some economists are looking eagerly at this potential natural experiment, to see what the effects are overall.