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.

We also shouldn't be debating removing GST from food

There are certain policies that make little sense from an economic perspective. As I noted yesterday, rent controls are one such policy. Another policy the government should not be considering is removing GST from food (and yet it seems that they are, and it is a policy position for Te Pāti Māori as well). This subject was well covered in this article in The Conversation by Steven Hickson last year (which I discussed here). Hickson wrote:

There are a number of potential complications.

Let’s start with the obvious – what would count as “food”? Is milk powder food? Probably yes, so what about milk? Or flavoured milk? Oranges are food, so what about 100% natural orange juice? A broad definition of “food” would include lollies, potato chips, McDonalds and KFC, but many would object to removing GST from these on health grounds.

We would then need to decide what is acceptable to exempt and what is not. The arguments would go on and on.

Politicians really need to read about the great Jaffa Cake controversy in the UK. We don't want to be tying up our courts trying to determine whether Jaffa Cakes are cakes, or biscuits. Or what constitutes food and should therefore be GST free. Are Tic Tacs a food and therefore should be GST free? What about edible underwear? Those are the sort of stupid arguments that removing GST on food would create.

On the other hand, I foresee a potentially lucrative business opportunity. <satire>I should set up a company, SpudCars, that sells 10kg bags of potatoes for $55,000. As a free gift, SpudCars will give each potato purchaser a free Tesla Model 3. The Tesla Model 3 currently retails for $57,572 including GST (after you factor in the clean car rebate). However, that price includes GST. SpudCars won't need to charge GST on the Teslas it gives away (because they are being given away for free, and the GST on $0 is equal to $0). The $55,000 bag of potatoes will not include GST either, if there is no GST on food. The buyer is better off by more than $2500, because they get an awesome bag of potatoes with a bonus car, for just $55,000, instead of slightly more than $57,572 if they bought a Tesla from a car dealer and a bag of potatoes from the supermarket. SpudCars can buy Teslas from the dealership for $57,572, claim the GST (of about $7,500) back from the government, and then sell a bag of potatoes for $55,000 with no GST included. That means that SpudCars profits by nearly $5,000 for every bag of potatoes it sells. It's a win-win for the buyer and for SpudCars. As a dirt-poor university professor though, I'll need some investors to get SpudCars up and running. If you want to get in on the action, and be a founding shareholder in SpudCars, drop me an email.</satire>

It should be easy to see the shenanigans and potential legal battles that removing GST from food creates. It shouldn't take an economics blog outlining a ridiculous scenario to make this clear. This is a policy failure in waiting, if the government ever chose to implement it.

Read more:

• Judge rules that snuggies are blankets, not clothes
• Stephen Hickson on why we shouldn't remove GST from food

There should be no debate at all about rent controls

Rent controls have a number of negative effects. They lead to excess demand for housing, which is worse in the long run than the short run. They create a deadweight loss (a loss of economic welfare overall). They reduce the quality of rental housing (to the extent that rent controls have deadly consequences), and increase the quantity of vacant housing. They may even increase inequality (see here and here). In fact, the Swedish economist Assar Lindbeck (who passed away in 2020) was quoted as saying:

“Rent control appears to be the most efficient technique presently known to destroy a city—except for bombing.”

And yet, despite the overwhelming evidence of the negative effects of rent controls, people still advocate for them. Or, they or argue that we need to re-examine them based on flimsy reasoning. For example, in this article in The Conversation, Tom Baker (University of Auckland) asks us to have an open mind about rent controls. An open mind couldn't fail to see that the evidence is strongly against rent controls as a way of helping low-income tenants. We don't need to rely on an economic model for this - the empirical evidence (in the posts linked above) supports it.

Fortunately, not everyone has starry-eyed views of rent controls and is unwilling to consider the weight of the evidence. This article in The Conversation by Ameeta Jain (Deakin University) concludes that:

While freezing rents would appear to be a simple method to increase rental housing affordability, the unintended consequences of any such move will have a long-term negative impact on the total availability of rental housing stock, reducing the quality of housing and increasing a black market in rental housing.

Global experience suggests that improving supply, by easing building restrictions and scrapping red tape for new developments, is likely to be a more effective policy tool in Australia.

As for helping low-income tenants, I said it best in this post in 2015:

This excess demand can have a range of negative effects, depending on how it is managed. Perhaps the excess demand is managed by waiting lists of various flavours (as in Stockholm or Copenhagen), which means that potential tenants have to wait years for a rent-controlled space to become available. Instead, perhaps landlords are left to manage the excess demand on their own, in which case the rent-controlled housing is more likely to be rented to higher income tenants. Why? The landlord has a lot of choice over tenants now (because of the excess demand). If they can choose to rent their house to the professional couple with two incomes, or the solo mother with no job and three young children, it doesn’t take an economics PhD to work out who is going to miss out. So in this case the rent control actually hurts the very people (low income tenants) that it was designed to help.

On top of that, landlords might be willing to accept side-payments (bribes) to ensure access to rental housing. Tenants are willing to pay the bribes to ensure they don't miss out on a place to live. This further stacks the rental market against low-income tenants.

The very tenants that rent controls are designed to help, end up being the tenants that are most hurt by the policy. If we are worried about low-income tenants, perhaps we should do something about their low income, or do something that raises supply of rental property (which would increase competition among landlords and reduce the equilibrium rent). Rent controls are a policy failure on so many dimensions and are best forgotten.

Read more:

• Why rent controls have worse effects over longer time horizons
• The deadweight loss of rent control
• The deadly consequences of rent control in Mumbai
• Rent control and inequality in San Francisco
• Rent control and the redistribution of wealth
• Rent control and vacant properties in India
• Rent control according to Seinfeld

The Tour de France, public goods, and the chicken game

I finally finished watching this year's Tour de France on Sunday. Yes, I was a week behind. That's because I was overseas when it started, and it took me that long to catch up (with big thanks to Sky On Demand!). Jonas Vingegaard well deserved his win. The individual time trial he rode on Stage 16 was amazing to watch (even if his team Jumbo Visma says so themselves).

Anyway, this is a blog about economics. Sports provide lots of great examples of economics in action, because economics is ultimately about choices, and so are sports. One striking example of economics in action in cycling road races occurs when there is a breakaway, and it is getting close to the finish line. The riders in the breakaway face a difficult choice. They can ride hard at the front of the breakaway, ensuring that the breakaway won't be caught by the peloton, and one of the breakaway riders will surely win the race. Or they can hold back, riding in the slipstream of the rider who is riding at the front, which lets them conserve energy for a sprint finish, but at the risk that the peloton catches them.

This exact scenario played out in Stage 18 of the Tour de France this year, with three riders approaching the finish. Victor Campenaerts rode hard towards the finish, ensuring the breakaway would succeed. However, it was Kasper Asgreen who won the stage, having conserved his energy for the final sprint among the breakaway riders.

Let's think about the incentives for a breakaway rider. Riding hard is a public good. It is non-rival (one cyclist benefiting from a rider riding hard at the front of the breakaway doesn't reduce the amount of the benefit available for the other riders in the breakaway) and non-excludable (if a rider is riding hard at the front of the breakaway, they can't easily prevent the other breakaway riders from sitting in their slipstream and conserving their energy).

Public goods, like riding hard at the front of the breakaway group, suffer from a free rider problem (pun intended!). Other riders can benefit from the front rider's hard work, without paying any of the cost themselves. It is difficult for a rider to justify riding hard at the front if other riders are unwilling to contribute, since they face all of the cost of riding hard, but the benefit (in terms of a better chance of winning the race) goes to the other riders (the free riders).

Ordinarily, the provision of public goods breaks down. They cannot be privately provided, because of the free rider problem. In this case though, cycling has developed norms that ensure some cooperation within the breakaway group. The riders tend to take turns at the front of the breakaway group, helping to increase the chances of success. However, the closer the race gets to the finish, the greater the incentives to free ride become. Regular cycling fans will no doubt remember many instances where a breakaway group has been caught, within sight of the finish line, because they failed to work together.

Another way of thinking about the incentives within a breakaway group is to use game theory. To make the problem simpler, let's say that the breakaway group only consists of two riders, and there are two strategies: (1) to ride hard; or (2) to hold back. We'll assume each rider makes their decision just once, and they make their decisions at the same time (a simultaneous game).  The payoffs for this scenario are shown in the table below. If both riders ride hard, they have a 50% chance of winning the race (since they will both be equally tired). If one rider rides hard and the other holds back, the rider that holds back wins the race for sure. If both riders hold back, then they are caught by the peloton, and neither of them wins (and they don't even finish in the top two in the race). What will happen?

To find the Nash equilibrium in this game, we use the 'best response method'. To do this, we track: for each player, for each strategy, what is the best response of the other player. Where both players are selecting a best response, they are doing the best they can, given the choice of the other player (this is the definition of Nash equilibrium). In this game, the best responses are:

1. If Rider B chooses to ride hard, Rider A's best response is to hold back (since winning for sure is better than a 50/50 chance of winning) [we track the best responses with ticks, and not-best-responses with crosses; Note: I'm also tracking which payoffs I am comparing with numbers corresponding to the numbers in this list];
2. If Rider B chooses to hold back, Rider A's best response is to ride hard (since losing and finishing in the top two is better being caught by the peloton and finishing much lower in the order);
3. If Rider A chooses to ride hard, Rider B's best response is to hold back (since winning for sure is better than a 50/50 chance of winning); and
4. If Rider A chooses to hold back, Rider B's best response is to ride hard (since losing and finishing in the top two is better being caught by the peloton and finishing much lower in the order).

In this scenario, there are no dominant strategies. Neither rider has a strategy that is always better for them, no matter what the other rider chooses to do. However, there are two Nash equilibriums (outcomes where both players are playing their best response), which occur when one rider rides hard, and the other holds back. Neither rider will want to be the rider that rides hard, so both may be holding out hoping that the other rider will ride hard. This is the free rider problem described earlier. This game is an example of the chicken game (which I have discussed here). If both riders hold back, hoping that the other rider will ride hard, both riders will be caught by the peloton.

The chicken game is an example of a coordination game. To end up at one of the equilibriums (or another), the players need to coordinate their actions. However, in this case neither rider really wants to coordinate on the other rider's preferred equilibrium. Both really want to hold back, especially closer to the finish line, which is why the breakaway can often be caught.

Riders are motivated by the chance to win the race. That is why breakaway groups form in the first place. However, the incentives outlined above work against the breakaway succeeding. And riders are aware of these issues. One thing that often happens is that, towards the end of a race, one rider will ride especially hard, breaking away from the breakaway group. There is no free rider problem when a rider is riding by themselves. Sadly, solo breakaways are seldom successful (except on mountain stages), because the effort required to remain clear from a group of breakaway riders who suddenly become more motivated to work together and catch the solo breakaway rider is very high. The solo breakaway rider is often caught, after which the chicken game and free riding begins again.

One thing that can increase the success of a breakaway is to have multiple teammates in the breakaway group. Teammates are more likely (but not certain) to be able to coordinate their strategies, and work together, reducing the free riding problem. That's why riders in the peloton are more vigilant and energetic in chasing down an early breakaway group that has multiple riders from the same team. Most of the time, a breakaway group will only go clear if every rider in the group is from a different team. Riders in the peloton don't want the breakaway to succeed, and having all breakaway riders from different teams decreases the chance that a rider from the breakaway wins the race.

There is a lot of strategy in sports, and cycling is no exception. There are also a lot of choices for athletes to make, and choices involves trade-offs. That, along with the transparent rules and the obvious goals of the athletes involved (they want to win), is why sports can provide a lot of useful illustrations of economic concepts.