New Gas Tax in the Ontario 2016 Budget

The previous post was rather weak so let’s try looking at something else from the new Ontario budget.

One of the funny, funny things that economists like to say about economics is that it is the simple made complex. An idea that seems very straightforward can be made to look extremely complicated once you model it out and try to quantify everything. There are a few good examples of this but since we are talking about politics and taxation (did I mentioned we are talking about taxation?) then we will use Ramsey’s Optimal Tax formula as our example.

Some definitions.

Deadweight Loss. This is basically waste in an economic system. If something changes in a model, like say a new tax, and there is money wasted then that is referred to as a deadweight loss.

Price Elasticity. The percentage change in the quantity demanded of a good for every percentage change in the price. If something is perfectly elastic then when the price changes, everyone stops buying it. If it is perfectly inelastic then people buy it at any price.

Hicksian Demand. This is a mathematical function that describes the bundle of goods a person can buy with minimal spending such that their total utility (enjoyment) remains unchanged. So as prices change, you change what you buy to keep yourself happy.

Externality. Something that is caused by a modelled system that is not accounted for in the model. If a factory is polluting the environment and pays no penalty for it then we say that is a negative externality. There is a social cost that is not taken into account.

What does the Ramsey Tax rule looks like while it is being derived? Well I don’t have any math plugins loaded so I am just going to use images.


That is: Minimize deadweight loss such that total new tax revenue is higher than current revenue

So a person wants to raise the most tax revenue while creating the least deadweight loss. Makes sense. What does that look like when you place the Hicksian demand function in there to calculate total tax revenue as well as the total DWL generated?  


Now we’re getting somewhere!  Next we do some Lagrange calculations and get our result for good i ( i being just some number. It is a placeholder for any good) and then do it all again for good j (some other good) and divide the two together. This gives us the outcome:


Fantastic! This is adequately complex.  (Full derivation here)

Now what does this formula tell us? Well, quite simply it means that if you want to raise the most revenue while creating the least deadweight loss, and therefore select the best possible product to tax, then you should select something that has highly inelastic demand . Or, tax things that people are going to buy anyway. The simple made complex.

Let’s apply this to the new budget. The government has two new taxes in there that we care about for this article. One is the higher cigarette tax and the other is the higher gas tax. Both of these are highly inelastic products. Cigarettes because they are addictive and gas because you are just going to buy the gas you need; it isn’t a luxury item. In both cases the government is trying to present them as a Pigouvian tax…

Forgot to define those. Pigouvian taxes are quite straightforward. They are designed to add a tax where there are negative externalities. The Pigouvian tax essentially puts a price on the externality and ideally the revenue generated would be used to offset the ill effects.

So the Ontario government brings in this gas tax claiming it is to save the environment and that they are doing this for the future of the world. Basically, selling it to the electorate as a Pigouvian tax. In reality they have all the sales data from the last decade where gas prices have had wild swings. They know the exact elasticity of gasoline. The result? A new tax on a highly inelastic product that would make Ramsey proud.

This isn’t being done for the environment; it’s a cash grab by a terrible provincial government