# Is my logic on taxation for this question legit?

At Fenway Park, home of the Boston Red Sox, seating is limited to 39,000. Hence, the number of tickets issued is fixed at that figure. Seeing a golden opportunity to raise revenue, the City of Boston levies a per ticket of 5 bucks to be paid by the ticket buyer. Boston sports fans, a famously civic-minded lot, dutifully send in the 5 bucks per ticket. Draw a well-labeled graph showing the impact of the tax. On whom does the tax burden fall - the team's owners, the fans, or both? Why?

Now, for this question, my take is that the tax burden fall on the fans, because the fans paid 5 bucks extra on tax, and the government imposes a 5 bucks tax. Hence, it doesn't affect the sellers/team's owners. But from what I've learnt is that tax burden is shared amongst sellers and buyers.

I'm equally confused. If it's shared, then who gets to decide the amount buyers and sellers have to split for the tax burden? (If the amount is not provided?) Thank you.

The burden of taxation is shared among suppliers and demanders according to the price elasticities of supply and demand. The more elastic side carries less of the tax burden.

To understand this, note that the tax effectively increases the price demanders pay and decreases the price suppliers get. Elasticity tells us how demanders and suppliers react to this price change. For demanders this means buying less and for suppliers it means supplying less. If you are more elastic then you react to the tax more (by definition of elasticity), which means you avoid it more.

To illustrate this, imagine a tax on cigarettes. We assume that smokers who are addicted will have to buy cigarettes at any price (as they are addicted). This means they do not react and have 0 elasticity of demand. In that case, imposing a tax on cigarettes (a price increase) will not affect how many cigarettes are bought. So the producers of cigarettes are making just as much profit as before, while the consumers are paying higher prices, hence the consumers carry the full burden of the tax.

You could imagine a similar argument, where the supplier produces less because of the tax, thereby causing prices to increase and hurting the consumer.

In your case the producer is totally inelastic, while consumers have some elasticity and hence carries the burden of the tax (as he cannot react and reduce the number of seats).

Alternatively imagine a tax put on producers, where the producers are inelastic, but consumers are elastic. The producers when trying to push the tax onto the consumers (raise the price) the consumers will buy less (are elastic) and thus reduce the suppliers profits, so the producer cannot push the full tax onto the consumers if he's maximizing profits. He can only push a part of it, which means his profits will partially fall and buyers will pay higher prices. Hence both carry the tax burden. The producer can push less of the tax increase the more elastic the consumers are compared to him.

We can also see this general point graphically. The figures I have for this are when the tax is on the producers so affects the supply, but the result is equivalent to a tax on the consumers affecting demand. The blue region represents the surplus lost by the consumer that is captured as tax revenue as a result of the tax and the red region represents the surplus lost by the producer that is captured as tax revenue as a result of the tax. The grey region is deadweight loss resulting from the tax -- it is surplus lost, but not captured as tax revenue. In the first plot below, supply is relatively inelastic (i.e. not very steep) and demand is quite elastic (i.e. steep). In the second, supply is relatively elastic (i.e. steep) and demand is quite inelastic (i.e. not very steep).

• @BB_King I added some images to your excellent answer in the hope of making it better still. If you think they detract, my apologies, and please undo the edits. To the OP, if you want to see lecture slides on this material, see the tax incidence section in this lecture. – Shane Jul 15 '16 at 2:30
• @Shane I strongly disagree with the language of the edit. "Let the blue region denote the tax paid by the consumers/demanders and the red region denote the tax paid by the suppliers/producers." This is a frequently used but absolutely incorrect description of what is happening. – Giskard Jul 15 '16 at 11:56
• @denesp Could you elaborate a little more on that? Are you making the distinction that the suppliers are still paying for the tax, but the tax incidence makes it so that the price received is not the "full burden" of the tax? – Kitsune Cavalry Jul 16 '16 at 3:38
• @Shane Indeed. Yet you are speaking in an economic context. Consider it was the villain's accountant who threatened Bond so. Would you not be confused? But another reason I find that your language unfortunate is because in this model the suppliers have no price setting power at. Hence they are unable to 'push taxes'. I find such blurring of concepts muddles things. I will admit that such use is widespread. – Giskard Jul 16 '16 at 11:40
• @denesp Only the last paragraph is my text -- the language regarding pushing is in the original. I've tried to strip my own writing of the verb to pay (in an edit that has been approved by one but rejected by another). I feel less comfortable doing that to the original, which is not my work (and fairly well upvoted). – Shane Jul 17 '16 at 2:14

It depends on whether all the tickets are sold or not. If sold out, all the the tax burden is borne by the buyers. If not, then it's shared.

## If sold out, buyers pay all the tax.

If all 39,000 tickets are sold, then your reasoning holds correct. The revenue the owners receive with the tax will equal the income to the owners without the tax.

$$R = P \cdot Q_{max}$$

Where $R$ is the total revenue from ticket sales to owners, $P$ is the average ticket price, $Q(P)$ is the total quantity of tickets sold and $Q_{max}$ is the total quantity of tickets available to be sold (39,000 in this case).

$$Q_{max} = 39,000$$

The total amount of tax revenue received by the government will equal the total amount of taxes paid by the ticket buyers.

$$T_{paid} = T_{received} = \5 \times 39,000 = \195,000$$

## If not, the tax burden is shared.

When the stadium does not sell out, then the price elasticity of demand kicks in and causes both parties to share the tax burden. Keep in mind, the ticket sellers still earn the same amount per ticket, their shared tax burden (economic loss) comes from a reduced number of ticket sales due to the increase in ticket cost paid by the ticket buyers. The reduction in ticket sales represents a cost of lost opportunity of a perishable asset (i.e., the unsold tickets).

The amount the buyers, in aggregate, reduce their ticket purchases will be proportional to the price elasticity of demand.

The below diagram shows the impact of taxation on ticket sales, price and quantity sold.

The tax burden falls on the ticket buyers, on the ticket sellers, on the hot dog vendors, on the cab drivers, on the children of the ticket buyers, and on a whole bunch of other people.

Ticket buyer: Because he paid $5 extra to buy the ticket. Ticket seller: as @Mowzer said, if the event wasn't sold out, it is possible some tickets weren't sold that would have been sold at$5 less, so the seller lost on those.

Hot dog vendors: some of the ticket buyers would have bought more from the vendors had they not paid the extra $5, so that cost fell on the vendors too. Cab drivers: some of the ticket buyers would have spent a few bucks on a cab after the game had they not paid the extra$5, so that cost fell on the cab drivers too.

Children of ticket buyers: some of ticket buyers would have spend a few bucks on ice cream the next day for their kids had they not paid the extra $5, so that cost fell on the kids too. And so forth. And for those frugal buyers that would have saved the \$5 in their savings account, that is \\$5 (times the number of such savers) that won't get lent out by the bank to a small business, hindering productivity increases and slowing down a growth in the standard of living that is brought about by such economic growth.