Fenway Park PS1 Question

Q:

In the text book it says that as the supply of a good becomes
more inelastic the tax incidence falls more heavily on the seller. However, if
the seller is selling the same amount of good and simply requests the additional
amount of tax from the consumer then where does the incidence come in? It seems
as if the incidence actually falls entirely on the consumer because they're
paying the tax in addition to the regular price of admission. Also, because
the supply is inelastic, the park will sell the same number of tickets
regardless of the tax. Or did I miss the fact that the stadium must lower the
price of the ticket so that with the tax it is equivalent to the original
ticket price?

A:

What you mentioned regarding the statement in the book is correct, and you can convince yourself that this is in fact the case by drawing a few diagrams. With regard to the problem set, it merely says that the consumers dutifully pay the tax. All we are trying to say is that they do in fact send in the $5 and don't get around paying the tax. This does not imply that consumers' demand doesn't change. Say for example that demand at $30 was 40,000 tickets, pre-tax. Demand would still be 40,000 tickets if the consumer had to shell out a total of $30, but in the case of the tax, the face value of the ticket would have to be $25 for this to be the case. So we get an effective demand curve like we did in class. Therefore, the seller can't just request the additional tax from the consumer, since the quantity demanded would be less if the total cost to the consumer was higher. The producer would not be selling all of the tickets and would want to lower the price in order to sell all of the tickets, thus bearing the burden of the tax. This should be pretty clear if you draw the diagram. I think it is the way the question is worded that makes it confusing, since it implies that the demand is unaffected by the tax.

One other note- be careful with your wording...you state "because the supply is inelastic, the park will sell the same number of tickets regardless of the tax". While it is true that they will SUPPLY the same number of tickets, the number of tickets actually sold is determined by both the supply and demand curves. In equilibrium, the number of tickets sold will be the intersection of the supply and demand curves. If the market is out of equilibrium, the quantity transacted will be the minimum of supply and demand (since the minimum is the limiting factor). Thus, the number of tickets the park actually sells is a function of the price it sets.