The Professor Asks

Two piers are located next to each other. One, government run, drastically undercharges for dock spots and so has to run a lottery every year to determine who has a right to dock at the pier. The other, privately run, charges approximately 5 times as much for a spot, but always has spots available for those willing to pay.

What happens to the price of a spot at the private pier if the government owned pier raises its price?

Here's my guess, assuming that the docking at one pier is as good as docking at the other:

Generally you'd think that if the price of a substitute goes up, then the item's price would go up too. So, if frozen yogurt goes up in price, people will substitute ice cream. The increased demand for ice cream will cause the price to go up.

I don't think that's the right way to think about this problem, however. Instead, raising the price at the government pier will cause some people who currently pay for a lottery spot at the pier to lose interest. Thus, demand will be lower for spots at the government pier at the higher price. But there is clearly excess demand, so they should still fill all the slots. Furthermore, some of the people at the private pier, who are now paying 5 times as much for spots are likely to get spots over at the public pier. Thus, demand for spots at the private pier will fall. Falling demand will result in the price for private pier spots to fall.

That's my answer.