I think it would depend on how elastic is the demand and the supply. If near the town pier there are more hotels and resort as well as a fish market then it will have more demand than the private pier.

Piers are generally 'essential facilities', so they could be a monopolist in a certain sense.

Secondly, it may depend on whether both piers stay on their competitive paths or, they collude and fix prices among them.

What do you think?

By the way, nice post and nice blog!

Mova,

Thanks for the comments, and am really glad to see that an intellectual discussion is made here.

I must admit that my whole analysis focuses on the price aspect as I believe that this is the intention of Mankiw's question in his post. As a result, the analysis would look rather simple.

If we note from the story, we can assume that the demand for the town pier is very high, so high that there is a shortage of supply and anyone who would like to rent a space in such pier must win a lottery first.

I don't know why the town pier becomes so famous, it might be the location, the facility, etc. But what we need to further analyze is why there are so many demands? Mankiw said that it must be the price, and I completely agree. Even if it has the best facility and location, the demand for the town pier wouldn't be that high if the price is really expensive. The fact that many people want to rent a space there indicates that the prices for such rent might be not too expensive.

In addition, if we see further to the story, the private pier is sitting next to the town pier, thus eliminating (most probably) the chance that there is a big difference of facilities or location between both piers. So, it would depend mostly on the price.

Now, on price fixing, I would agree that it may happen and affect the analysis. However, I doubt that in this case the town pier would want to make a cartel of piers with the private pier. What would be the benefit for the town pier? The town pier knows that there is an excess of demand, and they can increase the price up to the level where the demand may be lower but still meets the supply. In order to fix the price, I bet that the private pier would definitely need to pay the town pier or else there would be no incentive for the town pier to fix the prices.

Looking forward to see your future comments and many thanks.

Ah yes, in principle I would agree, a price change in the town pier may create an exodus of boats from private pier to the town pier so that the private pier will have to lower its price in order to keep its clients.

But there is an assumption here. We assume that the boats normally docking on the town pier will be bothered by the price raise and decide to dock elsewhere, presumably in the harbor. This, in turn, give slots for other boats originating from the private pier. And as a reaction to this, the private pier will be forced to lower its price.

However, if the boats normally docking at the town pier is willing to pay for higher price rather than going to the harbor, then there will be no movement of boats in the private pier to the town pier and as a consequence the private pier will not reduce its price.

Under the third scenario, a price change does bother some boats in the town pier, so they move to the harbor. However, some boats in the harbor consider the price system (as opposed to the lottery system) attractive, so they decide to pay a little more price for the town pier and fill in the slots there. In this scenario, there won't be any movement of boats from the private pier to the town pier since all slots there is filled anyhow. And as a consequence, the owner of the private pier will not be motivated to lower its price.

What do you think?

Mova,

Interesting analysis. You are right. In your scenarios, there would be no significant change in the amount of the users of the Town Pier.

So, the key question here is how much should the increased price be in order to: (i) ensure that the amount of the Town Pier users would decrease to a level where lottery would be no longer needed, (ii) discourage the harbor users to move to the Town Pier, and (iii) to provide an incentive for the private pier users to move to the Town Pier?

The only fact that we know is that the price of the private pier's slot is 5 times the price of the Town Pier's slot. The other fact is that some people prefer to use the harbor rather than paying the price of the private pier.

Unfortunately, I'm not an expert on mathematics and therefore am not able to calculate the exact amount of such new price. However, I believe that based on the above facts if the town pier wants to increase its price, it should not be at the same level with the private pier's price. While it may drive out the current users and discourage the harbor users to move to the Town Pier, there would be less (if none at all) incentives to the private pier users to move to the town pier.

Nevertheless, there is a great opportunity for the Town Pier to increase its price while still maintaining the amount of its users.