I’m going to dole out the answers to the first half of my honors exam slowly over the next several days. After that I’ll post the second half of the exam.
Let’s start with this one:
Question 3. Snidely Whiplash owns all the grocery stores and all the houses in the Yukon Territory. He charges a competitive price for groceries, and rents the houses at the highest price residents (who are all identical) are willing to pay. (If he charged any more, they’d all leave town). True or False: If Snidely raises the price of groceries, he’ll have to lower the price of housing, so he’ll be no better off than before.
Answer: It would be a great mistake for Snidely to raise the price of groceries.
Suppose you’re a customer who currently buys 15 bagels a week at a dollar apiece. Now Snidely doubles the price of bagels, and you choose to buy only 10 at two dollars apiece.
That’s bad for you in two ways: First, you’re paying an extra ten dollars for those ten bagels. Second, you end up with fewer bagels, which makes you sad. Since you were right on the verge of leaving town to begin with, Snidely’s got to make all of that up to you. He’s got to discount your rent by ten dollars plus compensation for the five forgone bagels.
So let’s look at both components. As far as the first ten bagels are concerned, you pay him an extra $10 and he gives it right back to you in the housing market. So far he’s even. As far as the remaining five bagels are concerned, he’s got to lower your rent by an amount commensurate with what you feel you’ve lost. Offsetting that, he saves the cost of providing those five bagels. But (and here is a subtle but key point) we know those five bagels cost him less than they were worth to you, because of the fact that he’s been willing to sell them to you in the past.
Therefore what he gives back to you in the housing market must exceed his savings from providing fewer bagels, leaving Snidely poorer than he was. He should never have raised the grocery prices in the first place.
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This gives me a chance to put in a plug for why you should take an economics class (at least if you enjoy this sort of puzzle). If you’re not used to this kind of thing, this reasoning probably looks convoluted enough to leave you thinking “Well, if you gave me an hour I could come up with an equally convoluted argument to prove the opposite”. And you’re right. You probably could. But your argument would be wrong, and mine is right. I know that because I didn’t just make it up; I discovered it by drawing a picture of the sort one learns to draw in economics classes. Once you’ve mastered the technique, these pictures force the right answer on you. It’s pretty cool, really. That’s why I like this stuff.
