From the Review Questions to Chapter 1: The Market in Hal Varian's Intermediate Microeconomics with Calculus, 9th ed.:
- Suppose that there are 25 people who had a reservation price of $\\\$500$, and the 26th person had a reservation price of $\\\$200$. What would the demand curve look like?
- In the above example, what would be the equilibrium price if there were 24 apartments to rent? What if there were 26 apartments to rent? What if there were 25 apartments to rent?
Please note that in this chapter, the supply of apartments is taken to be fixed.
I have drawn the demand curve, and attempted to solve the first two cases in the second question in the following way:
If there are 24 apartments, they go to the 24 people with the highest reservation price. This happens to be $\\\$500$, so that is the equilibrium price in this case.
When there are 26 apartments, we can imagine 25 landlords successfully leasing their property for $\\\$500$, and one landlord who is unable to net the $\\\$500$ lowering his price until he reaches $\\\$200$. This prompts a surge of potential tenants at his doorstep, but the apartment does not necessarily go to the tenant who had a reservation of price of $\\\$200$; it goes to whomever spends most time bargaining with the landlord, has the best connections, etc. Since this apartment generally goes to someone who had a reservation price of $\\\$500$, the new tenant vacates an apartment in her wake, which is then leased for $\\\$200$, and so on until everybody is living in a $\\\$200$ apartment.
The third case is confusing. The answer at the end of the book says that the equilibrium price would be "any price between $\\\$200$ and $\\\$500$" when there are 25 apartments. Why is this true? It seems to me that since the supply of apartments is fixed, the price of one apartment would depend only on the reservation price of tenants. If the equilibrium price is anything lower than $\\\$500$, landlords would have an incentive to arbitrarily increase the rent to the highest the market can absorb, i.e., $\\\$500$. What's keeping the equilibrium price below $\\\$500$?
Please also tell me if my reasoning about the other two cases is flawed, or there are other, better ways to reason about them.