**Technifi Expert’s Answer:**

**a) Suppose that person A decides to buy the condominium. What will be the highest price at which the demand for apartments will equal the supply of apartments? What will be the lowest price? Enter your answers in column A, in the table. Then calculate the equilibrium prices of apartments if B, C, … , decide to buy the condominium.**

Arranged in the descending order of reservation prices:

**Person** |
**Price** |
**Highest Price** |
**Lowest Price** |

A |
40 |
18 |
15 |

D |
35 |
18 |
15 |

C |
30 |
18 |
15 |

B |
25 |
18 |
15 |

F |
18 |
25 |
15 |

G |
15 |
25 |
18 |

E |
10 |
25 |
18 |

H |
5 |
25 |
18 |

When A decides to buy the condominium, it leaves four apartments in the market. The equilibrium price will be one where demand for apartments equals the supply. The highest price would be 18, because if the price goes above 18 the fourth individual (F) to demand the apartment (apart from D, C, B) would not be interested in renting as it will be above his/her reservation price. And the lowest price is 15 as similarly to before if the price decreases below 15, then person G will also want to rent and there will be excess demand.

The case is similar if either D/C/B decide to buy the condominium and not the apartment. The highest price is 18, because if the price goes above 18 the fourth individual (F) would not be interested in renting as explained above. Lowest price would be 15, as before, because if the price decrease below 15 person G will also want to rent and there will be excess demand.

###### On the other hand, if F buy the condominium, persons with highest four reservation price would be A,D,C,B. Therefore, the highest price would be 25 – reservation price of B, it can’t be higher than 25 since it would lead to excess supply (at any price greater than 25, B would leave the market since price greater than reservation price). And the lowest price would be 15 and not lower because if its lower than 15 then G as well would demand the apartment and then there would be excess demand.

In contrast, if G buy the condominium, persons with highest four reservation price would be A,D,C,B. Therefore, the highest price would be 25 which is the reservation price of B and it can’t be higher than 25 since it would lead to excess supply as explained above. And the lowest price would be 18 and not lower, because if its lower than 18 then F as well would demand the apartment and then there would be excess demand.

Similarly, if E/H decides to buy the condominium and not the apartment; the highest price is 25, because if the price goes above 25 the fourth individual (B) would not be interested in renting as it will be above his/her reservation price. The lowest price is 18 as similarly to before if the price decreases below 18, then person F will also want to rent and there will be excess demand.

**(b) Suppose that there were two people at each reservation price and 10 apartments. What is the highest price at which demand equals supply? Suppose that one of the apartments was turned into a condominium. Is that price still an equilibrium price? Yes.**

If there were two people at each reservation price and ten apartments, the price at which demand equals supply will be when people with the top ten reservation prices are able to come forth and rent. The top ten would be coming forth when the price is 18 and not greater than 18, it should also not decrease below 18. When price is 18 there are ten people demanding the apartment and 10 apartments, but if the price decrease below 18 then 11th person (G) would also want to rent the apartment. Therefore, equilibrium price is 18.

Later, if one of the apartments was turned into condominium the price will still be equilibrium price 18 at which people with top nine reservation prices come forth and rent the apartment. The top nine would be coming forth when the price is 18 and not greater than 18, it should also not be lower than 18. When price is 18 there are nine people demanding the apartment and 9 apartments, but if the price decrease below 18 then 10th person (G) would also want to rent the apartment. Therefore, equilibrium price is 18.

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