My textbook had the following question: The demand curve for apartments in a par
ID: 1251180 • Letter: M
Question
My textbook had the following question:The demand curve for apartments in a particular country is expressed in the formula:
R1 = 1500 – Q1
The supply curve for apartments in that country is expressed in the formula:
R1 = Q1
where Q1 represents the number of apartments and R1 represents the cost to rent an apartment
Now the gov decided to pass a law that the cost to rent should not exceed $375 per apartment.
In order to minimize the damage such a law will have on apartment owners, the government decided to allow landlords to force their tenants to pay “key money” for the right to pay such low rent.
Assuming the cost to rent an apartment is fixed at 5 percent of the value of the apartment, what is the maximum amount of money a tenant would have to pay in “key money” to his landlord?
The answer is supposed to be $3,750. I don't understand how they arrived at this answer. Please help. Thank you.
(In my calculation, before the law was passed the rent was $750. After it was passed, it went down to $375. The value of the apartment was 750 * 20 = 15,000. The current value - after the law - is 375 * 20 = 7,500. Therefore, I was sure the answer was 7,500)
Explanation / Answer
hint for an explaination-In most of the problems we work with the true demand curve constructed from the reservation prices of the consumers rather than the smoothed" demand curve that we used in the text. Remember that the reservation price of a consumer is that price where he is just indi®erent between renting or not renting the apartment. At any price below the reservation price the consumer will demand one apartment, at any price above the reservation price the consumer will de- mand zero apartments, and exactly at the reservation price the consumer will be indi®erent between having zero or one apartment. You should also observe that when demand curves have the stair- case" shape used here, there will typically be a range of prices where supply equals demand. Thus we will ask for the the highest and lowest price in the range. Suppose that we have 8 people who want to rent an apartment. Their reservation prices are given below. (To keep the numbers small, think of these numbers as being daily rent payments.) Person = A B C D E F G H Price = 40 25 30 35 10 18 15 5 (a) Plot the market demand curve in the following graph. (Hint: When the market price is equal to some consumer i's reservation price, there will be two di®erent quantities of apartments demanded, since consumer i will be indi®erent between having or not having an apartment.)
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