My textbook had the following question: A law was passed forbidding tenants from

Question

My textbook had the following question:

A law was passed forbidding tenants from divide their apartments and renting out the different portions.

We know these facts:

* The flexibility of the supply curve of rented apartments before the law was passed is 0.15

* Before the law was passed, there was a rise in the demand for rented apartments, and this rise in demand caused a 30 percent rise in the number of apartments that were rented out.

* We expect an additional increase in the demand for rented apartments, which will cause the number of rented apartments to rise by an additional 20 percent.

By how much percentage can we expect the price of renting an apartment to rise by?

The answer is supposed to be “by more than 133.33 percent”. I don't understand how they arrived at this answer. Please explain. Thank you.

Explanation / Answer

We don't care about the demand increase before the law, it's irrelevant for this problem. So demand is forecasted to increase by 20%. That means unless there is an artifical price ceiling, supply will meet this new demand by increasing prices. The flexibility (price-elasticity) of the supply curve at the current point is 0.15 That means when price goes up by 1%, supply goes up by 0.15%. Elasticity = percentage change in supply / percentage change in price We want to find out the percentage change in price, so: Percentage change in price = Percentage change in supply / Elasticity remember, we're assuming a market equilibrium will be reached, so for our purposes, percentage change in demand is equal ot percentage change in supply, so let's plug it in: Percentage change in price = .20 / .15 Percentage change in price = 1.333333 repeating or 133.33%

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