In a crowded city far away, the civic authorities decided that rents were too high. The long-run supply function of two-room rental apartments was given by q = 5 + 2p, and the long-run demand function was given by q = 225 - 4p, where p is the rental rate in crowns per week. The authorities made it illegal to rent an apartment for more than 30 crowns per week. To avoid a housing shortage, the authorities agreed to pay landlords enough of a subsidy to make supply equal to demand. How much would the weekly subsidy per apartment have to be to eliminate excess demand at the ceiling price?

Question

Quizplus · Accepted Answer

At the price ceiling of 30 crowns, the quantity supplied is q = 5 + 2(30) = 65, and the quantity demanded is q = 225 - 4(30) = 105. To eliminate excess demand, supply must equal demand, so the subsidy must increase supply to 105. The supply function becomes 105 = 5 + 2(p + subsidy). Solving for the subsidy gives a subsidy of 20 crowns.

In a Crowded City Far Away, the Civic Authorities Decided