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 = 18 + 3p and the long-run demand function was given by q = 267 - 4p, where p is the rental rate in crowns per week.The authorities made it illegal to rent an apartment for more than 27 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 27 crowns, the supply is q = 18 + 3(27) = 99 apartments, and the demand is q = 267 - 4(27) = 159 apartments. To eliminate excess demand, supply must equal demand, so the price must be adjusted. Setting the supply equal to demand: 18 + 3(p + s) = 267 - 4(p), where s is the subsidy. Solving for s gives a subsidy of 20 crowns.

In a Crowded City Far Away, the Civic Authorities Decided