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 ceiling price of 30 crowns per week, we need to equate the quantity demanded and quantity supplied. Solving the two equations for q, we get:

q=37.5-0.5p

q=10+2.5p

Setting them equal, we get:

37.5-0.5p=10+2.5p

Solving for p, we get:

p=9

So the equilibrium quantity at the ceiling price is:

q=37.5-0.5*9=33

To eliminate excess demand, we need to increase the quantity supplied from 20 to 33. The increase is 13 units. Multiplying the increase by the subsidy per unit, we get:

13*20=260

So the weekly subsidy per apartment should be 20 crowns.

In a Crowded City Far Away, the Civic Authorities Decided