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  14  5p, and the long-run demand function was given by q  329  5p, where p is the rental rate in crowns per week.The authorities made it illegal to rent an apartment for more than 25 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?

A) 6.50 crowns
B) 10 crowns
C) 13 crowns
D) 26 crowns
E) 19.50 crowns

To find the equilibrium rental rate, we set the supply function equal to the demand function:

 329  5p

 329 5p

 5p 329

 329F1F1F1– 5p

Plugging in the ceiling price of 25 crowns per week:

q  329  5(25)

q  204F1F1F1

The equilibrium quantity is given by:

q  204F1F1F1=329 5(25)=498.75

There is excess demand of:

q* q F1F1F198.75

To eliminate the excess demand, the authorities must subsidize each apartment by enough to increase the supply by 98.75 units. From the supply function, we can see that the cost per unit increase in supply is:

14

Therefore, the subsidy per apartment must be:

14(98.75)=13.94 crowns

Rounded to the nearest crown, the weekly subsidy per apartment should be 14 - 0.06 = 13 crowns, which is answer choice C.