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  20  5p and the long-run demand function was given by q  271  2p, where p is the rental rate in crowns per week.The authorities made it illegal to rent an apartment for more than 23 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) 9 crowns
B) 18 crowns
C) 36 crowns
D) 15 crowns
E) 27 crowns

To eliminate excess demand at the ceiling price of 23 crowns per week, we need to equate the quantity demanded with the quantity supplied.
Quantity demanded:
q = 271F1S1 - 2F1p
Substituting p = 23, we get
q = 271F1S1 - 46F1
Quantity supplied:
q = F1S1 + 5F1p/F10 + 20F1
Substituting p = 23, we get
q = F1S1 + 525F1/10 + 20F1 = F1S1 + 77F1
Equating quantity demanded with quantity supplied, we get
271F1S1 - 46F1 = F1S1 + 77F1
Solving for S1, we get
S1 = 13.57
The subsidy per apartment would be the difference between the market rental rate and the rental rate set by the authorities, which is 23 crowns per week.
Subsidy per apartment = 23 - p = 23 - 23 = 0 (No subsidy required)
Note that if the rental rate set by the authorities were below the equilibrium market rental rate, a subsidy would be required to ensure that quantity supplied equals quantity demanded.