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  15  3p and the long-run demand function was given by q  237  3p, 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?

A) 14 crowns
B) 7 crowns
C) 11 crowns
D) 28 crowns
E) 21 crowns

To find the weekly subsidy per apartment needed to eliminate excess demand at the ceiling price of 30 crowns, we first calculate the quantity supplied and demanded at this price.Supply function: $q_s=10+3p$ Demand function: $q_d=237-3p$ At $p=30$ :- Quantity supplied: $q_s=10+3(30)=100$ - Quantity demanded: $q_d=237-3(30)=147$ To eliminate excess demand, the supply needs to increase to match the demand at 147. Setting the supply equal to the demand and solving for the subsidy: $100+subsidy=147$ Subsidy = $147-100=47$ However, the subsidy is not directly asked for; we need to find the subsidy per apartment to make the supply price equal to the demand price at the ceiling price. The subsidy per apartment would be the difference in the price that equates supply and demand at the ceiling price.Without the exact calculation for the subsidy per apartment directly from the given functions, the key here is understanding that the subsidy needs to bridge the gap between the supply price and the ceiling price to make the market equilibrium. Given the options and the misunderstanding in the direct calculation from the provided functions, the correct choice would be to reevaluate how the subsidy is calculated based on the difference in equilibrium prices or quantities, which isn't directly solvable with the provided explanation. The initial explanation mistakenly calculated the total subsidy needed to match the total quantity demanded, not the per apartment subsidy to match the ceiling price. Reevaluating the approach for calculating the per apartment subsidy correctly involves understanding the economic principles of supply and demand and how subsidies affect them, but with the given information, a precise step-by-step calculation was misinterpreted. The correct answer involves calculating the difference in costs or prices to suppliers to ensure they are willing to supply what is demanded at the ceiling price, which was not accurately captured in the initial response.