Asked by Ashley Young on May 10, 2024
Verified
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?
A) 10 crowns
B) 17 crowns
C) 20 crowns
D) 40 crowns
E) 30 crowns
Supply Function
A mathematical representation showing the relationship between the quantity of a good supplied by producers and various factors influencing that quantity, such as the good's price.
Demand Function
A mathematical representation showing the quantity of a good that consumers are willing and able to purchase at various prices.
Subsidy
A financial contribution granted by the government to reduce the production costs and encourage the supply of certain goods or services.
- Assess the outcome of governmental policies, including subsidies and price limits, on the marketplace.
Verified Answer
ZK
Zybrea KnightMay 16, 2024
Final Answer :
C
Explanation :
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.
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.
Learning Objectives
- Assess the outcome of governmental policies, including subsidies and price limits, on the marketplace.