Due to Covid, the unemployment rate increases sharply. Many households are not able to afford to pay rent for their housing. The government decides to implement price controls so that households continue to afford their rent. The demand function in the perfectly competitive house-renting market is given by: P = 2000 – 2Q. The supply function is given by: P = 1500 + 3Q. Which of the following price ceilings will be binding?Group of answer choicesP = 1500P = 1850P = 1900P= 1800None of the other answers is correct.
Question
Due to Covid, the unemployment rate increases sharply. Many households are not able to afford to pay rent for their housing. The government decides to implement price controls so that households continue to afford their rent. The demand function in the perfectly competitive house-renting market is given by: P = 2000 – 2Q. The supply function is given by: P = 1500 + 3Q. Which of the following price ceilings will be binding?Group of answer choicesP = 1500P = 1850P = 1900P= 1800None of the other answers is correct.
Solution 1
To determine which price ceilings will be binding, we first need to find the equilibrium price in the market. This is where the demand and supply functions intersect, i.e., where P (demand) = P (supply).
So, we set the two equations equal to each other:
2000 - 2Q = 1500 + 3Q
Solving for Q, we get:
Q = (2000 - 1500) / (2 + 3) = 500 / 5 = 100
Substituting Q = 100 into either the demand or supply function to find the equilibrium price P, we get:
P = 2000 - 2*100 = 1800
A price ceiling is binding if it is set below the equilibrium price. So, in this case, the price ceilings that will be binding are P = 1500 and P = 1800. The price ceilings P = 1850 and P = 1900 are not binding because they are above the equilibrium price.
Solution 2
To determine which price ceilings will be binding, we first need to find the equilibrium price in the market without any price controls. This is where the demand and supply curves intersect, i.e., where the quantity demanded equals the quantity supplied.
Setting the demand function equal to the supply function, we get:
2000 - 2Q = 1500 + 3Q
Solving for Q, we get:
5Q = 500
Q = 100
Substituting Q = 100 into either the demand or supply function to find the equilibrium price, we get:
P = 2000 - 2*100 = 1800
So, the equilibrium price without any price controls is P = 1800.
A price ceiling is binding if it is set below the equilibrium price. Therefore, the price ceilings that will be binding in this case are P = 1500 and P = 1850. The price ceiling of P = 1800 is exactly at the equilibrium price, so it is not binding. The price ceiling of P = 1900 is above the equilibrium price, so it is also not binding.
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