Question

5. Consider the market for one-bedroom apartments in a large city, suppose the demand and supply for apartments in this city are given by the following equations: Q = 70,000 – 60R Q = -32,000 + 110R Where R is the rental price of an apartment in this city measured in dollars, Q is the quantity of apartments demanded and the number of apartments landlords are willing to rent out in this city. i. Find the market rent and equilibrium quantity of apartments in this city. ii. What happens if the if the government enact a rent control of $550 for an apartment in this city? Does this rent control cause a surplus or a shortage of apartments? Why? How large is the shortage e/surplus, if any? iii. What happens if the if the government enact a rent control of $800 for an apartment in this city? Does this rent control cause a surplus or a shortage of apartments? Why? How large is the shortage/surplus, if any? iv. Why is the government enacting rent control in this market?

Answer 1

The equation for demand of the apartments in the city is given by Q_d = 70,000 - 60R

The equation for supply of the apartments in the city is given by Q_s = - 32,000 + 110R

The market rent and equilibrium quantity of apartments in this city is found by equating the demand and supply equations

Q_d = Q_s

70,000 - 60R = - 32,000 + 110R

70,000 + 32,000 = 110R + 60R

102,000 = 170R

R = $ 600

The market rent for the apartments in the city = $ 600

Equilibrium quantity of apartments in the city = 70,000 - 60 x $ 600

Equilibrium quantity of apartments in the city = 34,000

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If the government enact a rent control of $550 for an apartment in this city

Quantity demanded of the apartment at the enacted rent control = 70,000 - 60 x $ 550

Quantity demanded of the apartment at the enacted rent control = 37,000 apartments

Quantity supplied of the apartment at the enacted rent control = - 32,000 + 110R

Quantity supplied of the apartment at the enacted rent control = - 32,000 + 110 x $ 550

Quantity supplied of the apartment at the enacted rent control = 28,500

This rent control causes a shortage of apartments by 8500 units. The enacted rent control causes a shortage because less number of apartment owners will be ready to rent out apartments at a rent which is less than the market rent.

The shortage of apartments is 8500 units

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If the government enact a rent control of $800 for an apartment in this city.

Quantity demanded of the apartment at the enacted rent control = 70,000 - 60 x $ 800

Quantity demanded of the apartment at the enacted rent control = 22,000

Quantity supplied of the apartment at the enacted rent control = - 32,000 + 110R

Quantity supplied of the apartment at the enacted rent control = - 32,000 + 110 x $ 800

Quantity supplied of the apartment at the enacted rent control = 56,000

This rent control cause a surplus of apartments because more apartments owners are willing to rent out apartment at a rent which is higher than the market rent of $ 600.

The surplus of apartment = 56,000 - 22,000

The surplus of apartment = 34,000

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The purpose of the government to enact rent control is to ensure that tenants are not charged very high rent by apartment owners. Rent control also serves the purpose of fixing a fair rent for apartment owners based on the prevailing conditions.