The demand for apartments is P = 1, 200 Q while the supply isP = Q units. The government imposes rent control at P =$300/month. Suppose demand grows in the market toP = 1, 400 Q. (LO7)a How is excess demand a↵ected by the growth in demand forapartments?b At what price would the government have to set the rentcontrol to keep excess demand at the same level as prior tothe growth in demand?TO BE DONE AT HOME
Question
The demand for apartments is P = 1, 200 � Q while the supply isP = Q units. The government imposes rent control at P =$300/month. Suppose demand grows in the market toP = 1, 400 � Q. (LO7)a How is excess demand a↵ected by the growth in demand forapartments?b At what price would the government have to set the rentcontrol to keep excess demand at the same level as prior tothe growth in demand?TO BE DONE AT HOME
Solution
Sure, let's break down the problem step by step.
a) How is excess demand affected by the growth in demand for apartments?
Excess demand is the difference between the quantity demanded and the quantity supplied at a given price. Initially, the demand and supply equations are P = 1,200 - Q and P = Q respectively. When the government imposes a rent control at P = $300/month, we can substitute P in both equations to find the quantities demanded and supplied.
For the demand equation: 300 = 1,200 - Qd (Qd stands for quantity demanded) Solving for Qd gives us Qd = 1,200 - 300 = 900 units
For the supply equation: 300 = Qs (Qs stands for quantity supplied) So, Qs = 300 units
The initial excess demand is therefore Qd - Qs = 900 - 300 = 600 units
Now, suppose demand grows to P = 1,400 - Q. We substitute P = 300 into the new demand equation to find the new quantity demanded.
300 = 1,400 - Qd' Solving for Qd' gives us Qd' = 1,400 - 300 = 1,100 units
The new excess demand is therefore Qd' - Qs = 1,100 - 300 = 800 units
So, the growth in demand for apartments increases the excess demand by 800 - 600 = 200 units.
b) At what price would the government have to set the rent control to keep excess demand at the same level as prior to the growth in demand?
To keep the excess demand at the same level as before (600 units), we need to find a new price P' such that the quantity demanded under the new demand equation equals the quantity supplied plus 600 units.
Setting up the equation gives us P' = 1,400 - (Qs + 600) Substituting Qs = P' into the equation gives us P' = 1,400 - (P' + 600) Solving for P' gives us P' = $500/month
So, the government would have to set the rent control at $500/month to keep the excess demand at the same level as prior to the growth in demand.
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