Question

the following equations: h and the market Lung lespon 4 Suppose that the inverse demand and supply schedules for rental n apartments in the city of Auckland are as given by the following e Demand: P - 2700 -0.120 Supply: P - 300+ 0.120 a. What is the market equilibrium rental price per month and then equilibrium number of apartments demanded and supplied? b. If the local authority can enforce a rent-control law that sets the maximum monthly rent at $900, will there be a surplus or a short Of how many units will this be? And how many units will actually rented each month? c. Suppose that the government decides to implement a policy to keep out the poor. It declares that the minimum rent that can be charged is $1.500 per month. If the government can enforce that price floor will there be a surplus or a shortage? Of how many units will this be? And how many units will actually be rented each month? d. Suppose that the government wishes to decrease the market equilibrium monthly rent to $900 by increasing the supply of housing, Assuming that demand remains unchanged, find the new equilibrium quantity and the new inverse supply curve. 2200 -0,129 P.2-20070, 12

Answer 1

Demand curve is given by

P=2700-0.12Qd

Supply curve is given by

P=-300+0.12Qs

a)

We know that quantity demanded is equal to quantity supplied at equilibrium price. So,

2700-0.12Q=-300+0.12Q

0.24Q=3000

Q=12500 (equilibrium quantity)

P=2700-0.12*12500=$1200 (equilibrium price)

b)

Price ceiling of $900 will be binding as it is below equilibrium price.

Let us calculate the quantity demanded at at price of $900. Set P=$900 in demand function

900=2700-0.12Qd

Qd=1800/0.12 =15000

Let us calculate the quantity supplied at at price of $900. Set P=$900 in supply function

900=-300+0.12Qs

Qs=1200/0.12=10000

We observe that Qd>Qs, it means there is a shortage in the market.

Shortage=Qd-Qs=15000-10000=5000 units

Actually rented out units=Qs=10000

c)

Price floor of $1500 will be binding as it is above equilibrium price.

Let us calculate the quantity demanded at at price of $1500. Set P=$1500 in demand function

1500=2700-0.12Qd

Qd=1200/0.12 =10000

Let us calculate the quantity supplied at at price of $1500. Set P=$1500 in supply function

1500=-300+0.12Qs

Qs=1800/0.12=15000

We observe that Qs>Qd, it means there is a surplus in the market.

Surplus=Qs-Qd=15000-10000=5000 units

Actually rented out units=Qd=10000

d)

We have seen in part b that quantity demanded is 15000 units at a price of $900.

In equilibrium,

Quantity demanded=Quantity supplied=15000

So, quantity supplied will be equal to 15000.

Let the new inverse supply function be

P=A+0.12Qs

So,

900=A+0.12*15000

900=A+1800

A=-900

So, new inverse supply function is given by

P=-900+0.12Qs