Question

An economist estimates that market demand for apartment in Boulder is Qd = 100 – 5P, with quantity measured in thousands of apartments, and price, the average monthly rental rate, measured in hundreds of dollars. The city’s board of realtors has shown that supply is Qs = 50 + 5P. What is the market price and quantity in terms of apartments in Boulder? Explain what will happen in this market if the city council forces average monthly rental rate to equal $100 (Note: since P, price, is measured in hundreds of dollars, then $100 is P=1).

Answer 1

At equilibrium Qd = Qs

100 - 5P = 50 + 5P

100 - 50 = 5P + 5P

50 = 10 P

P = 50/10

P = 5.

Since P, price is measured in hundred of dollar the P = 5 is $500.

And, Qd = Qs= Q . (At equilibrium)

Q = 100 - 5P

Q = 100 - 5(5)

Q= 75.

Since Q, quantity is measured in thousands, then Q=75 is 75000)

Hence equilibrium quantity is 75000 and equilibrium price is 500.

If monthly rental rate is $100 or P=1.

Qd = 100 -5P

Qd = 100 - 5(1)

Qd = 95

And, Qs= 50+5P

Qs= 50 + 5(1)

Qs= 55.

At P= $1, Qd is 95 and Qs is 55

Since quantity demanded is in excess of quantity supply, it means there is excess demand or shortage of supply in the market.