Question

Suppose the demand schedule in a market can be represented by the equation, QD = 500 - 10P , where QD is the quantity demanded and P is the price. Also, suppose the supply schedule can be represented by the equation Qs = 200 + 10P , where Qs is the quantity supplied.
a. Refer to Scenario 4-1. What is the equilibrium quantity in this market?
b. Refer to Scenario 4-1. Suppose the price is currently equal to 10 in this market. Is there a shortage or sur- plus in this market, and how large is the shortage/surplus?
c. Refer to Scenario 4-1. Suppose the price is currently equal to 18 in this market. Is there a shortage or sur- plus in this market, and how large is the shortage/surplus?
d. Refer to Scenario 4-1. Suppose the supply curve shifts to Qs = 300 + 10P What is the new equilibrium price and quantity in this market?

Answer 1

Answer:

a. The equilibrium quantity is 350 units.

b. There is a shortage of 100 units.

c. There is a surplus of 60 units.

d. The equilibrium price is $10 and equilibrium quantity is 400 units.

Explanation:

The demand schedule is given as QD = 500 - 10P.

The supply schedule is given as Qs = 200 + 10P.

a. At equilibrium the quantity demanded and quantity supplied are equal.

Qd = Qs

500 - 10P =  200 + 10P

20P = 300

P = $15

Putting this value of P in demand equation,

QD = 500 - 10P

QD = $500 - 10\ \times \ 15$

QD = 350

The equilibrium quantity is 350 units.

b. At price $10, the quantity demanded

= $500 - 10\times 10$

= 500 - 100

= 400

At price $10, the quantity supplied

= $200 + 10\times 10$

= 200 + 100

= 300

The quantity demanded is 100 units higher than the quantity supplied, this shows that there is a shortage of 100 units.

c. At price $18, the quantity demanded

= $500 - 10\times 18$

= 500 - 180

= 320

At price $10, the quantity supplied

= $200 + 10\times 18$

= 200 + 180

= 380

The quantity demanded is 60 units lower than quantity supplied, this indicates that there is a surplus of 60 units.

d. The new supply equation is Qs = 300 + 10P.

At equilibrium the quantity demanded and quantity supplied are equal.

Qd = Qs

500 - 10P =  300 + 10P

20P = 200

P = $10

Putting this value of P in demand equation,

QD = 500 - 10P

QD = $500 - 10\ \times \ 10$

QD = 400

The equilibrium quantity is 400 units.