Question

Suppose the inverse market demand equation is P = 95 – 10Q and the inverse market supply equation is P = 5 + 5Q. A price floor of $85 will result in:

a. a shortage of 10 units.

b. a shortage of 15 units.

c. a surplus of 10 units.

d. a surplus of 15 units.

e. None of the above.

Answer 1

Answer :

Market demand equation is :

P = 95 - 10Q

Market supply :

P = 5 + 5Q

At market equilibrium, supply equals demand, thus :

95 - 10Q = 5 + 5Q

95 - 5 = 5Q + 10Q = 15Q

15Q = 90 ; Q = 90/15 = 6 is the equilibrium quantity.

Putting this value at any of the demand or supply equation will give us the equilibrium price :

Supply say : P = 5 + 5Q = 5 + 5*6 = 35

So when there's a price floor is set at $85 (which is above the equilibrium price that means a binding constraint),this means the minimum price to be charged has to be $85.

When P = $85

Supply equation : P = 5 + 5Q

85 = 5 + 5Q

5Q = 80 ; Q = 80/5 = 16 is the quantity supplied at a price of $85

Demand equation : P = 95 - 10Q

85 = 95 - 10Q

10Q = 95 - 85 = 10

Q = 10/10 = 1 is the quantity demanded at a price of $85.

Thus quantity supplied > quantity demanded which means a surplus of = 16 - 1 = 15 units

Answer : Option d) a surplus of 15 units