Question

2. Assume that Q_D = 800 - 4P and Q_S = -100 +P. If the government imposes the price floor P=190, what is the deadweight loss of the economy?

        a.    $1,350

        b.    $937.50

        c.     $1,012.50

        d.    $1,000

        e.    $562.50

3. Assume that Q_D = 800 - 4P and Q_S = -100 +P. If the government imposes the price ceiling P=190, what is the consumer surplus?

a.   $225                   

b.   $675

c.    $800

d.   $1350

e.   Not enough information to determine consumer surplus.

Answer 1

(2) (d)

In free market equilibrium, QD = QS

800 - 4P = - 100 + P

5P = 900

P = 180

Q = - 100 + 180 = 80

When floor price = 190,

QD = 800 - (4 x 190) = 800 - 760 = 40

QS = - 100 + 190 = 90

Since consumers can buy only what producers will sell, market quantity = 40. When Q = 40,

From demand function: 40 = 800 - 4P, or 4P = 760, or P = 190

From supply function: 40 = - 100 + P, or P = 140

Deadweight loss = (1/2) x (80 - 40) x (190 - 140) = (1/2) x 40 x 50 = 1,000

(3) (c)

Free market price = 180 and quantity = 80 (Derived in Q2)

A ceiling price, to be binding, must be imposed lower than free market price. Since in this case ceiling price is 190, it is not binding and the free market equilibrium price and quantity will prevail.

From demand function, when QD = 0, P = 800/4 = 200 (Reservation price)

Consumer surplus = Area between demand curve & market price = (1/2) x (200 - 180) x 80 = 40 x 20 = 800