Question

Suppose that lobbyists for the whey protein industry are successful in getting the government to enact a minimum price law for protein. The demand equation for whey protein is ?? = 4000 − 300?, and the supply equation is ?? = −1000 + 200?, where ? is the number of containers sold per minute, and ? is the price per container.

7.1. Find the equilibrium price and quantity of protein before the minimum price law.

7.2. Draw a picture illustrating this equilibrium. Label axes, curves, and intercepts.

7.3. Suppose that the minimum price law stipulates a price floor of $12 per container of protein. How many containers will actually be sold in this market? After you calculate it, label it on your picture above.

7.4. Identify in your picture the deadweight loss associated with the price floor. Then in the space below, calculate the deadweight loss.

7.5. After the law was enacted, some whey protein producers grumbled that they were made worse off by this law that was supposed to help them. Explain in words why this may be true.

Answer 1

(7.1)

Setting QD = QS,

4000 - 300P = - 1000 + 200P

500P = 5000

P = 10

Q = - 1000 + 200 x 10 = - 1000 + 2000 = 1000

(7.2)

When QD = 0, P = 4000/300 = 13.33 (Vertical intercept) & when P = 0, QD = 4000 (Horizontal intercept).

When QS = 0, P = 1000/200 = 5 (Vertical intercept)

Equilibrium is at point E with price P0 and quantity Q0.

(7.3)

When P = 12,

QD = 4000 - 300 x 12 = 4000 - 3600 = 400

QS = - 1000 + 200 x 12 = - 1000 + 2400 = 1400

Since firms can sell only what consumers will buy, market quantity traded is QD = 400.

(7.4)

When Q = 400,

From supply function: P = (1000 + Q)/200 = (1000 + 400)/200 = 1400/200 = 7 (Supply price)

Deadweight loss = Area EFG = (1/2) x (Floor price - Supply price) x Difference in quantity

= (1/2) x (12 - 7) x (1000 - 400)

= (1/2) x 5 x 600

= $1500

(7.5)

At higher floor price, some producers were unable to sell their goods which caused a surplus (= QS - QD = 1400 - 400 = 1000), so they were made worse off.