Question

This question is related to Government Intervention: (Quotas):  

Consider the following supply and demand curves:

Demand: P=150-3Qd-.5I-Pj

Supply : P=2Qs+.25L

Suppose income, I, is 60, the price of good j, Pj, is 0, and L, the cost of labor, is 120.

1. Using this information, solve for the equilibrium price and quantity.

Suppose now that the government introduces a price floor of 90 when income, I, is 60, the price of good j, Pj, is 0, and L, the cost of labor, is 120.

2. Would this price restriction create a surplus or shortage?

3. Find the quantity of the good demanded, the consumer surplus, and the producer surplus.

4. What percent of the total surplus is lost due to the price floor?

5. Suppose now the cost of labor is increasing, by how much would labor costs have to increase for the price floor to no longer be binding? Briefly describe why it would make sense for the constraint to no-longer be binding.

Answer 1

Demand: P = 150 - 3Q - 0.5I - Pj

I = 60

Pj = 0

Put these values in demand equation,

Demand: P = 150 - 3Q - 30

P = 120 - 3Q ......(1)

Supply: P = 2Q + 0.25L

L = 120

Put value of L in supply equation.

P = 2Q + 30 .......(2)

At equilibrium, demand equals supply:

120 - 3Q = 2Q + 30

Q = 18

Put value of Q in either demand or supply equation which makes P = 66

If price floor of $90 is imposed, demand is 90 units while supply is more than it. It will create surplus of goods.

Consumer surplus before price floor is sum of portion A + B + C whose sum is (1/2) * (18 - 0) * (120 - 66) = 486

Producer surplus before price floor is sum of portion E + D whose sum is (1/2) * ((18 - 0) * (66 - 30) = 324

Total surplus before price floor = 486 + 324 = 810

Consumer surplus after price floor is sum of portion A whose sum is (1/2) * (10 - 0) * (120 - 90) = 150

Producer surplus after price floor is sum of portion of E + B + F whose sum is (1/2) * (10 - 0) * (50 - 30) + (90 - 50) * (10 - 0) = 100 + 400 = 500

Total surplus after price floor = 150 + 500 = 650

Decline in total surplus due to price floor = [(810 - 650) / 810] * 100 = 19.75%

Binding price floor is always set above equilibrium price while non binding price floor is set below equilibrium price. New supply curve is built when L = 280. To make price floor non binding, labor cost greater than 280 would shift supply curve to its left further from new supply.