strategy
NAME_______________________________________________________________
FE461 Professor Schmitt
First Problem Set
Due 31 January 2012
1. (20 points) Suppose Tyco International has complete control over the plastic hangar market. Suppose the inverse demand for hangars is given by: . Suppose that the total costs is given by:
a) What is the equilibrium price and quantity of hangars in the market if the market is competitive?
To find the competitive quantity we set price equal to marginal cost and solve for Q:
We obtain price by substituting the competitive quantity in the inverse demand function.
Or we could simply note that with P = MC, price must be equal to 1, and then substitute this in the inverse demand equation and solve for Q.
b) What is the equilibrium price and quantity of hangars if the market is monopolized?
With an inverse demand of , marginal revenue is given by (same intercept, twice as steeply sloped recall this comes from the demand being linear and TR = P*Q =and .
Setting this equal to marginal cost will yield the monopoly value of Q.
=1=MC Q = 16,000. Solving for price we obtain.
c) What is the deadweight or welfare loss of the monopoly in this market?
The competitive industry has no profits and so producer surplus is zero. Consumer surplus is given by the triangle that starts at 1, proceeds over to C, and then angles up to . The base is 32,000, the height is 2, and the area is ½(32,000)(2) = 32,000.
With a monopoly, consumer surplus is given by the triangle that starts at 2, proceeds over to A, and then angles up to 3. The base is 6,000, the height is 1, and the area is ½(16,000)(1) = 8,000. Profits or producer surplus for the monopolist are given by the rectangle beginning at 1, proceeding over to B, up to A and then back over to 2. This rectangle has dimensions 16,000x1 = 16,000. So total surplus with monopoly is 24,000. The loss from monopoly is then 32,000 - 24,000 or 8,000. One can also compute the area
FE461 Professor Schmitt
First Problem Set
Due 31 January 2012
1. (20 points) Suppose Tyco International has complete control over the plastic hangar market. Suppose the inverse demand for hangars is given by: . Suppose that the total costs is given by:
a) What is the equilibrium price and quantity of hangars in the market if the market is competitive?
To find the competitive quantity we set price equal to marginal cost and solve for Q:
We obtain price by substituting the competitive quantity in the inverse demand function.
Or we could simply note that with P = MC, price must be equal to 1, and then substitute this in the inverse demand equation and solve for Q.
b) What is the equilibrium price and quantity of hangars if the market is monopolized?
With an inverse demand of , marginal revenue is given by (same intercept, twice as steeply sloped recall this comes from the demand being linear and TR = P*Q =and .
Setting this equal to marginal cost will yield the monopoly value of Q.
=1=MC Q = 16,000. Solving for price we obtain.
c) What is the deadweight or welfare loss of the monopoly in this market?
The competitive industry has no profits and so producer surplus is zero. Consumer surplus is given by the triangle that starts at 1, proceeds over to C, and then angles up to . The base is 32,000, the height is 2, and the area is ½(32,000)(2) = 32,000.
With a monopoly, consumer surplus is given by the triangle that starts at 2, proceeds over to A, and then angles up to 3. The base is 6,000, the height is 1, and the area is ½(16,000)(1) = 8,000. Profits or producer surplus for the monopolist are given by the rectangle beginning at 1, proceeding over to B, up to A and then back over to 2. This rectangle has dimensions 16,000x1 = 16,000. So total surplus with monopoly is 24,000. The loss from monopoly is then 32,000 - 24,000 or 8,000. One can also compute the area