1. Suppose that the inverse demand curve facing a monopoly is given by: P = 500 - 10Q. The monopoly production costs are given by: C(Q) = 10Q2 + 100Q.

a. Find perfectly competitive (PC) equilibrium price and quantity.

b. Find monopoly equilibrium price and quantity.

c. Compare the perfectly competitive solution with the monopoly solution

d. Derive the Lerner Index

e. Derive the consumer surplus (CS) and producer surplus (PS). Also derive the deadweight loss.

2. A monopolist firm faces a demand with constant elasticity of -2.0. It has a constant marginal cost of $20 per unit and sets a price to maximize profit. If marginal cost should increase by 25%, would the price charged also rise by 25%? (PRM, Ch. 10)

3. A firm faces the following average revenue (demand) curve:

P = 120 - 0.02Q

where Q is weekly production and P is price, measured in cents per unit. The firm's cost function is given by

C = 60Q + 25,000

Assume that the firm maximizes profits.

a. What is the level of production, price, and total profit per week?

b. If the government decides to levy a tax of Rs. 14 per unit on this product, what will be the new level of production, price, and profit? (PRM, Ch. 10)

4. Suppose the market for widgets can be described by the following equations:

Demand: P = 10 - Q Supply: P = Q + 4

where P is the price in dollars per unit and Q is the quantity in thousands of units. Then:

a. What is the equilibrium price and quantity?

b. Suppose the government imposes a tax of $1 per unit to reduce widget consumption and raise government revenues. What will the new equilibrium quantity be? What price will the buyer pay? What amount per unit will the seller receive?

c. Suppose the government has a change of heart about the importance of widgets to the happiness of the American public. The tax is removed and a subsidy of

$1 per unit granted to widget producers. What will the equilibrium quantity be? What price will the buyer pay? What amount per unit (including the subsidy) will the seller receive? What will be the total cost to the government? (PRM, Ch.9)