A monopolist faces the demand curve P=11-Q and the cost function is C=6Q a) Draw the demand and...
Question:
A monopolist faces the demand curve P = 11 - Q and the cost function is Cm = 6Q.
a) What are the monopolist's profit maximizing price and quantity, and what is the resulting profit? Calculate the degree of monopoly power using the Lerner index.
b) What price would be charged and what output level would be produced by a perfectly competitive industry? Relative to part a, what are the changes in consumer surplus, producer surplus, and welfare?
Lerner Index:
As a monopoly is the sole producer in a market, it has the power to set the prices of its product(s). The Lerner index, developed by economist Abba Lerner, is a measure of a firm's market. It's calculated as the difference between the price a firm charges and the marginal cost, divided by the price the firm charges.
Answer and Explanation: 1
a) The monopolist will produce 2.5 units at a price of $8.50 and have an earnings profit of $6.25. The Lerner index is 0.29.
The total revenue for the monopoly is Q(11 - Q), and the marginal revenue is 11 - 2Q.
The marginal cost is constant at $6.
The monopoly maximizes its profits when the marginal revenue equals the marginal cost, i.e., 11 - 2Q = 6, which yields Q = 2.5, P = 8.5.
So the monopoly's profit can be calculated as follows:
2.5 * 8.5 - 6 * 2.5 = $6.25.
The Lerner index is: (8.5 - 6) / 8.5 = 0.29.
The consumer surplus is: 2.5(11 - 8.5) / 2 = $3.125.
The producer surplus is: 2.5(8.5 - 6) / 2 = $3.125.
So the total surplus is: 3.125 + 3.125 = $6.25.
b) In a competitive market, firms produce until the marginal cost is equal to the price, i.e., 6 = 11 - Q, which yields Q = 5 and P = $6.
In this case, the consumer surplus is: 5(11 - 6) / 2 = $7.50.
The producer surplus is: (6 - 6) * 5 / 2 = $0.
So the total surplus is $7.50.
Relative to the monopolist's equilibrium:
- The consumer surplus increases by 7.5 - 3.125 = $4.375.
- The producer surplus decreases by $3.125.
- The total surplus increases by (7.5 - 6.25) = $1.25.
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