. Suppose the demand curve for a monopolist is QD =500 - P, and the marginal revenue function is MR =500 – 2Q. The monopolist has a constant marginal and average total cost of $50 per unit.
a. Find the monopolist’s profit – maximizing output and price.
b. Calculate the monopolist’s profit.
c. What is the Lerner Index for this industry?
a 5
b. 70
c. q= p-4
a.3
b.85
c.q=p-4
To find the monopolist's profit-maximizing output and price, we need to first determine the monopolist's marginal cost. Given that the monopolist has a constant marginal and average total cost of $50 per unit, we can conclude that its marginal cost (MC) is also $50 per unit.
a. To find the monopolist's profit-maximizing output, we need to equate the marginal cost (MC) to the marginal revenue (MR) and solve for Q:
MC = MR
$50 = 500 - 2Q
Solving the above equation for Q:
2Q = 500 - $50
2Q = $450
Q = $450 / 2
Q = 225
Therefore, the monopolist's profit-maximizing output is 225 units.
b. To calculate the monopolist's profit, we need to subtract the total cost from the total revenue. The total revenue (TR) can be calculated by multiplying the price (P) with the quantity (Q):
TR = P * Q
TR = P * 225
The price (P) can be found by substituting the quantity (Q) into the demand curve equation:
QD = 500 - P
225 = 500 - P
Solving the above equation for P:
P = 500 - 225
P = $275
Therefore, the monopolist's profit-maximizing price is $275.
Now we can calculate the total revenue (TR) and total cost (TC) to find the monopolist's profit:
TR = P * Q = $275 * 225 = $61,875
TC = AC * Q = $50 * 225 = $11,250
Profit = TR - TC = $61,875 - $11,250 = $50,625
Therefore, the monopolist's profit is $50,625.
c. The Lerner Index is a measure of market power and monopoly pricing. It is calculated as the difference between the price (P) and the marginal cost (MC), divided by the price (P):
Lerner Index = (P - MC) / P
Using the values we already have:
Lerner Index = ($275 - $50) / $275
Lerner Index = $225 / $275
Lerner Index ≈ 0.8182
Therefore, the Lerner Index for this industry is approximately 0.8182. This indicates that the monopolist has a relatively high degree of market power and can set prices significantly above marginal cost.