The demand curve for a monopolist is Qd = 500 - P and the marginal revenue function is MR = 500 - 2P. The monoploist 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?
The demand curve for a monopolist is Qd = 500 - P and the marginal revenue function is MR = 500 - 2P. The monoploist 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?
To find the monopolist's profit maximizing output and price, we'll need to determine the point at which marginal revenue (MR) equals marginal cost (MC).
Given:
Demand curve: Qd = 500 - P
Marginal Revenue function: MR = 500 - 2P
Marginal cost (MC) = $50
a. Profit maximizing output and price:
To find the profit-maximizing output and price, we need to equate the marginal revenue (MR) and marginal cost (MC):
MR = MC
Given that MR = 500 - 2P and MC = $50, we can set up the equation:
500 - 2P = 50
Solving for P:
500 - 2P = 50
-2P = 50 - 500
-2P = -450
P = (-450) / (-2)
P = 225
Now, substitute the found price (P = 225) into the demand equation Qd = 500 - P to find the output level (Q):
Qd = 500 - P
Qd = 500 - 225
Qd = 275
Therefore, the profit maximizing output is 275 units, and the price is $225 per unit.
b. Monopolist's profit:
To calculate the monopolist's profit, we need to subtract the total cost (TC) from the total revenue (TR).
Total Revenue (TR) is given by:
TR = Q * P
Substituting the values we found earlier, TR = 275 * 225 = $61,875.
Total Cost (TC) is given by:
TC = MC * Q
Substituting the given MC ($50) and Q (275), TC = 50 * 275 = $13,750.
Therefore, the monopolist's profit can be calculated as:
Profit = TR - TC
Profit = $61,875 - $13,750
Profit = $48,125
c. Lerner Index:
The Lerner Index measures market power and is calculated as follows:
Lerner Index = (P - MC) / P
Using the given MC ($50) and the previously found price (P = $225), we can compute the Lerner Index:
Lerner Index = ($225 - $50) / $225
Lerner Index = $175 / $225
Lerner Index ≈ 0.78
The Lerner Index for this industry is approximately 0.78, indicating a relatively high level of market power.