The demand curve for a monopolist is Qd = 500 - P and the marginal revenue function is MR = 500 - 2P. The monopoloist 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?
Ansers
To find the monopolist's profit-maximizing output and price, we need to follow a few steps:
Step 1: Determine the monopolist's marginal cost (MC) function. Since the monopolist has a constant marginal and average total cost of $50 per unit, we can conclude that MC = $50.
Step 2: Set the marginal revenue (MR) equal to the marginal cost (MC) to find the profit-maximizing quantity. In this case, MR = MC:
500 - 2P = 50
Solving this equation for P, we get:
2P = 500 - 50
2P = 450
P = 225
Step 3: Substitute the price (P) back into the demand curve equation to find the corresponding quantity demanded:
Qd = 500 - P
Qd = 500 - 225
Qd = 275
Therefore, the monopolist's profit-maximizing output is 275 units, and the price is $225.
To calculate the monopolist's profit, we need to calculate total revenue (TR) and total cost (TC):
Total Revenue (TR) = Price (P) × Quantity (Q)
TR = $225 × 275
TR = $61,875
Total Cost (TC) = Cost per unit (MC) × Quantity (Q)
TC = $50 × 275
TC = $13,750
Profit (π) = Total Revenue (TR) - Total Cost (TC)
π = $61,875 - $13,750
π = $48,125
Therefore, the monopolist's profit is $48,125.
The Lerner Index measures the pricing power or the extent of market power that a firm has. It can be calculated using the formula:
Lerner Index = (P - MC) / P
In this case, we know MC = $50 and P = $225 (as determined in part a). Plugging these values into the formula, we get:
Lerner Index = ($225 - $50) / $225
Lerner Index = $175 / $225
Lerner Index = 0.778 or 77.8%
Therefore, the Lerner Index for this industry is 77.8%.