Determining the Monopolist's Price

Context

• Competitive Price: Equal to marginal cost, which is $50.
• Objective: Determine how much more a monopolist would charge compared to the competitive price.

Profit Maximizing Rule

• Rule: Marginal Revenue (MR) = Marginal Cost (MC)
• Given: MC = $50

Problem Breakdown

1. Marginal Revenue (MR) Equation:

   • Original given as complex expression: 1000/4 - 2/4 Q = 50
   • Simplified version: 250 - 1/2 Q = 50

2. Solving MR = MC:

   • Subtract 50 and add 1/2 Q from both sides:
     • 200 = 1/2 Q
     • Solve for Q: Q = 400

3. Determine Quantity

   • Monopolist produces 400 units.

Determine Monopolist's Price

• Use Demand to Find Price:
  • Demand equation: 400 = 1000 - 4P
  • Solve for P:
    • Rearrange: 4P = 600
    • Calculate P: P = 150

Monopolist's Price and Markup

• Price Charged: $150
• Markup Calculation:
  • Monopolist Price: $150
  • Subtract Marginal Cost: $50
  • Markup: $100

Summary

• Monopolist produces 400 units at a price of $150.
• The markup over marginal cost is $100.