Profit Maximization in Perfect Competition

Definition of Profit

• Profit (π) is defined as:
  • Total Revenue (TR) minus Total Cost (TC)
  • π = TR - TC

Deriving Conditions for Profit Maximization

1. Take the Derivative
   • To maximize profit, take the derivative of profit with respect to quantity (q) and set it equal to zero.
   • This leads to:
     • dπ/dq = d(TR)/dq - d(TC)/dq = 0
2. Marginal Revenue (MR) and Marginal Cost (MC)
   • The derivative of total revenue with respect to quantity is the marginal revenue (MR).
   • The derivative of total cost with respect to quantity is the marginal cost (MC).
   • Thus, the condition for profit maximization is:
     • MR = MC

Perfect Competition Characteristics

• In perfect competition, a firm is a price taker:
  • Marginal revenue (MR) is equal to the price (P).
• Therefore, the profit-maximizing condition becomes:
  • P = MR = MC

Visual Representation

• Market Diagram:

  • Illustrates market demand and supply curves.
  • Price (P*) determined at the intersection of demand and supply.
  • Quantity (Q*) traded in the market.

• Firm Diagram:

  • Represents the marginal cost curve for a representative firm.
  • The firm sets its price (P*) equal to its marginal cost (MC) to find the optimal production quantity (q*).

Optimal Production Quantity (q*)

• If a firm produces a quantity less than q* (e.g., q1):
  • Marginal Revenue > Marginal Cost → It should increase production.
• If a firm produces a quantity greater than q* (e.g., q2):
  • Marginal Cost > Marginal Revenue → It should decrease production.
• Therefore, the only optimum production quantity is q*.

Caveats to Profit Maximization

1. Short Run:
   • Price (P) must be greater than or equal to Average Variable Costs (AVC).
   • If P < AVC, the firm will shut down (produce zero).
2. Long Run:
   • Price (P) must be greater than or equal to Average Total Costs (ATC).
   • If P < ATC, the firm will exit the industry.

Conclusion

• Set price equal to marginal cost for profit maximization, but ensure the caveats (AVC and ATC conditions) are satisfied.
• Further resources available for deeper understanding and practice problems.