Microeconomics: Profit Maximization and Competitive Supply

Course Information and Course Introduction

• Course: Microeconomics Spring 2026

• Instructor: Masahito Watanabe (渡辺雅仁)

• Institution: Tokyo International University, Department of Economics

• Date: June 8, 2026

• Session: Day 16 (of 26)

Today’s Outline

• Quick Recap from Last Time: Brief review of previous materials.

• The Cost of Production (Chapter 7): Continuation or recap of production costs.

• Profit Maximization and Competitive Supply (Chapter 8):

  • Marginal Revenue, Marginal Cost, and Profit Maximization.

  • Decision criteria for when a firm should shut down.

  • The short-run supply curve for a competitive firm.

  • Long-run competitive equilibrium.

Profit Maximization and Competitive Supply (Chapter 8)

The Firm’s Problem

• Cost Minimization: Involves the choice of inputs, specifically Capital ($K$) and Labor ($L$), for a given level of output.

• Profit Maximization: Involves the choice of the output level ($q$).

Perfectly Competitive Market (Benchmark Characteristics)

1. Many Buyers and Sellers: This results in each participant being a price taker, meaning they cannot influence the market price individually.

2. Product Homogeneity: The products offered by different firms are identical or nearly identical.

3. Free Entry and Exit: There are no significant barriers to entering or leaving the industry.

4. Perfect Information: All market participants have full knowledge of prices, technologies, and market conditions.

Fundamental Profit Maximization Principles

Profit-Maximizing Output Decision

• Profit Definition: Profit ($\pi$) is the difference between Total Revenue ($R$) and Total Cost ($C$).

  • $\pi(q) = R(q) - C(q)$

• Optimal Choice: A firm chooses output $q^*$ such that profit, representing the difference $AB$ between revenue curve $R$ and cost curve $C$, is maximized.

• Marginal Analysis: At the profit-maximizing output level, the slope of the revenue curve (Marginal Revenue, $MR$) is equal to the slope of the cost curve (Marginal Cost, $MC$).

The Condition for Profit Maximization

• Mathematical Derivation:

  • $\frac{\Delta \pi}{\Delta q} = \frac{\Delta R}{\Delta q} - \frac{\Delta C}{\Delta q} = 0$

  • $\frac{\Delta R}{\Delta q}$ is defined as Marginal Revenue ($MR$).

  • $\frac{\Delta C}{\Delta q}$ is defined as Marginal Cost ($MC$).

• Universal Condition: $MR(q) = MC(q)$. This condition applies to all firms, whether they are in a competitive market or not.

Profit Maximization for a Competitive Firm

• Price Taker Status: In a competitive market, the price ($P$) is given to the firm.

• Revenue Formulation:

  • Total Revenue ($R$) = $P \times q$

  • Marginal Revenue ($MR$) = $\frac{\Delta R}{\Delta q} = P$

  • Average Revenue ($AR$) = $\frac{R}{q} = P$

• Profit Function for Competitive Firm:

  • $\pi(q) = R(q) - C(q) = P \times q - C(q)$

• Competitive Specific Condition:

  • Profit maximization occurs where $MR(q) = MC(q)$.

  • Because $MR = P$ in competition, the condition becomes $P = MC(q)$.

Exercise from Last Year’s Final Exam

Scenario Setup

Consider a perfectly competitive market with the following equations:

• Demand: $Q_D = 1500 - 10P$

• Supply: $Q_S = 300 + 10P$

• Where $Q_D$ is quantity demanded, $Q_S$ is quantity supplied, and $P$ is price.

Firm A Cost Structure:

• Average Cost: $AC = 5q + \frac{180}{q}$

• Marginal Cost: $MC = 10q$

• Where $q$ is the quantity produced by Firm A.

Exercise Questions and Solutions

(1) Find the equilibrium price and quantity?

• Solution: At equilibrium, $Q_D = Q_S$.

  • $1500 - 10P = 300 + 10P$

  • $1200 = 20P$

  • $P^* = 60$

  • $Q^* = Q_D(60) = 1500 - 10 \times 60 = 900$

• Result: Equilibrium price $P^* = 60$; Equilibrium quantity $Q^* = 900$.

(2) What is the total cost of Firm A? (Express TC in terms of q)

• Solution: Since $AC = \frac{TC}{q}$, then $TC = AC \times q$.

  • $TC = (5q + \frac{180}{q}) \times q = 5q^2 + 180$

• Result: $TC = 5q^2 + 180$.

(3) What are the variable cost VC and fixed cost FC of this firm?

• Solution: $TC = VC + FC$.

  • Variable part (dependent on $q$): $VC = 5q^2$

  • Fixed part (constant): $FC = 180$

(4) What is the profit-maximizing quantity produced by Firm A?

• Solution: Using the competitive condition $P = MC$.

  • From part (1), $P = 60$.

  • Given $MC = 10q$.

  • $60 = 10q \rightarrow q^* = 6$.

• Result: $q^* = 6$.

(5) How much is the profit for Firm A when it is maximizing profit?

• Solution: $\pi = TR - TC$

  • $TR = P^* \times q^* = 60 \times 6 = 360$

  • $TC = 5(6^2) + 180 = 5(36) + 180 = 180 + 180 = 360$

  • $\pi = 360 - 360 = 0$

• Result: Profit is zero ($\pi = 0$).

(6) Suppose all firms have the same cost structure. How many firms are in the market?

• Solution: Total market quantity divided by individual firm quantity.

  • $n = \frac{Q^*}{q^*} = \frac{900}{6} = 150$

• Result: There are 150 firms participating in the market.

The Decision to Shut Down

Incurring Losses

• If a firm's fixed cost is too high, it may incur a loss (negative profit).

• Condition for loss: P < AC.

• In this state, $\pi = TR - TC = P \times q - AC \times q$, which is represented graphically by the area differences (ABCD < 0).

The Shutdown Condition

• The Question: Should the firm shut down and leave the industry when profit is negative?

• Profit Analysis: \pi = TR - TC = P \times q - VC(q) - FC < 0.

• If the firm shuts down (q = 0): The profit becomes $\pi = -FC$.

• Stay Open Logic: As long as P \times q > VC(q), producing a positive output (q > 0) allows the firm to increase its total profit (or reduce its loss) by covering a portion of the Fixed Costs.

• Threshold: P \times q > VC \rightarrow P > \frac{VC}{q} = AVC.

• Shutdown Rule: A competitive firm should shut down if the market price is below the Average Variable Cost ($AVC$).

  • Condition for Shutting Down: P < AVC.

The Short-run Supply Curve

• Definition: The competitive firm's short-run supply curve is the portion of its Marginal Cost ($MC$) curve that lies above the Average Variable Cost ($AVC$) curve.

Long-Run Competitive Equilibrium

Free Entry and Exit Dynamics

• Entry: A firm enters the industry when it can earn a positive long-run profit.

• Exit: A firm exits the industry when it faces the prospect of a long-run loss.

Characteristics of Long-Run Competitive Equilibrium

1. Profit Maximization: All firms in the industry are maximizing profit ($P = MC$).

2. No Incentive to Move: No firm has an incentive to enter or exit because all firms are earning zero economic profit.

3. Market Clearance: The market price is established such that the quantity supplied by the industry exactly equals the quantity demanded by consumers.