Lecture 4: Perfect Competition and Market Analysis of Competitive Markets

Profit Maximization and the Competitive Firm

• Firms are assumed to maximize profit ($\pi$), which is defined as the difference between total revenue ($R$) and total cost ($C$).
• The basic formula for profit is: $\pi(q) = R(q) - C(q)$.
• At the profit-maximizing level of output ($q^*$), the difference between revenue and costs is at its greatest point.
• Marginal Revenue (MR) is defined as the additional revenue generated from producing one more unit of output. It is represented by the slope of the revenue curve: $MR = \frac{dR}{dq}$.
• Marginal Cost (MC) is defined as the additional cost incurred from producing one more unit of output. It is represented by the slope of the cost curve: $MC = \frac{dC}{dq}$.

Short-Run Profit Maximization Conditions

• A firm evaluates its output levels based on the relationship between MR and MC:
  • If $MR > MC$, the firm should increase output to increase total profit.
  • If $MR < MC$, the firm should decrease output to increase total profit.
  • Profit is maximized where $MR = MC$. This occurs when the slope of the revenue curve is identical to the slope of the cost curve.
• Mathematically, profit maximization occurs when: $\frac{d\pi}{dq} = \frac{dR}{dq} - \frac{dC}{dq} = 0$. This implies $MR(q) - MC(q) = 0$, or $MR(q) = MC(q)$.

Characteristics of Perfect Competition

• The model of perfect competition rests on three primary characteristics:
  1. Price Taking: Each individual firm represents such a small portion of the market that it cannot influence the market price. The firm accepts the market price as given.
  2. Product Homogeneity: All firms in the market produce identical or nearly identical products. These products are perfect substitutes for one another.
  3. Free Entry and Exit: There are no significant costs or limitations preventing a firm from entering or leaving the industry. This ensures that resources can flow freely toward their most productive use.
• For a competitive firm, the demand curve is horizontal at the market price ($P$). This means the firm can sell any amount of output at that price. Consequently:
  • $P(q) = P$
  • Revenue is a linear function: $R(q) = P \times q$
  • Marginal Revenue equals the price: $MR(q) = P$
  • Average Revenue equals the price: $AR(q) = P$

The Competitive Marginal Cost Pricing Rule

• Under perfect competition, the rule for maximizing profit is to set output where Marginal Cost equals the Market Price: $MC(q) = P$.
• Graphical Analysis of Profit:
  • Profit is represented by the area of a rectangle: $\pi = (P - ATC) \times q$.
  • If the price is above the Average Total Cost ($P > ATC$), the firm earns a positive economic profit.
  • If the price equals the Average Total Cost ($P = ATC$), the firm earns zero economic profit (normal profit).
  • Lost profit occurs if output is set at $q_1 < q^*$ or $q_2 > q^*$ because the firm misses opportunities where $MR = MC$.

Short-Run Production and the Shut-Down Decision

• The firm's supply curve in the short run is the portion of the Marginal Cost ($MC$) curve that lies above the minimum Average Variable Cost ($AVC$).
• Production at a Profit: If $P > ATC$, the firm continues to produce and earns a profit for all prices above the minimum of the Average Total Cost curve.
• Production at a Loss: If $AVC < P < ATC$, the firm should continue to produce in the short run despite being at an economic loss. By producing, the firm generates enough revenue to cover all variable costs and a portion of its fixed costs. Shutting down would result in a loss equal to the total fixed costs ($FC$), whereas producing results in a smaller loss.
• Shut-Down Decision: If $P < AVC$, the firm is not even earning enough to cover its variable costs. It minimizes losses by producing nothing ($q = 0$), thus losing only its fixed costs. The "shut-down point" is the minimum point on the $AVC$ curve.
• In the long run, if $P < ATC$, the firm should exit the market entirely.

From Individual to Market Supply

• The short-run market supply curve ($S$) is the horizontal sum of the individual supply curves of all firms in the industry.
• As the price increases, each firm increases its quantity supplied according to its individual marginal cost curve, leading to an upward-sloping market supply curve.

Producer Surplus in the Short Run

• Individual Firm Producer Surplus (PS):
  • Defined as the sum of the differences between the market price and the marginal cost for every unit produced ($P - MC$).
  • It is the area below the market price and above the Marginal Cost curve.
  • Alternatively: $PS = R - VC$, where $VC$ is total variable costs.
  • Note the difference between Profit ($\pi$) and Producer Surplus: $\pi = R - VC - FC$, therefore $PS = \pi + FC$ or $\pi = PS - FC$.
• Market Producer Surplus: The total market producer surplus is the area between the market supply curve and the equilibrium market price from output 0 to $Q^*$.

Long-Run Competitive Equilibrium

• In the long run, firms can change all inputs, including plant size, and firms can enter or exit the market.
• Entry and Exit Mechanics: If firms in the industry earn positive economic profits ($P > LAC$), new firms will enter. This increases market supply ($S_1 \rightarrow S_2$), which drives down the market price. The process continues until economic profit is zero ($P = LAC$).
• Conditions for Long-Run Equilibrium:
  1. All firms maximize profit ($LMC = P$).
  2. All firms earn zero economic profit ($LAC = P$), meaning there is no incentive to enter or exit.
  3. The market clears: quantity supplied equals quantity demanded at the equilibrium price.
• Zero Economic Profit Interpretation: This does not mean accounting profit is zero. It means the firm's owners are earning a return on their investment that is exactly equal to what they could earn elsewhere (opportunity cost is covered).

Long-Run Market Supply Curves

• The shape of the long-run market supply curve ($S_L$) depends on how input prices change as industry output expands:
  1. Constant-Cost Industry: Input prices remain unchanged as the industry expands. The long-run supply curve is a horizontal line at a price equal to the minimum Average Cost ($LAC$).
  2. Increasing-Cost Industry: Increased demand for inputs causes their prices to rise as the industry expands. This shifts the individual cost curves upward, resulting in an upward-sloping long-run supply curve.
  3. Decreasing-Cost Industry: Industry expansion leads to lower input prices (e.g., via economies of scale in the production of components). This results in a downward-sloping long-run supply curve.

Market Efficiency and Surplus

• Total Surplus: The sum of Consumer Surplus (CS) and Producer Surplus (PS). It measures the total welfare benefit of the market.
• Efficiency: A perfectly competitive market is efficient because it maximizes total surplus at the equilibrium price ($P_0, Q_0$). Total welfare is maximized when the market is left to reach its equilibrium without intervention.
• Deadweight Loss (DWL): The net loss of total surplus caused by market regulations or interventions. It represents lost opportunities for mutually beneficial trades.

Market Interventions and Welfare Effects

• Price Controls:
  • Maximal Price (Price Ceiling): Regulated price $P_{max} < P_0$. Supply drops to $Q_1$. Consumers lose area B, producers lose areas A and C. Net welfare loss (DWL) is $B + C$. Example: Rent control in Amsterdam leads to housing shortages.
  • Minimal Price (Price Floor): Regulated price $P_{min} > P_0$. Demand drops to $Q_3$. If firms produce the excess supply $Q_2 - Q_3$, DWL can be as large as $B + C + D$.
• Price Supports: The government sets a price $P_s > P_0$ and buys the excess supply ($Q_g = Q_2 - Q_1$). Producers gain surplus ($A+B+D$), but the cost to the government is $P_s \times (Q_2 - Q_1)$. Example: US wheat support leads to produce dumping overseas.
• Import Quotas and Tariffs:
  • In a free market with world price $P_w$, domestic consumers enjoy high quantities.
  • Import Prohibition: Price rises to domestic equilibrium $P_0$. Consumers lose surplus, and DWL is $B + C$.
  • Tariff ($T$): A tax on imports. Government gains revenue (area D). Net domestic loss is $-B - C$.
  • Quota: A limit on quantity. Compared to a tariff, the revenue (area D) often goes to foreign producers rather than the domestic government. Net domestic loss is $-B - C - D$.
• Taxes and Subsidies:
  • Specific Tax ($t$): Buyers pay $P_b$ and sellers receive $P_s$, where $P_b - P_s = t$. Traded quantity falls to $Q_1$. Government collects revenue ($A + D$). DWL is $B + C$. Taxes are though to facilitate social efficiency (e.g., funding public services or curbing pollution).
  • Specific Subsidy ($s$): The government covers part of the price ($P_s - P_b = s$). Traded quantity rises to $Q_1$. While buyers and sellers gain, the government loses significantly more. DWL arises from excessive, inefficient trades. Example: EU agricultural subsidies hurt overseas producers and increase production costs.