3.2 Profit maximization and the competitive firm's supply curve

Profit maximization is key for competitive firms. They produce where price equals marginal cost, following the upward-sloping part of their marginal cost curve. This rule helps firms decide how much to make in both short and long run.

A firm's supply curve comes from its marginal cost curve. In the short run, it's the part above average variable costs. Long-term, it's above long-run average costs. Understanding this helps explain how firms and industries respond to price changes.

Profit Maximization for Competitive Firms

Profit Maximization Rule

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• Profit maximization rule dictates producing at output level where marginal revenue (MR) equals marginal cost (MC)
• In perfectly competitive markets, price equals marginal revenue for all units sold (firms are price takers)
• Profit-maximizing condition expressed as $P = MR = MC$, where P represents market price
• Firms should increase production when $MR > MC$ and decrease when $MR < MC$ to maximize profits
• Second-order condition for profit maximization requires MC curve slope to exceed MR curve slope at intersection point
• Rule applies to both short-run and long-run decision-making for competitive firms (wheat farmers, small retail stores)

Profit Maximization Analysis

• Analyze firm's cost structure including fixed costs (rent, equipment) and variable costs (labor, raw materials)
• Determine market price for the product (set by market forces in competitive markets)
• Calculate marginal revenue which equals market price in perfect competition
• Compute marginal cost at different output levels
• Identify output level where $MR = MC$ on the upward-sloping portion of MC curve
• Verify second-order condition satisfied ensuring profit maximum rather than minimum

Supply Curve Derivation for Competitive Firms

Short-Run Supply Curve

• Competitive firm's supply curve derived from portion of marginal cost curve above average variable cost (AVC) curve
• Shutdown point occurs where marginal cost curve intersects AVC curve at its minimum point
• Firm's supply curve starts at shutdown point and follows upward-sloping portion of marginal cost curve
• Zero output produced at prices below shutdown point in short run
• Supply curve elasticity depends on marginal cost curve shape (steeper MC curve leads to less elastic supply)
• Short-run supply decisions influenced by fixed costs (factory rent) and variable costs (labor, materials)

Long-Run Supply Curve

• Long-run supply curve derived from portion of long-run marginal cost (LRMC) curve above long-run average cost (LRAC) curve
• Entry and exit of firms affects long-run industry supply
• Perfectly elastic long-run supply curve in constant-cost industries (identical cost structures for all firms)
• Upward-sloping long-run supply curve in increasing-cost industries (resource scarcity or differences in firm efficiencies)
• Downward-sloping long-run supply curve in decreasing-cost industries (economies of scale at industry level)
• Long-run adjustments include changes in plant size, technology adoption, and resource allocation

Price, Marginal Revenue, and Marginal Cost

Relationships in Competitive Markets

• Price remains constant and equal to marginal revenue for all units sold in perfectly competitive markets
• Marginal cost curve typically U-shaped due to law of diminishing marginal returns
• Firm's optimal output level occurs where horizontal price line intersects upward-sloping portion of marginal cost curve
• Market price changes lead to movements along firm's marginal cost curve affecting optimal output level
• Area between price line and marginal cost curve represents firm's producer surplus
• Price elasticity of supply determined by relationship between price changes and quantity supplied changes along marginal cost curve

Graphical Analysis

• Plot price as horizontal line on graph (perfectly elastic demand for individual firm)
• Draw U-shaped marginal cost curve
• Identify intersection point of price line and marginal cost curve
• Shade area between price line and marginal cost curve to visualize producer surplus
• Illustrate how price changes shift optimal output level along marginal cost curve
• Demonstrate supply curve derivation by tracing firm's responses to different price levels

Short-Run Profit Maximization for Competitive Firms

Determining Optimal Output

• Identify profit-maximizing output level where $P = MC$ on upward-sloping portion of marginal cost curve
• Ensure chosen output level satisfies shutdown condition by being above average variable cost curve
• Calculate total revenue (TR) by multiplying market price by quantity produced at optimal output level
• Compute total cost (TC) by adding fixed costs to area under marginal cost curve up to optimal output level
• Determine firm's economic profit or loss by subtracting total cost from total revenue ($π = TR - TC$)
• Compare profit-maximizing output level to break-even point ($P = ATC$) and shutdown point to assess firm's short-run operating decision

Profit Analysis and Decision Making

• Evaluate different scenarios based on market price levels (high profit, normal profit, loss-minimizing, shutdown)
• Calculate profit or loss at various output levels to verify profit maximization
• Analyze impact of cost changes (input prices, technology) on profit-maximizing output and overall profitability
• Consider short-run alternatives like temporarily suspending production if price falls below average variable cost
• Assess implications of operating at a loss in short run (covering variable costs but not all fixed costs)
• Explore strategies for improving profitability (cost reduction, efficiency improvements, product differentiation)