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Profit Maximization

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Average and Marginal Cost Curves: Shapes and RelationshipsShort-Run Costs+7 more→→Capital Accumulation and the Golden RuleCompetitive Firm Output Decision and Supply+12 more
profit maximization MR=MC economic profit marginal revenue

Core Idea

A profit-maximizing firm produces the quantity where marginal revenue (MR) equals marginal cost (MC), provided price exceeds average variable cost. Profit equals total revenue minus total cost; economic profit differs from accounting profit by subtracting implicit (opportunity) costs. MR = MC is the universal profit-maximization condition across all market structures, though MR differs by structure: for a price-taker, MR = P; for a monopolist, MR < P. The second-order condition requires MC to be rising at the optimum.

How It's Best Learned

First demonstrate MR = MC numerically using a table of revenues and costs, then graphically, then using calculus. Compare economic and accounting profit explicitly using a numerical example with implicit costs.

Common Misconceptions

Explainer

Profit is total revenue minus total cost — but maximizing it is not as simple as making revenue as large as possible or cost as small as possible. The key insight is marginal analysis: at any given output level, ask whether producing one more unit would add more to revenue or more to cost. If the answer is revenue (MR > MC), produce more. If the answer is cost (MC > MR), produce less. At the quantity where MR = MC, no further adjustment improves profit — you have found the optimum.

This MR = MC rule applies universally across all market structures, but what marginal revenue looks like varies. For a perfectly competitive firm that takes the market price as given, every unit sells at the same price P, so MR = P. For a monopolist who must lower price to sell more, MR < P because the price cut applies to all previous units. Despite this difference, the logic of comparing marginal revenue to marginal cost remains identical.

A critical distinction that trips up many students is economic profit versus accounting profit. Accounting profit subtracts only explicit costs — wages paid, inputs purchased, rent written on an invoice. Economic profit also subtracts implicit costs: the value of what the owner's time, capital, and resources could have earned in their best alternative use. A bakery owner who earns $80,000 revenue, pays $60,000 in explicit costs, but could have earned $30,000 working for someone else has an accounting profit of $20,000 but an economic profit of −$10,000. The business is actually destroying value relative to the alternative.

This is why zero economic profit is not a crisis. It means the firm is earning exactly the competitive return — all resources, including the owner's opportunity cost, are being fully compensated. In a competitive market, zero long-run economic profit is the normal equilibrium outcome. Firms enter when economic profit is positive (attracting competition) and exit when it is negative (resources leave for better uses). The market settles at zero economic profit, which is efficient, not dismal.

One technical condition often glossed over: the second-order condition. The MR = MC intersection identifies a profit maximum only if MC is rising at that point (or equivalently, if the profit function is concave there). If MC is falling, you may be at a profit minimum instead. For most standard cost curves with the typical U-shaped average cost structure, this condition holds at the relevant output levels, but it is worth verifying when working with unusual cost functions.

Practice Questions 3 questions

Prerequisite Chain

Understanding Zero → The Number Zero → Counting to Five → Counting to 10 → Counting to 20 → Counting a Set of Objects Up to 20 → Cardinality: The Last Number Counted → Matching Numerals to Quantities → Subitizing Small Quantities → Addition Within 10 → Number Bonds to 10 → Addition Within 20 → Doubles and Near Doubles → Doubles Facts Within 10 → Near Doubles Facts Within 20 → Mental Math Strategies for Addition → Mental Math: Adding and Subtracting Tens → Addition Within 100 → Repeated Addition as Multiplication → Multiplication as Equal Groups → Multiplication: Arrays → Basic Multiplication Facts (0s, 1s, 2s, 5s, 10s) → Multiplication Facts Within 100 → Division as Equal Sharing → Division as Grouping (Measurement Division) → Division: Grouping (Repeated Subtraction) Model → Division: Fair Sharing Model → Division as Equal Sharing → Division as Grouping → Basic Division Facts → Division Facts Within 100 → Multiplication and Division Fact Families → Relationship Between Multiplication and Division → Division Facts as Inverse of Multiplication → Remainders and Quotients in Division → Division Word Problems → Multi-Step Word Problems → Solving Multi-Step Word Problems → Multiplication Word Problems → Division Word Problems → Introduction to Long Division → Factors and Multiples → Prime and Composite Numbers → Equivalent Fractions → Relating Fractions and Decimals → Decimal Place Value → Integers and the Number Line → Comparing and Ordering Integers → Absolute Value → Adding Integers → Subtracting Integers → Multiplying Integers → Dividing Integers → Unit Rates → Proportions → Percent Concept → Converting Between Fractions, Decimals, and Percents → Operations with Rational Numbers → Two-Step Equations → Solving Multi-Step Equations → Equations with Variables on Both Sides → Literal Equations → Slope-Intercept Form → Point-Slope Form → Writing Linear Equations → Parallel and Perpendicular Line Slopes → Graphing Linear Equations → Piecewise Functions → One-Sided Limits → Continuity Definition → Limits and Continuity in Multiple Variables → Functions of Several Variables → Continuity in Multiple Variables → Partial Derivatives: Definition and Computation → Differentiability in Multiple Variables → Differentiability in Multivariable Functions → Total Differential and Linear Approximation → Chain Rule for Multivariable Functions → Implicit Differentiation → Related Rates → Optimization Problems → Critical Points of Multivariable Functions → Critical Points and Classification of Extrema → Second Partial Test for Local Extrema (Hessian) → The Hessian Matrix and Second Derivative Test → Unconstrained Optimization: Finding Extrema → Optimization in Multiple Variables → Lagrange Multipliers → Constrained Optimization and Lagrange Multipliers → Utility and Preferences → Marginal Utility and Diminishing Returns → Profit Maximization

Longest path: 92 steps · 459 total prerequisite topics

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