MATH REVIEW:
Some Tools for E
Economic Analysis
i A l i
Functions, Derivatives & Optimization Procedures
But First, the Context
Role of Math in Econ
• An Integral Part of Economics
– A Means to an End?
– An End Unto Itself?
• Math as:
– An Analytic Framework
– A Tool
– A Way to:
• Structure Complex Situations
• Organize Information
• Examine/Evaluate/Predict Economic Behavior
Basic Premise in Economics:
• Purposeful Behavior
– Logic or Pattern to Actions
– Discover, Model, & Use Info
• Standard Economic Assumption: p
“Optimizing”
– MAXIMIZING BEHAVIOR
• Households: Maximize Utility or Satisfaction
• Firms: Maximize Profits; (Wealth; NPV)
– MINIMIZING BEHAVIOR
• Minimize Costs
• Minimize Defects?
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Justifications for Maximizing Assumption
• Simple & Intuitive
• Aids in Model Building
– Optimization Techniques
• Useful Approximation…”as if...”
• Powerful and Flexible
– Easily Extended – Can Introduce Complications
Baseline Firm Objective:
• "Maximize” Something
• Simplest Case: Current Period Profits
• Alternatives/Extensions
– Long Run Profits – Shareholder Wealth/Value Shareholder Wealth/Value
• NPV of Multi‐Period Profit Stream
• Max Subject to Constraints
– Unit or Dollar Sales Revenue
• While Acknowledging Potential Problems:
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Hard to Specify Exact “Objective Function”
Constraints: Legal, Social, Environmental, Behavioral
Often Don't Know/Understand Constraints
Often Difficult to Quantify Constraints
Principles for Decision Making
• Marginal and Incremental Analysis:
– Examine Impact of Small Changes
– "Decisions Made at the Margin" (or should be)
• Difference Tied to Magnitude of Change
– “Marginal”  Small Change  Derivative
– Incremental Bigger Change (Same Principle)
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Decision Making as an
“Optimization Problem”
• Optimizing Means Max or Min – Maximizing
– Minimizing 
MARG BEN = MARG COST
• We Need to Consider the Basic Mechanics:
– The Set Up & Solve Process
– Framework for Analysis of Critical Issues
– (Can Soften/Adapt Prior to Implementation) Wrap Up:
• Economics Assumes Purposeful Behavior
• Economic Behavior Modeled Using Math Tools
• Optimization Techniques (Max/Min)
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• Fundamental Principle:
– “Decision Making at the Margin”
– Marginal Benefits = Marginal Cost 3