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Using Mathematics to Learn Economics

Explore the essential mathematical tools and concepts that are fundamental for learning economics. This guide covers key skills such as equilibrium analysis, comparative statics, and optimization methods including Lagrangian multipliers. It delves into different types of functions like demand and supply curves, cost functions, and their applications in decision-making. By mastering these techniques, you will enhance your analytical capabilities and effectively develop strategies for economic problem-solving.

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Using Mathematics to Learn Economics

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  1. Using Mathematics to Learn Economics • Short-hand skills • Equilibrium (static) analysis • Comparative statics analysis • Differentiation • Partial derivatives • Optimization • Use in decision making

  2. Rules of Differential Calculus • Constant rule • Power-function rule • Sum-difference rule • Partial derivatives

  3. Optimization Techniques • Unconstrained optimization • Constrained optimization • Substitution method • Lagrangian multiplier method

  4. Lagrangian Method • Objective functions are often constrained by one or more “constraints” (time, capacity, or money) • Max L = (objective fn) -{constraint = 0} • Min L = (objective fn) +{constraint = 0} • An artificial variable is created for each constraint, traditionally called lambda, .

  5. Example using Lagrangian Function • Minimize Crime in your town • Police, P, costs $15,000 each. • Jail, J, costs $10,000 each. • Budget is $900,000. • Crime function is estimated: C = 5600 - 4PJ

  6. Typical Mathematical Functions • Demand and supply curves • Total revenue functions • Production function • Cost functions • Profit functions

  7. Specific Functional Forms • Linear • Q = a0 + b0X + c0Y; b0 =dQ/dX • Log linear • Log Q = a1 + b1X + c0Y; b1 =%dQ/dX • Double log • Log Q = a2 + b2 logX + c2 logY; b2 = (%dQ)/(%dX) • Power function • Q = a4 + b4X + c4X2; dQ/dX = b4 + 2c4X

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