Using Mathematics to Learn Economics

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