Lecture 3 (Pingle): Macroeconomics, Functions, Differentiation and Comparative Statics
Monday, August 20, 10Am-Noon
Functions and Notation
 A function is a rule
 General functional forms versus specific functional forms
 Imposing restrictions on general functional forms to capture economic behaviors
 Multivariable functions
Differentiation
 The derivative as a measure of responsiveness
 Rules of Differentiation
o Constant rule
o Power rule
o Constant coefficient rule
o Sum rule
o Product rule
o Natural log rule
o Chain rule
 Partial differentiation
 Implicit differentiation
 Differentials
 Total differential and total derivative
 Differentiating some functions used more regularly in economics (Cobb-Douglas, natural log,
exponential)
Comparative static analysis
 Modeling an economic system using a system of equations
o Exogenous variable versus endogenous variable
 Comparative static analysis
o Finding comparative static multipliers when the system cannot be solved
o Interpreting comparative static multipliers
Some Other Useful Skills
 Using the natural log and differentiation to find an elasticity and to convert a model that is “in the
levels” to a model that is “in the growth rates.”
 Using the natural log to linerize a nonlinear relations (For exponential functions and power
functions)
 Understanding the relationship between the number e, the exponential function, the natural log
function, constant growth, and constant elasticity.
Handouts
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Handout- Some Notes on Functions and Notation
Handout-Differentiation
Handout-Comparative Static Analysis
Lecture 3 (Pingle): Differential Equations
Wednesday, August 22, 3:00PM - 5:00PM
1. A dynamic system
a. Differential Equation
b. Classifying variables of a dynamic model
c. A solution
2. Steady State
a. Finding the steady state
b. Comparative static analysis
3. Stability
a. Phase diagram
b. Stability condition for one variable model
4. Two state variable model
a. Using a phase diagram to characterize the dynamics of the system