Economics 300, Mathematica Demonstrations by Topic
Professor Cramton
These Mathematica demonstrations are intended to illustrate a
particular topic in the course. Mathematica 7 (player or the full program) is
required to make use of the demonstrations. If you download the source program,
you will not only be able to use the demonstration, but you will be able to see
the code that makes it work, and modify the code to do other things. You may
want to create your own demonstration of some topic in the course. Please feel
free to do so, and to post your demonstration on the course blog. At the end of
the semester, I will select the demonstration of the year, which I view as the most creative,
useful, and significant demonstration among those posted. The author(s) of the
demonstration of the year will receive
a $200 Amazon.com gift certificate (or fraction thereof in the event of a tie or
multiple authors).
Date
Topic
Jan 27
Ch. 1 – The
Mathematical Framework of Economic Analysis
Jan 29
Ch. 2 – An
Introduction to Functions
Multivariate
functions
Cobb-Douglas production functions
Tinbergen-Solow production function
(a modified version of Cobb-Douglas)
Constant elasticity of substitution
production
An example of a production function
Bubble chart comparisons of countries
Edgeworth box
Gordon-Schaefer model
Properties of
functions
Limits and
continuity
Discontinuity
Uniform continuity
Limit laws
Finite limit at a finite point
Infinite limit at a finite point
Finite limit at infinity
Infinite limit at infinity
Rate of change
Instantaneous rate of change
Average rate of change: exploring more
functions
Instantaneous rate of change: exploring
more functions
Graphing Derivatives
Secant and tangent lines (an
example relating instantaneous and average rate of change)
Useful functions
Cubic equation
Annotated quadratic polynomial
Polynomial graph generator
Continuous exponential growth
Exploration versus consumption (no source code)
Feb 5 Ch. 3 – Exponential Functions
Continuous exponential growth
Rule of 72 (an example of
interest rate)
[To do: Different interest compounding (p5)]
Discounted present value
Net present value
NPV and its contributions
The present value of future gas use
Price-yield curve
Feb 10
Ch. 3 –
Logarithmic Functions
[To do: Different log functions (p18)]
Rules for logarithms
Feb 12
Ch. 4 – Section
1 only - Systems of Equations and Comparative Statics
Basic supply and demand
Supply and demand
Per unit tax (an example of supply and demand)
Shifts in the demand curve
Consumer and producer surplus
Price controls
Hazards of propping up: bubbles and
chaos
Feb 17
Ch. 6 – Basics
of Differential Calculus
Average rate of
change and quotient
Instantaneous rate of change
Average rate of change: exploring more
functions
Instantaneous rate of change: exploring
more functions
Graphing Derivatives
Secant and tangent lines (an
example relating instantaneous and average rate of change)
Polynomials and derivatives
Limits and
continuity
Discontinuity
Uniform continuity
Limit laws
Finite limit at a finite point
Infinite limit at a finite point
Finite limit at infinity
Infinite limit at infinity
Mar 3 Ch. 7 – Univariate Calculus
Derivative as a function
Derivatives of exponential functions
Rules of
differentiation
Product rule
Quotient rule
Chain rule
Second derivatives
Instantaneous rate of change: exploring
more functions with the first and second derivatives
Mar 5 Ch. 7 – Univariate Calculus -
Elasticity
Revenue and elasticity
Elasticity, total revenue, and the linear demand curve
Long-run average total cost
Short-run cost curves
Mar 10
Ch. 8 –
Multivariate Calculus
Partial derivatives
Partial derivatives in 3D
Cobb-Douglas production functions
Implicit functions
Implicit function game
Differential of
multivariate functions
Slope fields
Chain rule
Mar 24
Ch. 9 – Extreme
Values of Univariate Functions
Global extrema on an interval
Maximizing the area of a rectangle with
fixed perimeter
Population selector
Mar 25
Ch. 10 – Extreme
Values of Multivariate Functions
Tangent planes on a 3D graph
Tangent Circles
Tangent planes to quadratic surfaces
Tangent to a surface
Saddle points and inflection points
Apr 9 Ch. 11– Constrained Optimization
Constrained optimization
Demand for insurance
(Lagrangian method)
Envelope theorem: numerical examples
Changes in the budget line
Minimizing the surface area of a
cylinder with a fixed volume
Convergence of minimization methods
Graphical linear programming for two
variables
Income and substitution effects
Optimal bin packing with random lengths
Profit maximization in perfect competition
Apr 21
Probability
Monty hall problem
Venn diagrams
The perfect Venn diagram
Venn diagrams for two sets
Conditional probability
(partly contain independence)
Apr 23
Decision making under Uncertainty
Expected returns of the Dow industrials, beta model
Stock market returns by party
Sample versus theoretical distribution
Sector chart applied to GDP
Purchasing power calculator
Rank plots for countries
Apr 28
Risk Theory
Constant risk aversion utility functions
Premium Ratios With Capital Costs Included
Risk aversion, load, and optimal insurance
Risk premiums
Certainty equivalent wealth
Investment leverage effect
Adverse selection
Moral hazard and least-cost contracts:
impact of changes in agent preferences
Moral hazard and least-cost contracts:
impact of changes in conditional probabilities
Apr 30
Game Theory
Prisoner's dilemma
Stable marriage
Nash equilibria in 3×3 games
Set of Nash equilibria in 2x2 mixed extended games
Nash equilibria with continuous strategies
May 12
Market Games
Merger guidelines
Monopoly profit and loss
Walrasian equilibrium or disequilibrium
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