Economic Analysis with Maxima

Edwin (Ted) Woollett


Edwin (Ted) Woollett Maxima by Example Computational Physics with Maxima or R

Economics Software

  1. --Econ1.mac ( Dec. 22, 2022) : Econ1.mac is a text file of Maxima software for Economic Analysis.
    Included are useful functions such as:
    1. Analyze (expr, critPts), in which expr depends on two variables, which do not have to be x and y.
      critPts is either one critical point, such as [x = 2,y = 3] or a list of several critical points of the two variable expression expr. Analyze is designed for unconstrained maxima and minima only. The nature of the given critical point(s) including the values of the three 2nd derivatives which need to be checked are returned.
    2. plotCP (expr, [v1 = v1val, v2 = v2val]) or plotCP (expr, v1, v1val,dv1, v2, v2val, dv2).
      plotCP calls wxdraw3d to make a 3d plot of the surface expr as a function of variables v1 and v2 near the critical point (v1val, v2val). Such a plot has meaning for unconstrained optima.
    3. LPM (amatrix, minorNum) returns the minorNum'th leading principal minor of the square amatrix. minorNum can be 1, 2, 3, ... , length(amatrix).
    4. Bhessian (expr, gList, varList) returns the bordered Hessian matrix, given the Lagrangian expression expr, a list of equality constraints gList, and a list of variables varList.
    5. Msolve (J, X, Z) calls solve for solutions to the matrix equation J . X = Z. The elements of the matrix column vector X contain symbols which stand for the unknowns. J is a square n x n matrix and X and Z are each n dimensional matrix column vectors.
    6. optimum (func, varL, constraints) handles one or more equality constraints with the syntax
      optimum (f,varL) case no equality constraints, calls CPtest
      optimum (f,varL, g) case one equality constraint g = 0, calls BHtest
      optimum (f, var, [g])
      optimum (f, varL, [g1, g2]) where both g1 = 0 and g2 = 0. etc.
      optimum defines a global list cp, screens solutions to only accept solns with real non-negative values of the search variables %vL.
    7. optimumAll(func, varL, constraints) is the same as optimum, but accepts ALL solutions returned by solve even if they are negative or complex.
    Included in the Dec. 22, 2022 update are functions developed for the chapters LPsimplex.wxmx, LPduality.wxmx, and LPmatrix.wxmx such as:
    1. tableau (tRows), which displays the current simplex tableau, given a list of row-lists,
    2. tratio(tRows, ncol), which calculates and displays the ratios needed in the minimum ratio test, given tRows and the column number of the entering variable in the tableau, when using the top z-row method in LPsimplex.wxmx,
    3. bratio(tRows, ncol), which calculates and displays the ratios needed in the minimum ratio test, given tRows and the column number of the entering variable in the tableau, when using the bottom z-row tableau method as used in LPduality.wxmx,
    4. b2ratio(tRows, ncol), which calculates and displays the ratios needed in the minimum ratio test, given tRows and the column number of the entering variable in the tableau, when using the bottom z-row tableau method with artificial variables, splitting the z-row into two z-rows, as used in LPduality.wxmx,
    5. pivot1 (tRows, [nrow, ncol] ), which carries out one simplex step toward an optimal solution, swapping a basic variable with a non-basic variable,
    6. Mtableau(), which displays the current matrix tableau, using the matrix simplex method described in LPsimplex.wxmx,
    7. Mratio(colNum), which displays the ratios needed in the minimum ratio test, given the current matrix tableau and the column number of the entering variable,
    8. Mpivot(n_Enter, n_Leave), which carries out one simplex step, swapping a basic variable with a non-basic variable, and displaying the new matrix tableau,
    9. toMTab (tRows ), which converts the tableau row lists into a matrix tableau display. The 9/28/2022 update of Econ1.mac corrects an error in the function toMTab by requiring a global matrix column vector c is defined before the first call to toMTab. Then z = transpose(c) . X is the objective function to be maximixed.
    10. Mbtableau(), which displays the current tableau by using parts of the current matrices and creating a simple table, resulting in a simpler display of the results of the matrix simplex method described in LPsimplex.wxmx,
    11. Mbpivot(n_Enter, n_Leave), which carries out one simplex step, swapping a basic variable with a non-basic variable, and displaying the new tableau by calling Mbtableau.
    12. DMratio(rowNum), which displays the ratios needed in the minimum absolute ratio test used to select the entering variable in the B/N Dual Simplex Method.
  2. --Econ1.pdf : A pdf translation of the contents of Econ1.mac, 29 pp. Dec. 22, 2022
  3. --KKT.mac : KKT.mac is a text file of Maxima software defining the Maxima function
            KKT (f(x,y),  maxmin,   constraint),
    in which maxmin is either max or min, and constraint is either a single function g(x,y) or two functions g1(x,y), g2(x,y), which implements the Karush-Kuhn-Tucker method of finding either the maximum or minimum subject to the constraint(s).
    In the two constraint case, for example:
       for the max search we need g1 >= 0 and g2 >=0 and for the min search we need g1 <= 0 and g2 <=0.
    Similar conditions are used with our gridSearch function defined in Econ1.mac.
    Both KKT and gridSearch are used in Dowling Ch. 13B. Aug. 5, 2021
  4. --KKT.pdf : A pdf translation of the contents of KKT.mac, 28 pp, Aug. 5, 2021
Introduction to Mathematical Economics, Edward T. Dowling

We use Maxima to solve a few of the problems (and draw some of the plots) in some of the chapters of the supplemental text: Introduction to Mathematical Economics, 3rd ed, (Schaum's Outline Series), by Edward T. Dowling (1992, 2001), McGraw-Hill. This modestly priced text is a bargain with many worked out examples, and is available either in paperback or on Kindle. You should compare the examples worked out "by hand" in this text with what we do using Maxima. We add supplemental commentary and examples gleaned from other sources when it seems appropriate.

Dowling Ch. 2, Economic Applications of Graphs and Equations

Dowling, Chapter 2 Topics

  1. Isocost Lines
  2. Production Possibilities Curves
  3. Supply and Demand Analysis
  4. Income Determination Models
  5. IS-LM Analysis
  6. Using wxdraw2d for Economics Plots
  1. --Dowling02.wxmx : A wxMaxima notebook on Plots and Equations in Economics, April 21, 2022
  2. --Dowling02fit.pdf : An approximate pdf translation of Dowling02fit.wxmx, an edited version created to allow
    "print to pdf" in Windows 10 to capture all the content; not perfect but is searchable using Ctrl-F,
    50 pages, April 21, 2022
    Dowling Ch. 4, Derivatives and Economics

    Dowling, Chapter 4 Topics

    1. Concavity and Convexity
    2. Relative Extrema
    3. Inflection Points
    4. Optimization of Functions
    5. Successive Derivative Test for Optimization
    6. Marginal Concepts
    7. Optimizing Economic Functions
    8. Relations Among Total, Marginal and Average Functions
    1. --Dowling04.wxmx : Dowling Ch. 4 problems solved using Maxima, April 25, 2022
    2. --Dowling04fit.pdf : An approximate pdf translation of Dowling04fit.wxmx, an edited version created to allow "print to pdf" in Windows 10 to capture all the content; not perfect but is searchable using Ctrl-F, 28 pages,
      April 25, 2022
    Dowling Ch. 5, Multivariable Functions in Economics, Part I

    Dowling, Chapter 5 Topics

    1. Optimization with No Constraints
      1. Conditions for a Relative Minimum or Maximum
      2. Conditions for Saddle or Inflection Points
      3. Using jacobian for 1st Derivatives
      4. Using hessian (expr, varList) for 2nd Derivatives
      5. Analyze (expr, critPts), plotCP (expr, critPt)
      6. The Maxima mnewton numerical search method for values of (x,y) such that f(x,y) = 0
    2. Optimization with Equality Constraints
      1. optimum (f, varList, constraints)
      2. Plots of Constraint Plus Curves of Constant Objective Function
      3. Significance of the Lagrange Multiplier
    3. Total and Partial Derivatives
    4. Total Derivatives
    5. Implicit and Inverse Function Rules
    1. --Dowling05.wxmx : Dowling Ch.5 problems solved using Maxima, April 27, 2022
    2. --Dowling05fit.pdf : An approximate pdf translation of Dowling05fit.wxmx, an edited version created to allow "print to pdf" in Windows 10 to capture all the content; not perfect but is searchable using Ctrl-F, 31 pages, April 27, 2022
    3. Dowling05.wxmx uses the software file Econ1.mac available above.
    Dowling Ch. 6, Multivariable Functions in Economics, Part II

    Dowling, Chapter 6 Topics

    1. Marginal Productivity
    2. Income Determination Multipliers, Comparative Statics
    3. Income and Cross Price Elasticities of Demand
    4. Optimizing Economic Functions
    5. Constrained Optimization in Economics
    6. The Concept of Economic Utility
    7. Maximize Utility Subject to a Budget Constraint
    1. --Dowling06.wxmx : Dowling Ch. 6 problems solved using Maxima, May 6, 2022
    2. --Dowling06fit.pdf : An approximate pdf translation of Dowling06fit.wxmx, an edited version created to allow "print to pdf" in Windows 10 to capture all the content; not perfect but is searchable using Ctrl-F, 46 pages,
      May 6, 2022
    3. Dowling06.wxmx uses the software file Econ1.mac available above.
    Dowling Ch. 8, Compounding, Discounting, Interest Rates

    Dowling, Chapter 8 Topics

    1. Basic and Natural Exponential Functions
    2. Exponential Equations
    3. Plot of a Logarithmic Function
    4. Series Expansion of ln(1 + x)
    5. Compounding, Discounting, Interest Rates
    6. Effective vs Nominal Rates of Interest
    7. Discounting, Discount Rate
    8. Converting Basic Exponential to Natural Exponential Functions
    9. Estimating Growth Rates from Data Points
    1. --Dowling08.wxmx : Dowling Ch. 8 problems solved using Maxima, May 10, 2022
    2. --Dowling08fit.pdf : An approximate pdf translation of Dowling08fit.wxmx, an edited version created to allow "print to pdf" in Windows 10 to capture all the content; not perfect but is searchable using Ctrl-F, 26 pages, May 10, 2022
    3. Dowling08.wxmx uses the software file Econ1.mac available above.
    Dowling Ch. 9, Rate of Growth, Optimal Timing, Present Value

    Dowling, Chapter 9 Topics

    1. Economic Problems: Maximization wrt One Variable
    2. Economics Rate of Growth Problems
    3. Optimal Timing Problems - Dowling
    4. Cobb-Douglas Demand Function
    5. Optimal Timing Problems - Chiang & Wainwright
    1. --Dowling09.wxmx : Dowling Ch. 9 problems solved using Maxima, May 19, 2022
    2. --Dowling09fit.pdf : An approximate pdf translation of Dowling09fit.wxmx, an edited version created to allow "print to pdf" in Windows 10 to capture all the content; not perfect but is searchable using Ctrl-F, 31 pages,
      May 19, 2022
    Dowling, Ch.12, Free and Constrained Optimization

    Dowling, Ch.12, Topics

    1. Optimization, PartA (12A)
      1. Rank of a Matrix, Linear Independence
      2. The Minors of a Matrix
      3. Leading Principal Minors of a Matrix
      4. The Jacobian Matrix, Linear Independence
      5. Quadratic Forms and the Discriminant Matrix
      6. Taylor's Theorem and the Hessian Matrix
      7. Unconstrained Optimization
    2. Optimization, Part B (12B)
      1. Optimization with Equality Constraints
      2. Input-Output Analysis for an Open Economy
      3. Eigenvalue Tests for Positive or Negative Definiteness
      4. Binding and Nonbinding Constraints in Economics
    1. --Dowling12A.wxmx : Optimization, Part A, June 13, 2022
    2. --Dowling12Afit.pdf : An approximate pdf translation of Dowling12Afit.wxmx, an edited version created to allow "print to pdf" in Windows 10 to capture all the content; not perfect but is searchable using Ctrl-F, 39 pages, June 13, 2022
    3. --Dowling12B.wxmx : Optimization, Part B, June 13, 2022
    4. --Dowling12Bfit.pdf : An approximate pdf translation of Dowling12Bfit.wxmx, an edited version created to allow "print to pdf" in Windows 10 to capture all the content; not perfect but is searchable using Ctrl-F, 66 pages, June 13, 2022
    Dowling, Ch.13A, Comparative Statics

    Dowling, Ch.13A, Topics

    1. Matrix Methods
    2. Statics with Unconstrained Optimization
    3. Statics with Constrained Optimization
    1. --Dowling13A.wxmx : Symbolic Comparative Statics problems solved using wxMaxima, with an emphasis on matrix methods. July 27, 2021
    2. --Dowling13Afit.pdf : An approximate pdf translation of Dowling13Afit.wxmx, an edited version created to allow "print to pdf" in Windows 10 to capture all the content; not perfect but is searchable using Ctrl-F, 55 pages,
      July 27, 2021
    LPsimplex:
    Optimization with Both Linear Objective and Constraints

    The software file Econ1.mac (see at the top of this page) has been updated to provide Maxima functions used in this chapter. An error in the function toMTab(Rows) has been corrected by requiring the global matix column vector c to be defined before the first call to toMTab. The file LPsimplex.wxmx 11/14/2022 update redefines c as a matrix column vector, so z = transpose(c) . X in the matrix tableau method.

    LPsimplex, Topics

    1. Graphical Methods for 2d LP's
    2. Use of maximize_lp and minimize_lp from Maxima's simplex package
    3. Simplex Method with tableau(Rows) and pivot1(Rows,[row,col])
    4. Matrix Simplex Method with Mdefine(), Mtableau() and Mpivot(Enter, Leave)
    1. --LPsimplex.wxmx : Simplex Optimization for "Linear Programming Problems", Nov. 14, 2022
    2. --LPsimplexfit.pdf : An approximate pdf translation of LPsimplexfit.wxmx, an edited version created to allow "print to pdf" in Windows 10 to capture all the content; not perfect but is searchable using Ctrl-F, 89 pages, Nov. 14, 2022.
    LPduality:
    Dual LP Systems

    The software file Econ1.mac (see at the top of this page) has been updated to provide Maxima functions used in this chapter.

    LPduality, Topics

    1. Tableau "z-row" on Bottom Convention
    2. Symmetric Dual LP Systems
    3. Two Phase Simplex Method
    4. Complementary Slackness Principle
    5. Unsymmetric Dual LP Systems
    6. General Rules for Forming Duals
    1. --LPduality.wxmx : Dual LP Systems, Nov. 14, 2022
    2. --LPduality.pdf : An approximate pdf translation of LPdualityfit.wxmx, an edited version created to allow "print to pdf" in Windows 10 to capture all the content; not perfect but is searchable using Ctrl-F, 74 pages, Nov. 14, 2022.
    LPmatrix:
    Matrix Simplex Methods

    The software file Econ1.mac (see at the top of this page) has been updated to provide Maxima functions used in this chapter.

    LPmatrix, Topics

    1. Functions Mbtableau and Mbpivot "z-row" on Bottom Convention
    2. Artificial Variable LP's using Matrix Big M or Butenko's Matrix Dual Simplex Method
    3. The Bronson/Naadimuthu Dual Simplex Method using Matrix Methods
    4. Use of the Function DMratio(rowNum) with the B/N Dual Simplex Method
    1. --LPmatrix.wxmx : Matrix Simplex Methods, Dec. 22, 2022
    2. --LPmatrixfit.pdf : An approximate pdf translation of LPmatrixfit.wxmx, an edited version created to allow "print to pdf" in Windows 10 to capture all the content; not perfect but is searchable using Ctrl-F, 57 pages, Dec. 22, 2022.
    Dowling, Ch.13B, Optimization with Inequality Constraints

    Dowling, Ch.13B, Topics

    1. Graphical Method
    2. Karush-Kuhn-Tucker (KKT) Method
    3. Grid Search with Constraints Method
    1. --Dowling13B.wxmx : Optimization with Inequality Constraints; problems solved using wxMaxima. For each problem, we start with graphical methods, then apply the KKT method and also the grid search method. July 27, 2021
    2. --Dowling13Bfit.pdf : An approximate pdf translation of Dowling13Bfit.wxmx, an edited version created to allow "print to pdf" in Windows 10 to capture all the content; not perfect but is searchable using Ctrl-F, 28 pages,
      July 27, 2021
    Dowling Ch. 14, Integrals and Economics

    Dowling, Chapter 14 Topics

    1. Investment and Capital Formation
    2. Cost Functions
    3. Total and Marginal Revenue
    4. Consumption Function, Marginal Propensity to Consume
    5. Savings Function, Marginal Propensity to Save
    1. --Dowling14.wxmx : Dowling Ch.14 problems solved using Maxima, Aug. 27, 2021
    2. --Dowling14fit.pdf : An approximate pdf translation of Dowling14fit.wxmx, an edited version created to allow "print to pdf" in Windows 10 to capture all the content; not perfect but is searchable using Ctrl-F, 23 pages,
      Aug. 27, 2021
    Dowling Ch. 15, The Definite Integral and Economics

    Dowling, Chapter 15 Topics

    1. Consumers' and Producers' Surplus
    2. Frequency Functions and Probability
    1. --Dowling15.wxmx : Dowling Ch.15 problems solved using Maxima, Sept. 1, 2021
    2. --Dowling15fit.pdf : An approximate pdf translation of Dowling15fit.wxmx, an edited version created to allow "print to pdf" in Windows 10 to capture all the content; not perfect but is searchable using Ctrl-F, 23 pages,
      Sept. 1, 2021
    Dowling Ch. 16, First Order Ordinary Differential Equations and Economics

    Dowling, Chapter 16 Topics

    1. First Order ODE's: Definitions and Concepts
    2. First Order Linear ODE's
    3. First Order Nonlinear ODE's
    4. Economic Applications
    5. Direction Field Plots
    6. Phase Diagram Analysis of Stability
    1. --Dowling16.wxmx : Dowling Ch.16 problems solved using Maxima, Sept. 14, 2021
    2. --Dowling16fit.pdf : An approximate pdf translation of Dowling16fit.wxmx, an edited version created to allow "print to pdf" in Windows 10 to capture all the content; not perfect but is searchable using Ctrl-F, 29 pages,
      Sept. 14, 2021
      Four jpeg files used with Dowling16.wxmx to show plotdf use, Sept. 14, 2021.
    3. --pdf01.jpg
    4. --pdf02.jpg
    5. --pdf03.jpg
    6. --pdf04.jpg
    Dowling Ch. 17, First Order Difference Equations and Economics

    The Dec. 13, 2021 update to Dowling Ch. 17 uses the draw2d function points(xL,yL) instead of fix(t) with the explicit function. The Nov. 5, 2021 update to Dowling Ch. 17 corrects some errors in Dowling17.wxmx and clarifies the reasoning in some sections. This version makes use of Econ2.mac for the function DE1.

    Dowling, Chapter 17 Topics

    1. First Order Difference Equations: Definitions and Concepts
    2. General Solution
    3. Stability with Graphics Illustrations
    4. Lagged Income Determination Model
    5. The Cobweb Model
    6. The Harrod Model
    7. Other Economic Applications
    8. Phase Diagram Analysis of Stability
    1. --Dowling17.wxmx : Dowling Ch.17 problems solved using Maxima, Dec. 13, 2021
    2. --Dowling17fit.pdf : An approximate pdf translation of Dowling17fit.wxmx, an edited version created to allow "print to pdf" in Windows 10 to capture all the content; not perfect but is searchable using Ctrl-F, 43 pages,
      Dec. 13, 2021
    3. --Econ2.mac : Maxima code for function DE1, with syntax DE1(a,b,t,y0), or DE1(a,b,t) which returns y[t] as determined by the linear first order difference equation y[t] = b*y[t-1] + a, for t = 0,1,2,..., and other Maxima functions, April 7, 2022
    4. --Econ2.pdf : A pdf translation of Econ2.mac, 12 pages, April 7, 2022
    Dowling Ch. 18A, Second Order Ordinary Differential Equations and Economics

    Dowling, Chapter 18A Topics

    1. Fast Track ode2 Method
    2. Numerical Initial Value Problems
    3. General Solutions for 2nd Order ODE's
    4. Market Model with Price Expectations
    5. ODE's with a Variable term
    6. Higher Order ODE's using desolve
    1. --Dowling18A.wxmx : Dowling Ch.18 problems solved using Maxima, Oct. 27, 2021
    2. --Dowling18Afit.pdf : An approximate pdf translation of Dowling18Afit.wxmx, an edited version created to allow "print to pdf" in Windows 10 to capture all the content; not perfect but is searchable using Ctrl-F, 35 pages,
      Oct. 27, 2021
    3. --Econ2.mac : Maxima code for Maxima function Lode2, with syntax Lode2(y,t,type,A,B,C), where type = real, complex, or double, and other Maxima functions, April 7, 2022
    4. --Econ2.pdf : A pdf translation of Econ2.mac, 12 pages, April 7, 2022
    Dowling Ch. 18B, Second Order Difference Equations and Economics

    Dowling, Chapter 18B Topics

    1. Second Order Difference Equations
    2. Stability of Solutions
    3. Using Maxima's solve.rec for Recurrence Relation Equations
    4. Multiplier-Accelerator Model of National Income
      a = acceleration coefficient, b = propensity to consume (MPC)
      1. Distinct Real Roots
      2. Double Real Roots
      3. Complex Roots
      4. Summary Plot of (a,b) Plane Solution Regions
    5. Samuelson's Economic Instability Example
    1. --Dowling18B.wxmx : Dowling Ch.18 problems dealing with second order difference equations solved using Maxima, Dec. 9, 2021
    2. --Dowling18Bfit.pdf : An approximate pdf translation of Dowling18Bfit.wxmx, an edited version created to allow "print to pdf" in Windows 10 to capture all the content; not perfect but is searchable using Ctrl-F, 55 pages,
      Dec. 9, 2021
    3. --Econ2.mac : Maxima code for functions ytlist(b1,b2,a,y[0],y[1],tmax), MAlist (a,b,IaG0,Y[0],Y[1],tmax), makeLists(LL), and other Maxima functions, April 7, 2022
    4. --Econ2.pdf : A pdf translation of Econ2.mac, 12 pages, April 7, 2022
    Dowling Ch. 18C, Inflation and Unemployment Models in Both Continuous and Discrete Time

    Dowling, Chapter 18C Topics

    1. Inflation and Unemployment Models in Continuous Time
      1. Time Path of the Expected Inflation Rate
      2. The Phillips Curve in Context
      3. Chaotic Inflation-Unemployment Relation Example
    2. 2nd Order Linear Ordinary Differential Equations with a Variable Term
    3. Higher Order (> 2nd) ODE's Solution using Dsolve
    4. Review of Second Order Linear Difference Equations
    5. Inflation & Unemployment Models in Discrete Time
      1. The Time Path of the Inflation Rate p[t]
      2. The Time Path of the Unemployment Rate U[t]
    6. 2nd Order Linear Difference Equation with a Variable Term
    7. Higher Order (> 2nd) Linear Difference Equations
    1. --Dowling18C.wxmx : Models of Inflation and Unemployment in Both Continuous and Discrete time, Jan. 25, 2022
    2. --Dowling18Cfit.pdf : An approximate pdf translation of Dowling18Cfit.wxmx, an edited version created to allow "print to pdf" in Windows 10 to capture all the content; not perfect but is searchable using Ctrl-F, 63 pages,
      Jan. 25, 2022
    3. --Econ2.mac : Maxima code for functions ytlist(b1,b2,a,y[0],y[1],tmax), and other Maxima functions, April 7, 2022
    4. --Econ2.pdf : A pdf translation of Econ2.mac, 12 pages, April 7, 2022
    Dowling Ch. 19A, Solutions of Sets of First Order Ordinary Differential Equations

    Dowling, Chapter 19A Topics

    1. Solution Methods Using desolve
    2. Solution Methods Using Runge-Kutta Method rk
    3. Solution Methods Using Matrix Methods
      1. Review of Maxima Matrix Functions
      2. Solving the Matrix Equation dY/dt = A . Y(t) + B
      3. Using the ODE1S (A, B, Y0) Matrix Method for Set of First Order ODE's
      4. Using matrixexp (A, t) . Y0
    4. Stability and Phase Diagram Analysis of Set of Two First Order ODE's
    5. Inflation and Unemployment Model as a Set of ODE's
    6. Proof of Convergence of the Inflation-Unemployment Model
    1. --Dowling19A.wxmx : Solutions of Sets of First Order Ordinary Differential Equations, Feb. 25, 2022
    2. --Dowling19Afit.pdf : An approximate pdf translation of Dowling19Afit.wxmx, an edited version created to allow "print to pdf" in Windows 10 to capture all the content; not perfect but is searchable using Ctrl-F, 47 pages,
      Feb. 25, 2022
    3. --Econ2.mac : Maxima code for functions ODE1S(A,B,Y0) and ODE2S(A1,A2,B,Y0) and other Maxima functions, April 7, 2022
    4. --Econ2.pdf : A pdf translation of Econ2.mac, 12 pages, April 7, 2022
    Dowling Ch. 19B, Solutions of Sets of First Order Difference Equations

    Dowling, Chapter 19B Topics

    1. Matrix Solution of Y[t] = A . Y[t-1] + B
      1. Using Ytlist (A, B, Y0, tmax)
      2. Using DE1S (A, B, t, Y0)
    2. Matrix Solution of A1 . Y[t] = A2 . Y[t-1] + B
      1. Using Ytlist (D, E, Y0, tmax)
      2. Using DE2S (A1, A2, B, t, Y0)
    3. Inflation and Unemployment, First Order Difference Eqn. Set Model
    1. --Dowling19B.wxmx : Solutions of Sets of First Order Difference Equations, Mar. 9, 2022
    2. --Dowling19Bfit.pdf : An approximate pdf translation of Dowling19Bfit.wxmx, an edited version created to allow "print to pdf" in Windows 10 to capture all the content; not perfect but is searchable using Ctrl-F, 32 pages,
      Mar. 9, 2022
    3. --Econ2.mac : Maxima code for functions Ytlist (A,B,Y0,tmax) and DE2S(A1,A2,B,t,Y0) and other Maxima functions, April 7, 2022
    4. --Econ2.pdf : A pdf translation of Econ2.mac, 12 pages, April 7, 2022
    Dowling Ch. 20, Dynamic Optimization

    Dowling, Chapter 20 Topics

    1. Calculus of Variations and Euler's Equations
    2. Sufficient Conditions for an Optimizing Solution
    3. Numerical Examples
    4. Symbolic Economic Applications
    5. Constrained Optimization
    1. --Dowling20.wxmx : Dynamic Optimization, April 7, 2022
    2. --Dowling20fit.pdf : An approximate pdf translation of Dowling20fit.wxmx, an edited version created to allow "print to pdf" in Windows 10 to capture all the content; not perfect but is searchable using Ctrl-F, 29 pages,
      April 7, 2022
    3. --Econ2.mac : Maxima code for functions Extremal (F(t,x,xp)) and NumSuffCond(F(t,x,xp)), NumDynamic (F(t,x,xp)) and other Maxima functions, April 7, 2022
    4. --Econ2.pdf : A pdf translation of Econ2.mac, 12 pages, April 7, 2022
    Dowling Ch. 21, Optimal Control Theory

    Dowling, Chapter 21 Topics

    1. Necessary Conditions for a Maximum with Fixed Endpoint Conditions
    2. Sufficient Conditions for a Maximum
    3. Necessary Conditions for a Maximum with x(T) = Free and Unrestricted
    4. Necessary Conditions for a Maximum with x(T) >= xmin
    5. The Current-Valued Hamiltonian Hc
    1. --Dowling21.wxmx : Optimal Control Theory, April 7, 2022
    2. --Dowling21fit.pdf : An approximate pdf translation of Dowling21fit.wxmx, an edited version created to allow "print to pdf" in Windows 10 to capture all the content; not perfect but is searchable using Ctrl-F, 43 pages, April 7, 2022
    3. --Econ2.mac : Maxima code for functions ConcaveTest (f,x,y) and Zindef_float(A,B) and other Maxima functions, April 7, 2022
    4. --Econ2.pdf : A pdf translation of Econ2.mac, 12 pages, April 7, 2022
    Microeconomic Theory & Computation, M.R. Hammock & J.W. Mixon

    We use Maxima to expand on the topics and treatment of the text: Microeconomic Theory and Computation:
    Applying the Maxima Open-Source Computer Algebra System, by Michael R. Hammock and J. Wilson Mixon,
    Springer, 2013.

    Chapter 2, Simple Models

    Hammock & Mixon, Chapter 2 Topics

    1. Preface
    2. References
    3. Numerical Extras
    4. Production Possibilities
    5. Competitive Markets
    6. Elasticities
    7. Taxes and Efficiency

    1. --Hammock-Mixon02.wxmx : Hammock and Mixon's Ch. 2 discussed using Maxima, Feb. 17, 2021
    2. --Hammock-Mixon02TOC.pdf : Table of contents: Hammock-Mixon02.wxmx, 4 pages, Feb. 22, 2021
    3. --Hammock-Mixon02fit.pdf : An approximate pdf translation of Hammock-Mixon02fit.wxmx, an edited version created to allow "print to pdf" in Windows 10 to capture most of the content; not perfect but is searchable
      using Ctrl-F, 96 pages, Mar. 11, 2021
    Examples of Using wxdraw2d

    1. --wxdraw2d.wxmx : Many examples of using wxdraw2d for graphics. Feb 17, 2021
    2. --wxdraw2d_examples.pdf : An approximate pdf translation of wxdraw2d.wxmx, 33 pages, Feb 22, 2021
    Introduction to Maxima for Economics, by Josef Leydold & Martin Petry

    Introduction to Maxima for Economics (pdf)