Abstract
The open-source software system Maxima can compute and manipulate data symbolically, numerically, and graphically. Systems like Maxima are called Computer Algebra Systems. Maxima’s capabilities can greatly aid the study of economics. Its symbolic abilities can reduce the amount of tedious algebra that can be required to solve problems. Also, its use reduces the chance of computational errors. More importantly, Maxima’s numeric and graphical abilities help analysts go further into a given problem and extract insights and interpretations that might otherwise be missed. This chapter introduces the salient aspects of Maxima as it applies to microeconomic analysis.
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Notes
- 1.
Maxima can also be run in the Android environment but (at the time that this material was written) without full graphical capabilities.
- 2.
Centered dots indicate multiplication. Later in the book, variable names will contain a series of letters, like mpl to denote marginal product of labor. With our notation m ⋅ p ⋅ l would denote a product of three variables, m, p, and l, while mpl is a variable.
- 3.
Some earlier versions use the F6 key to enter a text cell.
- 4.
Maxima will return a complex number if instructed to extract the logarithm of a negative floating-point number.
Here is the output for log(−44. 0): 3.1416*%i+3.7842.
- 5.
Reducing floating-point print precision does not reduce the precision with which Maxima stores the variable’s value in its memory. The printing precision level can be returned to the default value (16) with fpprintprec:0.
- 6.
This aspect of the output can lead to confusion, because Maxima responds in the same way if the input is gibberish. For example, arctan(%pi/2) would yield the output arctan(π∕2), but arctan is not a meaningful command, so Maxima just reports the input without trying to evaluate it.
- 7.
The option draw_realpart=false does not keep implicit from drawing the real part of a complex expression.
- 8.
It incorporates material from [1].
- 9.
As before, the matrix command is used to generate a table. Removing this command and ending each command with a semicolon would generate three output lines.
- 10.
Entering expop = 3 or any higher value would give the same result.
- 11.
Maxima offers fairly sophisticated programming capabilities.
- 12.
You can remove this temporarily with comment brackets, thus: /* dimensions = [300,300] */
- 13.
An annotated list of useful sources appears in Further Readings.
References
An annotated list of useful sources appears in Further Readings.
Abramowitz M, Stegun IA (eds) (1964) Handbook of mathematical functions. U.S. Government Printing Office, Washington
Development Team (2013) Maxima reference manual. http://maxima.sourceforge.net/documentation.html
Woolett EL (2012) Maxima by example. http://maxima.sourceforge.net/documentation.html
Further Readings
Leydold J, Petry M (2011) Introduction to maxima for economics. http://statmath.wu.ac.at/~leydold/maxima/ provides a good overview of Maxima and introduces its use in economics
Maxima Development Team (2013) Maxima reference manual. http://maxima.sourceforge.net/documentation.html. The standard reference, provided in five languages, is also available inline via the wxMaxima help menu or the F1 key
Urroz GE (2009) Maxima book. http://www.neng.usu.edu/cee/faculty/gurro/Maxima.html. A good, though slightly dated, introduction to wxMaxima
Vodopivec A (2013) wxMaxima. http://andrejv.github.io/wxmaxima/index.html. This website, maintained by wxMaxima’s creator, contains workbooks that provide guidance, along with links to related material
Woolett EL (2012) Maxima by example. http://maxima.sourceforge.net/documentation.html. The material at this site introduces Maxima and applies it to topics that are direct to physicists, but develops techniques that economists often use
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Hammock, M.R., Mixon, J.W. (2013). Introduction. In: Microeconomic Theory and Computation. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-9417-1_1
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