Some Update Notes
on The Economics Pack

Thomas Cool, Consultancy & Econometrics,

March 21 2003, Report No 2003-03-21

JEL A00 (programming)


The 1995 paper "Economics programs written in Mathematica" has evolved by 2003 into "The Economics Pack" that has users in many countries in the world. The supply and demand situation is satisfactory - with quality supply and a decent level of interest in the community of economists - but distribution remains a bottleneck.  The contrast between the wonderful features of Mathematica and the distributional bottleneck is remarkable.


I noted that The Economics Pack was listed in the top ten of software entries at but that people referred to Cool (1995, 1996) which is rather outdated.

Hence the following update notes are useful.

PM. I have considered updating the original reference, as is the general intention of EconWPA, but it is useful to keep that original as it is.

Link to the proper page

The proper link is to while the Pack can be bought online at

PM. The original paper Cool (1995, 1996) links to, which site has been dormant for some years now. I’d rather not remove that link, it might wake up some day again. Still very active is

Software contents and documentation

The software has been much extended. See above link for the new table of contents.

The Pack can be downloaded there as well (version Mathematica and installed. There is now a large number of help files, that can be integrated in the standard Mathematica Help function.

PM. To run the software, you of course need a password. It remains advisable to first install before you buy the password, so that you know what to expect. For example, it can be instructive to look at the help files and palettes (which is not running the software yet).

When you buy the Pack, you are advised to also buy the printed User Guide, Cool (1999, 2001). This User Guide actually is a print of the help files. You can also refer to this User Guide by its entry in the Journal of Economic Literature, volume 37, no. 3, September 1999 (reference number is JEL 1999-0820). I found the printed User Guide a valuable tool myself.

Specific content issues are:

Reviews by Ron Shone

Ron Shone (1998) reviewed the Pack earlier. Shone (2000) is also a good review of Mathematica 4.0, and Shone (1997) a good book on dynamics using different programs.

The current version of the Pack (with all the Help files etcetera) was also reviewed by Ron Shone, but got never published because the EJ stopped software reviews.

Ron sent me a copy of that review, but it contained various "screen dumps" that tend to look good on paper but distract on the internet, so I did not put it on my site.

I can usefully quote these lines, though:

"This is a much-improved version of the CoolEconomicsPack that I reviewed earlier for the Economic Journal, Shone (1999). The present version is a much more useful package and is integrated within Mathematica to the extent that the manual (which did not exist before) is now part of Mathematica’s browser window as well as in hard copy.


The number of routines contained in the Economics Pack is numerous, and one could easily overlook a useful one. In section 6.7, for instance, there is a probability package that deals with prospects and the equivalent value of prospects. There follows a discussion of risk and typical routines for handling problems to do with insurance. Thus, we find routines on certainty equivalence and Pratt’s measure of risk.



Thomas Cool opens his manual with the statement, "These notebooks and packages have been developed for economics, business and finance." This is exactly what they are. He goes on, "These packages may help you to get the job done." One may add, "done better." Cool sees Mathematica as extending the general language of mathematics to the computer and so enhances its usefulness still further. He sees it almost as a new revolution. He therefore sees the user guide as a way to ‘use the routines’ and not as a discussion of the economic problem or how a solution routine has been programmed.

We can ask three basic questions about the routines:

Are they easy to use?

Are they comprehensive?

Can they be adapted?

Put briefly my answers are: (1) No, (2) Yes, and (3) Yes. My first review, Shone (1999) criticised Cool for not having a manual and so it was difficult to know how all the routines fitted together. He clearly has satisfied this with a 555-page manual! But the Thomas Cool package is constrained by its own extensiveness. Because there are so many routines, the 555 pages can barely state the instructions for inputting information into them. These input statements follow the strict syntax of Mathematica. But exactly how the user should input instructions, which use these in some combination of statements, is not usually provided. The user, therefore, must often find this out by trial and error. This is not satisfactory. The solution is quite simple – but possibly not one that the producer of the manual would like. It is: provide numerous examples to illustrate how the input instructions should be used. This is exactly what the Mathematica manual does. Unfortunately, this would (I suspect) increase the manual to almost 1000 pages! The only alternative is to limit the extent of the routines. If the Economics Pack is to have wider use, as it deserves, then it needs to be made far more user friendly with far more simple examples to illustrate how the different routines can be used."

Perhaps I better put that review on the site as well. I agree with Ron that more examples are useful. But examples depend upon the purpose, and before you know you started a textbook on a special topic that is difficult to publish.

For me, the power of the Pack remains that it is (a) basic, (b) integrated, (c) reliable, (d) in Mathematica, so that when you start on a subject, you can start and proceed rather quickly.

Apart from the table of contents, you can also look at the list of papers on my site that I have worked on. I mostly use Mathematica, so one can image the link between subject area and Pack.

Review by Erik de Regt

Erik de Regt (1999) gave an internal review for the economics faculty of Maastricht University. This internal review was not intended for publication, but I can refer to it as a useful exercise.

His conclusion at the time was that the Pack contains ‘mature and green’ material, and that its usefulness has to be established in practice.

I can agree with that. Note: the development of the Pack is much directed by my research. Starting from a green stage, the software must show its usefulness, then must be documented, help functions must be designed, and all this integrated in a large environment.

Let me explain what was useful in this reviewing exercise by giving an example. Consider the following steps in thinking about software design:

  1. Standard Mathematica functions F are defined as F[expr, x] so that one might expect the input format Elasticity[expr, x]. Thus Elasticity[f[x], x] would work as standardly expected.
  2. In the Pack, Elasticity[f, x] originally had been defined as the elasticity of f[x] for x. The idea is that this saves the effort of typing [x], while elasticities generally are required for functions f anyhow. Thus, when you define f[x_] := a x + b, then Elasticity[f, x] evaluates as a x / (a x + b).
  3. When you subsequently wonder about the elasticity for the constant b, and try Elasticity[f, b], then you get the elasticity of f[b] = a b + b for b (which is 1), while you intended to get the elasticity of a x + b for b (which is b / (a x + b)).
  4. Thus, the definition of Elasticity under (2) appears to be counter-intuitive and/or creating confusion because of the standard in (1).
  5. As this issue transpired from above review, I have reconsidered the issue at some length. First of all, the issue does not have much impact. One perhaps as easily writes x / f[x] D[f[x], x], and thus the separate introduction of Elasticity has different objectives: (a) to support students who are new to the subject, (b) to clarify the reading of routines, (c) to reduce the possibility of (routine) errors because of typing errors or oversights. It is useful to be aware of these aspects. Secondly, as an intermediate way to solve the matter, I extended the definition of Elasticity with pattern recognition, so that Elasticity[f[x], y] is now recognised (where y can be x). A consequence still is that Elasticity[constant, x] interpretes constant as a function or is unevaluated when that constant is an actual number. I am still not happy with this, and have decided to go back to the standard format Elasticity[expr, x] in a new version of the Pack, and adding Elasticity[f, x, @] as shorthand for Elasticity[f[x], x]. The latter might be a useful general approach for function definitions.
  6. All this is a perhaps long deliberation, but there is some reason of gratitude for Alfred Marshall’s invention, and it should be implemented conveniently. (Part of the quality of the Pack is perhaps not the complexity of its routines, but that such issues have been contemplated.)


User responses

Some users responded to a questionnaire:

"(...) you have accomplished a great task. (..) I hope it becomes celebrated more and more."
Asahi Noguchi of Senshu University, 1998

"The quality of the Pack is excellent. The price of the Pack is fair. My advice to other people is: use the Pack. (Though currently I seldom use the Pack myself.)"
Frank J. Iannarilli, Jr., Aerodyne Research, Inc., March 23, 2000

"The quality of the Pack is excellent. The price of the Pack is fair. My advice to other people is: use the Pack. I use the Pack standardly."
Fritz Breuss, University of Vienna, April 22, 2000

"The quality of the Pack is excellent. The price of the Pack is fair. My advice to other people is: use the Pack. (Though currently I never use the Pack myself.)"
Anonymous, March 23, 2000

I actually haven't had enough time to look at the Pack. It appears that you can't use the Pack without being fairly acquainted with Mathematica. But, whenever I look up something, ik seems fairly good to me. So the quality of the Pack is good, and the price is fair.
Anonymous (since I don't actually use the Pack), April 6, 2000

The Economics Pack webpage contains a link to a User Group page (at netbabbler) but up to now there is only one question.

Results with the Economics Pack

For a review of the results with the Pack, see my English papers list on my website.

The prime result is Cool (2000) "Definition & Reality in the General Theory of Political Economy" (DRGTPE), JEL reference number JEL 2000-1325, vol. 38, no. 4, December 2000. This extends Keynes’s General Theory with the Public Choice explanation of endogenous policy making. Various papers, such as on unemployment, social welfare, risk and general equilibrium modelling, are put together here.

To my knowledge, there are no other results that use the Pack. I did a query on the internet, and did find a number of links that surprised me.

Relation to other software issues

I found occasion to write Cool (1999) suggesting that Mathematica would be the general software tool and Cool (2000a) suggesting that MathML is a tedious approach to a Mathematical mark-up language (while there already is Mathematica). I could imagine that also a Linux version is written using the Mathematica language. My suggestion is that mathematicians agree that Mathematica codes mathematics most naturally, and that WRI cannot claim ownership to a language and standard that has evolved over millenia. In other words, we should not confuse language, standardisation and ownership. Note that there is also the distinction between the language and standard (e.g. used in packages and kernel) and the user interface (frontend). Commercial companies should compete only on the latter. Of course, it would be best when Stephen Wolfram would agree on this point of view too.

Distribution issues

Distribution is remarkedly difficult.

From March 1998 till October 1999 the Economics Pack sold from WRI. My contract with WRI gave them 50% of the gross price, and it was my intention to allow them to sell all over the world. It turns out that WRI itself only sells to North America (NAM) and that it has a network of resellers for the rest of the world. WRI initially interpreted the contract as that they should substract the resellers's margins, so that my gross (!) earnings were 50% of 60% = 30% or sometimes even less. When this transpired, they first didn't react to my objection. I first had to write that I considered the contract void, before WRI responded. WRI was willing to stop its practice, but, only by limiting sales to NAM - because that is how they operate. That was OK for me. Then they came up with a contract addendum that suggested that the WRI interpretation of the contract up to then was the sound one instead of a wrong one. In these negotiations the idea came up to also put the gross sales price in writing. This was in itself a good idea. But they also wanted the price in the contract, and that is awkward, because when I would change the price, for example because of a product improvement, then I would need WRI’s signature. This discussion became confusing. I got an email from the WRI head of finance that there was no intention that their signature would be required, and I got legal papers that suggested that it would be required. I signed the papers and added a line that this contract did not imply that WRI could determine the selling price. It appeared that this was not acceptable to them, and the Pack was removed from their site. I still wonder what their problem is.

In discussions with Springer Telos and Pearson it appeared that publishers face a difficult market. A book with software is double expensive - both the print and the software. An added problem is that The Economics Pack requires Mathematica.

(PM. Typical is this point. When I accepted my first teaching job in 1997, I preferred mathematics and statistics as subjects, since these are more straightforward for a first teaching job. My heart lies with economics, but I have my hesitations about the idea of discussing the subtleties of the subject with an audience of generally uninterested adolescents. Because of this choice and situation, I was less in a position to write software to support a specific textbook on economics. There is enough material to do so, but I haven’t had the time and occasion. In the same vein, I have another position now, first at Erasmus University, but now merged into Erasmus MC, and I had the plan to write a book on finance and risk, but have to shelve that for a while. The current research subjects are epidemiology and health economics.)

Fortunately, I found Gopher Publishers that sell online and print on demand. When I have time, I should try to find a similar service provider in NAM, so that payments can be in dollars and shipping costs will be lower.

Information Rules

A suggestion in Shapiro & Varian (1998), "Information Rules", is to hand out free copies of the software, to create an ‘established base’.

I have a limited policy on that. When an author of a book considers including software based on the Pack in that book, that I can provide a license to that person for free. My approach thus is to ‘piggy-back’ on the established bases that already exist.

I admit that there is some temptation in giving away the software and see thousands of students eagerly working with one’s product. The alternative point of view however comes from the experience of WRI that a good product can sell without such methods. Even, the earlier software version, though licensed, was not protected and did not depend upon a password. I added these features to limit undesirable copying.

My alternative to giving away free copies is to charge a price that also students can afford. A drawback is that a low price might suggest low quality (which apparently would not be the case for a zero price). My hope is then that economists are sufficiently sophisticated not to base their decisions on price alone.

A comparable situation is with Rolf Mertig’s program to import and export Excel files into Mathematica, at I can’t advise him that he gives this away for free. Such a program could eventually be integrated into Mathematica itself, but then that price rises again... These issues are not so difficult as they appear: the bottom line here is that people are advised to simply pay the price of quality software.


The conclusion is that supply and demand are OK, with quality supply and a decent level of interest in the community of economists, but that the bottleneck is distribution.

Given the wonderful features of Mathematica, this bottleneck still is rather surprising.


Carter, M. (1996a), "Linear programming with Mathematica: The Simplex Algorithm", in Varian (1996)
Carter, M. (1996b), "Linear programming with Mathematica: Sensitivity analysis", in Varian (1996)

Cool (1995, 1996), " Economics programs written in Mathematica", at

Cool (1999, 2001), "The Economics Pack. User Guide", ISBN 90-804774-1-9,,

Cool (2000) "Definition & Reality in the General Theory of Political Economy", Samuel van Houten Genootschap,

Cool (2000a), "The Disappointment and Embarrassment of MathML - update: Including Reactions and Answers",

Cool (2001), "Voting Theory for Democracy", ISBN 90-804774-3-5,,

Cool, (1999), "Beating the software jungle", at

Drenth, K. and Th. Cool (2000), "Transport Science for Operations Management", for undergraduate students, ISBN 9080477427,

Noguchi, A. (1993), "General equilibrium models", with S. Levy, in Varian (1993)

Regt, E. de (1999), "Het Economics Pack", internal review, Maastricht University. See also my comments

Shapiro & Varian (1998), "Information Rules", Harvard Business Press

Shone R. (1998), "CoolEconomicsPack 1.0 for Mathematica 3.0 running under Windows 95", Economic Journal, July 1 1998, v 108 n 449, page 1229-1234.

Shone R. (2000), "Mathematica v4.0 for Windows 95 / 98 / NT", The Economic Journal February 2000, page F171-186

Shone, R. (1997), "Economic dynamics", CUP

Varian, H.R. ed (1993), "Economic and financial modeling with Mathematica", Springer Telos

Varian, H.R. ed (1996), "Computational economics and finance", Springer Telos