On the merits of mathematical models

The article on economics and physics by Doyne Farmer, Martin Shubik, and Eric Smith reviews several interesting studies for senior- or graduate-level physics students who are well grounded in statistics. A much simpler study, one that I think would be informative and suitable for freshman physics and economics students, would be a measure of the operational efficiency of a country.

Other economic systems might also offer appeal, such as a comparison of the operational efficiencies of farms. Selecting a study on countries, however, has the advantage that the data for the total annual input energy consumed in a country are readily available from government websites.

The output energy required for calculating a country’s operating efficiency would be more difficult to assemble. Instead, a simple measure of the total output is the country’s gross domestic product. The resulting ratio of GDP to annual input-energy consumption would not be an efficiency but it would offer a measure of how well a country utilizes its energy for generating wealth. The ratio could be called an efficiency index and is conveniently expressed in terms of dollars per mega-joule. The ratio would be valuable in examining long-term trends, if one corrects for inflation, and would also be useful for comparing the operational efficiencies of different countries.