The overall economy is the subject of macroeconomics. Introductory texts use the equations given in Figure IV-15a to describe the main features of an economy. Saving (S) is proportional to income (Y); income is the sum of the income money saved (S) and that spent on consumption (C); savings goes into investment (I) and is equal to it. These relationships are shown in Figure IV-15a as money flows in dashed lines that circulate between the production sector of the economy and the consumer sector of the economy.

Flows of real resources, products, and services are drawn in solid line flowing in opposite direction from the money. The storage of real economic assets was added (K). The energy source is a factor in the production process, and interaction symbols are added with production a product of the pressure of the energy source (E), consumer services (C), and capital assets (K). Since there was no resource limitation given the version in Figure IV-15a, the necessary energy resource is shown as constant, which means it is unlimited (even though there is no such thing in the long run). In other words, energy is supplied as needed.

In this model money circulation was made proportional to production rate so that growth of production was accompanied by growth of money circulation. When the model is simulated, exponential growth of the real assets and of the circulating money results. This feature was used in Figure IV-13a also to illustrate one of the early minimodels of economics, the Domarr - Harrod model, which adds new money as a constant proportion per year. In the simulation run the energy availability is kept unlimited (E constant), and exponential growth results (a in the graph of Figure IV-15c).

Figure IV-15b is the energy diagram for the same model but with a steady renewable flow source. See section II-2. Here, a steady renewable source is substituted (Figure IV-15b), the simulation grows and levels off (b) in Figure IV-15c.

Although the equations of macroeconomics were used, the type of resource controlled the nature of growth. This exercise helps show the way economic systems are similar to general models for auto-catalytic systems, but with additional flexible money mechanisms which facilitate human participation in the patterns that may maximize performance.

Examples of Macroeconomic Systems

The macroeconomic models are often applied to nations, states, and regions. The provisions for source control added to these mini-models make the macroeconomics equations dynamic and realistic.

"What If" Experimental Problems

1. What is the effect of an increase in depreciation rate of the growing assets? Double K2.
   


2. What is the effect of increasing the percent of the income saved and reinvested? Increase K5.
   


3. What is the effect of increasing the availability of energy in the exponential case in Figure IV-15a? Increase E.
   What is the effect of increasing the inflow of energy in the flow limited system in Figure IV-15b? Increase J.

COMPUTER MINIMODELS AND SIMULATION EXERCISES FOR SCIENCE AND SOCIAL STUDIES

Howard T. Odum* and Elisabeth C. Odum+
* Dept. of Environmental Engineering Sciences, UF
+ Santa Fe Community College, Gainesville

Center for Environmental Policy, 424 Black Hall
University of Florida, Gainesville, FL, 32611
Copyright 1994

Autorização concedida gentilmente pelos autores para publicação na Internet
Laboratório de Engenharia Ecológica e Informática Aplicada - LEIA - Unicamp
Enrique Ortega
Mileine Furlanetti de Lima Zanghetin
Campinas, SP, 20 de julho de 2007