# Energy-economic theory and mathematical models for combining the systems of man and nature, case study: The urban region of Miami, Florida

This paper presents a study of the urban region of Miami, Fla. with consideration of energy flow and the relationship between energy theory and economics. Much of this work is based on the theories and work of Dr Howard T. Odum at the University of Florida. A theory of energy quality is presented which is an attempt to relate energies of different concentrations in their ability to do work. This theory allows comparison of the systems of man and nature. Another theory is proposed which seeks to describe the ability of a region to compete based on its flows of natural and fossil fuel energies. Economic, natural system, and energy data were compiled for the Miami urban region from 1950-1972. Cross-correlation of this data showed significant levels of correlation between the rate of change of fossil fuel use and the rates of change of population, budget, sales tax, income, building structure, and number of telephones. Calculation of several urban indicators for 1972 showed a fossil fuel energy density of 300 kcal/m2/day in the urbanized area, a per capita energy consumption of 53.8 × 106 kcal/capita/year, a ratio of natural to fossil fuel energies of 0.25, a developed area of 260 miles2 (673.4 km2), and a rate of development of 6.5 miles2 (16.8 km2) per year. An overall model of Miami is presented with flows and storages quantified for 1972. Based on this model a simpler model was simulated on an analog computer. This model consisted of a system of first-order in time, non-linear differential equations which included fossil fuel energy flows, main economic flows, external price functions, building structure, natural energies, and population. This model was simulated for several linearly increasing future price functions and several sets of future energy functions. Natural energies within the region were calculated by determining the land areas associated with various ecosystem types. Estimating the productivities of these systems on a per area basis allowed calculation of total energy flows. The energies associated with winds, tides, waves, and fresh/salt water concentration gradients were also determined. It was found that the ratio of natural to fossil fuel energy changed from 1.77 in 1950 to 0.25 in 1972.

Miami