Linear and Higher-power Equations

Abstract

We have already used equations on a number of occasions, and throughout this book we shall continue to use them. Equations frequently summarise important facts. Thus the fact that the simple interest (I) at an interest rate (r) on a principal (P) is the rate multiplied by the principal can be summarized as I = rP. Equations can also be descriptive and useful for management decisions. In Chapter 3 we saw how the I = rP equation can be helpful in capital investment appraisal decisions. Equations can provide models either at macroeconomic level — for instance, the input output model for the economy (Chapter 5) — or at the microeconomic level. One example of the latter is that for a product produced by a firm, total costs are a + bx, where a are the fixed costs, b the variable costs per unit and x the number of units produced (provided that certain basic assumptions and conditions are met). If we call total costs y, these costs are then given by the equation y = a + bx.