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Unformatted text preview: ucsc supplementary notes ams/econ 11a Modelling Economic Variables c 2010 Yonatan Katznelson 1. Mathematical models The two central topics of AMS/Econ 11A are differential calculus on the one hand, and its applications to business and economics on the other. Economists use mathematics to model the behavior of a wide variety of economic variables and their interactions. These models can be very simple, describing nothing more than a linear or quadratic relationship between two variables, and they can be complex, involving many variables and intricate functional relationships. Economists use purely mathematical tools like calculus and linear algebra to analyze these models and better understand the hypothetical relationships between the economic variables. Most mathematical models of economic behavior boil down to an equation or, more generally, a system of equations. Broadly speaking, these equations describe three distinct types of relationships. • Identities which serve as definitions. For example, the equation π = r- c, identifies profit ( π ) as the difference between revenue ( r ) and cost ( c ). This is the definition of profit. • Functional equations which describe how one variable depends on others. For ex- ample the equation Q = AK α L 1- α describes how a firm’s output ( Q ) depends on capital and labor input ( K and L , respectively). • Equilibrium equations. These are equations, or systems of equations, that describe structural equilibria in various economic systems. An equilibrium point is literally a point of balance and in economics, equilibrium refers to a state wherein all of the various market forces are in balance and the system as a whole is stable, or unmoving. The best known equilibrium equation in economics is Q s = Q d , i.e., quantity supplied = quantity demanded (where the variable Q will always signify quantity, in some form or another). The solution of this equation is the point of market equilibrium , which is the point where a market stabilizes and determines the price of a good and the quantity of that good that is trading hands. In the sections that follow I will survey some of the basic economic variables that we will encounter in the course, and some of the relations between them....
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This note was uploaded on 03/16/2010 for the course ECON 11A taught by Professor Qian during the Spring '08 term at UCSC.
- Spring '08