math - Math Review for Principles of Macroeconomics Ariel...

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Math Review for Principles of Macroeconomics Ariel Singerman January 16, 2008 1 Introduction In economics, we often make use of mathematical tools to understand economic relationships. Graphs are of fundamental importance to understand the economic relationships between variables such as price and quantity. This handout is intended to be a review of high school mathematics that will prove to be useful in this macroe- conomics class. 2 Functions of one variable One variable is a function of another if the Frst variable depends upon the second. A function f is a rule that assigns to each value of a variable x , one value of y . y = f ( x ) in the above expression the values that y take depend on the values of x . Therefore, we call x the independent variable and y the dependent variable. examples: y = x linear function y =3+4 x linearfunction y = x 4 +5 x 3 +56 nonlinearfunction 1
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2.1 Linear Functions In this class we will often use linear functions. All straight lines (linear functions) have the same general representation with an equation of the form: y = a + bx a is then called the vertical intercept, because it marks the point where the graph of the equation hits the vertical axis. x =0 y = a b is the slope of the line, which tells us how much y changes every time x changes by one unit. How to determine the slope of a straight line? To do this, we divide the change in the vertically measured variable by the change in the horizontally measured variable. Slope of a straight line = change in vertical variable change in horizontal variable = rise run Note that the parameters a and b are in no way restricted to be positive. Both parameters can be positive, negative, or zero. Furthermore, the value of a has no e±ect on the slope of the line.
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math - Math Review for Principles of Macroeconomics Ariel...

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