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ECON 1540 Lecture Notes - Logarithm

Course Code
ECON 1540
Othon Alexandrakis

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Econ. 1540 Lecture #2, D.N. DeJong
Mathematical Background
Linear Equations
Nonlinear Equations
Measuring Rates of Change: the logarithmic function
Modeling growth: the exponential function
Econ. 1540 Lecture #2, D.N. DeJong
Linear Equations
Y = a + bX a, b positive parameters
a: intercept – portion of Y that is independent of X (i.e., value of
Y when X=0).
b: slope response of Y to a change in X (i.e., ratio of the change
in Y to the change in X rise over run).
Key feature: slope is not a function of position on the line (i.e.,
not a function of the value of X).
Measuring the total change in Y resulting from a given change in
X: Y = slopeX, or Y = bX
Links to calculus:
slopes are analogous to derivatives: Y/X = b;
total changes are measured using differentiation:
Y = Y/XX
Econ. 1540 Lecture #2, D.N. DeJong
Nonlinear Equations
Key difference between linear and nonlinear equations: slope
becomes a function of X.
Generic representation: Y = f(X)
Slope: Y/X
Change in Y resulting from a change in X: Y = Y/X X