TA Notes - January 31.pdf

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Department
Economics
Course
ECON 325
Professor
Geoff Stevens
Semester
Spring

Description
Notes for ECON325 discussion on January 31, ex post 1. math review a. function is a mapping from input to output input ▯ (consumption, for example) and output ▯ ▯ (utility obtained by consuming ▯) b. first order derivative mathematical definition: ▯ ▯ ▯ + ℎ − ▯ ▯▯ ▯ ▯ ▯ = lim▯→▯ ℎ first order derivative is a slope of a function at that point graphical intuition: ▯ ▯▯ ℎ ▯ - ▯ ▯ > 0 : a function ▯ is increasing at ▯ ▯ ▯ > 0 for any ▯ : ▯ is monotonically increasing - ▯ ▯ < 0 : a function ▯ is decreasing at ▯ ▯ ▯ < 0 for any ▯ : ▯ is monotonically decreasing - ▯ ▯ = 0 : a function ▯ is flat at ▯ c. second order derivative simply the first order derivative of the first order derivative - ▯▯▯▯▯ > 0 : a function ▯ is convex at ▯, meaning the slope is increasing at ▯ - ▯▯▯▯▯ < 0 : a function ▯ is concave at ▯, meaning the slope is decreasing at ▯ ▯ ▯▯ ▯ ▯▯ ▯ ▯▯ ▯ ▯▯ ▯ ▯ ▯ ▯ concave function, increasing and decreasing convex function, increasing and decreasing d. log function ▯ ▯ = log ▯ , in economics it is natural logarithm unless the base is explicitly written log ▯ is undefined for ▯ ≤ 0 nice properties for utility function: ▯ - ▯ ▯▯ = 1 ▯ → monotonically and strictly increasing (more is better than less) ▯▯ ▯ - ▯ ▯ = −1 ▯ ⁄ → concave for any ▯ (diminishing marginal utility) log ▯▯ 1 ▯ e. Cobb-Douglas func
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