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ECON 410 Test 1 cheatsheet

# ECON 410 Test 1 cheatsheet - (a/b(c/d = ad/bc cross...

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(a/b)/(c/d) = ad/bc cross multiply Optimization: if f’ is + then increase, if – decrease, 0 = perfect Take first order condition (FOC) derivate = 0 (for single variable f” must be negative) (for multi the partial derivatives of each variable must = 0) Log Rules: exp(ln(x)) = x ln(exp(x)) = x ln(xy) = ln(x) + ln(y) ln(x/y) = ln(x) – n(y) ln(x a) = aln(x) ln(1) = 0 exp(0) = 1 Chain Rule [f(x) * g(x)]’ = f’(g(x))g’(x) Preferences: preferences are rational if they are complete and transitive Symmetric: for each x and y, if x+_ y then y+_ x Transitive: for every x, y, and z, either x+_ y and y+_ z then x+_ z Strict Convexity: preference for diversity Continuity: whenever a+_b and a is “close” to the bundle c, then c+_b Indifference Curves with Rational, Monotonic, Convex Preferences 1) downward sloping 2) “thin” 3) non-crossing 4) preferred as they move farther from the origin 5) everywhere 6) convex (bowed in) Perfect Compliments: goods a consumer consumes only in fixed proportions (right angle graph) U(x 1
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