Topic 03: Optimal Decision Making. Overview Unconstrained Optimization Univariate Calculus – review Constrained Optimization Multivariate Calculus - review Constrained Optimization. Overview. Many economic decisions involve trying to decide what is the “best” decision to make.
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Name Function DerivativeExample
dY/dX = 0
dY/dX = 5
dY/dX = dG/dX + dH/dX
Example: Y = 5•X + 5•X2dY/dX = 5 + 10•X
dY/dX = (dG/dX)H + (dH/dX)G
Example:Y = (5•X)(5•X2 )
dY/dX = 5(5•X2 ) + (10•X)(5•X) = 75•X2
Example: Y = (5•X) / (5•X2)
dY/dX = 5(5•X2) -(10•X)(5•X)
= -25X2 / 25X4 = -X-2
then dY/dX = (dG/dH)•(dH/dX)
Example: Y=(5+5X)2 ,
dY/dX = 2(5 + 5•X)1(5) = 50 + 50•X
a function of Q
frequency per decade
Max P = 50 + 5•X2
Max P = 100•Q - Q2
¶S/¶X = 200 - 20X + 20Y= 0
¶S/¶Y = 100 - 40Y + 20X = 0
us by the limits of our money, time, and energy.
and one or more constraints.
Subject to g(x1 , x2 , ..., xn ) <b
Subject to g(x1 , x2, ..., xn )> b