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Microanalysis
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Created by
Mabel Williams
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Cards (11)
Concave inequality:
f(pa + (1-p)b
) >=
pf(a) + (1-p)f(b)
for p in (0,1)
Concavity can be shown if hessian is
negative
definite (positive determinant,
negative
trace)
Envelope theorem
says we only need to worry about
direct effects
at the optimum
Concave problem (concave objective function and convex (linear) constraints) means
K-T conditions
are necessary and sufficient for a
global maxima
Non-negativity constraints may be neglected if
marginal utility
tends to
infinity
as x tends to 0
If the
constraint qualification
is satisfied,
conditions
are necessary
need to check if
K-T
solutions are correct by checking alternative constraints / checking if
Lagrange multipliers
are positive
a
multiplier
is a measure of the change in the objective function when the constraint is
relaxed
when f is (strictly) concave, a local
maximum
or stationary point is a (unique)
global maximum
if a function is not differentiable /
C1
, we cannot appeal to
K-T
conditions
if F is strictly
convex
,
FOCs
are necessary and sufficient for a global minimum