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Economics
Proof of EnvelopeTheoremfor constrainedoptimization problems(from Varian)
Consider a parameterized maximization problem of the form
max g(x1,x2,a)
M(a ):
s u ch that h(n1,n2,o) :0.
The Lagrangian for this problem is
E:
g ( rr,az,a) - l h(o1, rz,a),
and the first-order conditions are
Idxt -.ril:o
drr
(27.4)
3 -)3 :o
OfrZ
Ofiz
h(ay,x2,@ ): 0.
These conditions determine the optimal choice functions (a{a),rz(o)),
which in turn determine the ma;