ii. Find
d
L
da
evaluated at the solution
x
⋆
,
λ
⋆
. What is its interpretation?
2. Consider the inequality-constrained profit maximization problem
max
x
π
(
x
) = 10
x
−
x
2
subject to
x
≥
c
.
(a) Why do we express the constraint as
−
x
+
c
≤
0?
WARNING: ALWAYS DO THIS WHEN FACED WITH A CONSTRAINT
x
≥
c
.
(b) Clearly state the Lagrangian and all the Kuhn-Tucker conditions associated with this problem.
Make sure to use your answer in a).
3