🔬 Tutorial problems iota#
.1#
Find the largest domain
is concave.
How about strictly concave?
It is useful to review the Hessian based conditions for concavity and the conditions for definiteness of a Hessian of
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.2#
Show that the function
Because the function is not differentiable everywhere in its domain, using the definition of concavity could be an easier way.
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.3#
Consider the function
Give a necessary and sufficient (if and only if) condition on
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.4#
Let
Show that
Obviously, you should draw intuition from the preceding question.
Also, what does linear independence of the columns of
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.5#
Consider the maximization problem
subject to
Show that this problem has a solution if and only if
Solve the problem by substitution and using the tangency (relative slope) condition. Discuss, which solution approach is easier.
To answer the first part of the question, review facts of existence of optima.
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