Hessian Matrix : Maximizing Profit

Question: The profit maximizing input choice

A competitive firm's profit function can be written as
π := p * q - w * L - r * k
where p is the competitive price of the product and w and r the per unit cost of the two inputs labour (L) and capital (k).

the firm takes p,w, and r as given and chooses L and k to maximize profits.
If the relationship between inputs and output is given by
q := Lα * kα
the profit function takes the form
π := p * Lα * kα - w * L - r * k

What restriction must be placed on the parameter α to ensure that the second order conditions for an extreme value of π are satisfied.

See attached file for full problem description.

© SolutionLibrary Inc. solutionlibary.com 9836dcf9d7 https://solutionlibrary.com/math/linear-transformation/hessian-matrix-maximizing-profit-3em6