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The production function of a profit-maximizing company is ? = ?^2/3 where ? is the amount...

The production function of a profit-maximizing company is ? = ?^2/3 where ? is the amount of the single output and ? ≥ 0 is the amount of the single input is called.
a) For the input factor, determine the sign and the course of marginal productivity.
b) Please determine for a given output price ? and for a given input price ? the factor demand function x∗(?, ?) and the offer function ?(?∗(?, ?))
of the company.
c) Now please indicate the profit function ?(?, ?). Show that the gain function has a degree of homogeneity of 1 and enter a economic interpretation.
d) Please check the validity for the profit function you have determined of Hotellings Lemma regarding factor demand and
Supply function.

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