The total production of a particular commodity is given by the Cobb-Douglas function: f(x,y)=bx^α*y^(1−α), b is...

The total production of a particular commodity is given by the Cobb-Douglas function: f(x,y)=bx^α*y^(1−α), b is a given positive constant and 0<α<1 . Assume that we want to maximize production with a given cost constraint mx+ny−p=0 where m and n are the cost of a unit of labour and a unit of capital, respectively, and p the total cost.

Show that each term will always be negative guaranteeing a maximum (in the sufficiency H test) using the values obtained of x and y for maximum production.

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milcah answered 1 year ago

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