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A producer produces good y using a single input x according to the production function y=x^a where 0<a<1. The producer can sell as much as he wants at a unit price p, but must pay wage w for every unit of x used.
1) What are the first and second-order condition for the profit maximization problem?
2) Derive the expression for the profit maximizing level of output y*(p,w,a), the profit maximizing level of input x*(p,w,a), and the optimal profit pi*(p,w,a) = py*(p,w,a) - wx*(p,w,a)
3)What happens if a =1
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