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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
consider the maximization problem u(c,l) subject to pc + wl = wT + Y, where c is consumption, l is leisure time, T is total time endowment, and Y is non-wage income. prove that if leisure is an inferior good then the labor supply function is upwar..
Now suppose that the demand increases by 10 units at each price.fill in the new quanity demanded in table above5.determine the new equilibrium price and quanity 6.reproduce the graph tha u drew for question 4 and label oringinal demand and supply
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