Using utility function to solve for optimal choice
Suppose that the typical consumer has the following utility function:
U(N, Y) = N×Y,
where Y = income or expenditures on goods, and N = leisure (non-work) hours. The wage rate is given by w = $10. The consumer is initially taxed at the proportional rate of t1 = .4. The consumer has no unearned income (Y* = 0). The time constraint is given by
24 = N + H,
where H is hours of work.
Solve for the optimal choice. Graph this solution. How many hours of work is the consumer working? What is her income?
Can you show me the steps needed to solve the this problem?