Hidetaka has just graduated from technical school with student loans that will cost him $25,000 per year.

He now has to decide where to work in order to pay o his debt. At his current place of employment he is

paid $50 for each hour of work. His annual utility function is U(N,W) = ln(N) + 2ln(5000 - W) where W

is the number of working hours during the year, and N is net income after expenses, taxes, and debt service.

(a) What is Hidetaka's budget constraint linking N and W? Offer two representations of the equation

and explain the economic intuition behind each.

(b) Given the preferences above, find the optimal number of hours that Hidetaka should work in order

to maximize his utility.

(c) If taxes go up so Hidetaka is only receives an effective salary of $40 per hour of work, will he work

more or fewer hours? Explain the economic intuition for the result.