At the University of Purplexium a typical student's preferences over her daily consumption of pounds of food (F) and hours of leisure (Y) are described by the utility function U(F, Y) = FY. The student has 16 hours that are available each day for work or leisure. The price of food is $1 per pound and the wage rate is W per hour. She also receives M per day in income from her parents.
a. What is her daily budget constraint for F and Y in terms of W and M?
b. What is her best bundle of food and leisure (expressed as a function of W and M)? What is her labor supply function?
c. If there are 50 such students and the demand function for labor at the university is Ld = 800/W, what is the competitive equilibrium wage as a function of M? How do changes in M affect the competitive equilibrium outcome?