Consider a consumer with the following utility function for consumption and leisure: U (RC) = 160 In N+Y where N is the hours of leisure ("recreation") consumed per day (24 maximum) and Yis dollars spent on consumption (p = 1). The consumer has an hourly wage w. (a) Assume the consumer derives all income from work at a wage rate w.Derive the labor supply function, LS(w). (b) For what values of w does the consumer work zero hours? (Hint: does a corner solution arise?) (c) Suppose that w=10. How many hours does this consumer work? If the wage rate increases tow'=16, how many hours do they work? What is the total effect on the supply of labor