Consider a consumer with the following utility function for consumption and leisure: U (R, C ) = 160 ln N + Y where N is the hours of leisure (“recreation”) consumed per day (24 maximum) and Y is 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 to w′ = 16, how many hours do they work? What is the total effect on the supply of labor?
Consider a consumer with the following utility function for consumption and leisure: U (R, C ) = 160 ln N + Y where N is the hours of leisure (“recreation”) consumed per day (24 maximum) and Y is 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 to w′ = 16, how many hours do they work? What is the total effect on the supply of labor?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Consider a consumer with the following utility function for consumption and leisure:
U (R, C ) = 160 ln N + Y
where N is the hours of leisure (“recreation”) consumed per day (24 maximum) and Y is 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 to w′ = 16, how many hours do they work? What is the total effect on the supply of labor?
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