Microeconomic Theory
12th Edition
ISBN: 9781337517942
Author: NICHOLSON
Publisher: Cengage
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Chapter 16, Problem 16.10P
To determine
To discuss:The signs of cross substitution effects.
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Consider a single mother with the utility function U = 2/3 log(x) + 1/3 log(), where x is consumption and is leisure. The mother can work up to 100 hours per month. Any of the 100 hours that are not worked are leisure hours. She earns a wage of $10 per hour and pays no taxes. The consumption price is normalized to $1. To be able to work, she has to incur a child care cost of $5 for every hour worked. a. Suppose that there is no tax and welfare benefits. How many hours will she work and what will be her consumption level? Draw the graph depicting her budget set with consumption on the vertical axis and leisure on the horizontal axis. b. Suppose that the government introduces a negative income tax (NIT) that guarantees an income of $200 per month. The benefit is taken away one for one as earnings increase. Draw the new budget set. Compute the new number of hours worked and consumption level. Has consumption increased and is the mother better off? Why or why not? c. Now…
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?
A student has a part-time job in a restaurant. For this she is paid $8 per hour. Her utility function for earning $I and spending S hours studying is U(I,S) = I^1/4 S^3/4 (The utility function is a measure of the `usefulness' or `worth' to the student of a certain combination of money and study time). The total amount of time she spends each week working in the restaurant and studying is 100 hours. How should she divide up her time in order to maximise her utility?
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