A3 2. Assume that individuals have the utility function over consumption (c) and labor (1) given byU (c,1) = 2c+0 log (20 – 1),where 0 is a constant parameter reflecting disutility from work. Suppose the only income that individ-uals have is from labor income.(a) Suppose labor income is taxed at rate T. Solve for utility-maximizing labor supply as a functionof w, T, and 0.(b) For this part (b) only, suppose the wage rate w = $10. There are 100 individuals in this economy,where a half of the population with OL = 20 and the rest of the population with On = 40.Calculate how much revenue the government will raise if it imposes a flat 20% labor income tax(T = 0.2) on all 100 individuals. Does this tax rate maximize the revenue?(c) Now suppose that individuals have the utility function over consumption (c) and labor (1) givenbyU (c, 1)= log c+ 0 (20 – 1)instead. Labor income is taxed at rate T. Solve for utility-maximizing labor supply as a functionof w, T, and 0.

The utility function measures the preferences of the set of goods and services.

2. Assume that individuals have the utility function over consumption (c) and labor (1) given by U (c,1) = 2c+0 log (20 – 1), where 0 is a constant parameter reflecting disutility from work. Suppose the only income that individ- uals have is from labor income. (a) Suppose labor income is taxed at rate T. Solve for utility-maximizing labor supply as a function of w, T, and 0.

2. Assume that individuals have the utility function over consumption (c) and labor (1) given by U (c,1) = 2c+0 log (20 – 1), where 0 is a constant parameter reflecting disutility from work. Suppose the only income that individ- uals have is from labor income. (a) Suppose labor income is taxed at rate T. Solve for utility-maximizing labor supply as a function of w, T, and 0.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter10: Cost Functions

Section: Chapter Questions

Problem 10.10P

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Suppose that following represents the utility function of the individual U(c,l)=log⁡(c)+log⁡(l) c = consumption level of the individual and l = leisure, while the market wage is 10 and available time is 20. 1) Find and draw the labor supply function. 2) Suppose that the government introduces a cash grant for the labor (who is in the labor force) in the amount of R. Find and draw the labor supply function? Compare it to the labor supply function you have found in a). 3) Discuss the existence of reservation wage in the settings described in a and b? If your answer is : “there are no reservation wages under those settings”, please introduce a change in the policy described in b) to make sure that the reservation wage would exist.
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Consider a worker who is endowed with T hours of time and investment income V per week, faces a wage rate w per hour, and whose preferences over the consumption of goods, the price of a unit of which is p, and leisure can be represented by the utility function U(C,L) = C1/2L1/2. Find the worker’s labour supply. When is it positive? Will the worker ever work more than half their time endowment? (25%)
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Suppose that the owner of Boyer Construction is feeling the pinch of incrs associated with worker’s compensation and has decided to cut the wages of its two employees (Albert and Sid) from $25 per hour to $22 per hour. Assume that Albert and Sid view income and leisure as “goods,” that both experience a diminishing rate of marginal substitution between income and leisure, and that the workers have the same before- and after-tax budget constraints at each wage. Draw each worker’s opportunity set for each hourly wage. At the wage of $25 per hour, both Albert and Sid are observed to consume 12 hours of leisure (and, equivalently, supply 12 hours of labor). After wages were cut to $22, Albert consumes 10 hours of leisure and Sid consumes 14 hours of leisure. Determine the number of hours of labor each worker supplies at a wage of $22 per hour. How can you explain the seemingly contradictory result that the workers supply a different number of labor hours? (LO2, LO3, LO7)
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Suppose that the owner of Boyer Construction is feeling the pinch of increased premiums associated with worker’s compensation and has decided to cut the wages of its two employees (Albert and Sid) from $25 per hour to $22 per hour. Assume that Albert and Sid view income and leisure as “goods,” that both experience a diminishing rate of marginal substitution between income and leisure, and that the workers have the same before- and after-tax budget constraints at each wage. Draw each worker’s opportunity set for each hourly wage. At the wage of $25 per hour, both Albert and Sid are observed to consume 12 hours of leisure (and, equivalently, supply 12 hours of labor). After wages were cut to $22, Albert consumes 10 hours of leisure and Sid consumes 14 hours of leisure. Determine the number of hours of labor each worker supplies at a wage of $22 per hour. How can you explain the seemingly contradictory result that the workers supply a different number of labor hours?