Problem 4 Consider the leisure demand/labor supply model studied in class, and let the consumer have a specific utility function U(N,Y) = N2/3y1/3 As in lecture, let the price of consumption be normalized to 1, and let w denote the wage. (a) Say that w = 10. What are the optimal N* and Y*? How many hours does the agent work? Draw a sketch to illustrate this situation. (b) Solve for the general demand functions N(w) and Y(w) as a function of the wage, as well as the labor supply function H(w). Calculate the elasticity of labor supply with respect to the wage, w. Do you notice anything special about this particular example? (c) Say the wage rises to some w' > w. What is the change in leisure demand N(w)? Carefully draw a sketch that decomposes this into an income effect and a substitution effect. (d) Sketch the labor supply function. (e) Let H(w) be the labor supply as a function of the (take-home) wage w. Say now that the government imposes an income tax of a. Let T(a) denote the total tax revenue raised as a function of a. What is dT/da? Explain.

Problem 4 Consider the leisure demand/labor supply model studied in class, and let the consumer have a specific utility function U(N,Y) = N2/3y1/3 As in lecture, let the price of consumption be normalized to 1, and let w denote the wage. (a) Say that w = 10. What are the optimal N* and Y*? How many hours does the agent work? Draw a sketch to illustrate this situation. (b) Solve for the general demand functions N(w) and Y(w) as a function of the wage, as well as the labor supply function H(w). Calculate the elasticity of labor supply with respect to the wage, w. Do you notice anything special about this particular example? (c) Say the wage rises to some w' > w. What is the change in leisure demand N(w)? Carefully draw a sketch that decomposes this into an income effect and a substitution effect. (d) Sketch the labor supply function. (e) Let H(w) be the labor supply as a function of the (take-home) wage w. Say now that the government imposes an income tax of a. Let T(a) denote the total tax revenue raised as a function of a. What is dT/da? Explain.

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

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Chapter1: Making Economics Decisions

Section: Chapter Questions

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Question

Problem 4
Consider the leisure demand/labor supply model studied in class, and let the consumer have a spccific utility
function
U(N, Y) = N2/3y!/3.
As in lecture, let the price of consumption be normalized to 1, and let w denote the wage.
(a) Say that w = 10. What are the optimal N* and Y*? How many hours does the agent work? Draw a sketch
to illustrate this situation.
(b) Solve for the general demand functions N(w) and Y(w) as a function of the wage, as well as the labor supply
function H(w). Calculate the elasticity of labor supply with respect to the wage, w. Do you notice anything
special about this particular example?
(c) Say the wage rises to some w' > w. What is the change in leisure demand N(w)? Carefully draw a sketch
that decomposes this into an income effect and a substitution effect.
(d) Sketch the labor supply function.
(e) Let H(w) be the labor supply as a function of the (take-home) wage w. Say now that the government imposes
an income tax of a. Let T(a) denote the total tax revenue raised as a function of a. What
dT/da? Explain.

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3. Consider the economic model of an individual's labor-leisure choice with the following components: C represents units of the consumption good L represents hours of leisure H represents hours of paid work p represents the unit price of the consumption good w represents the hourly wage rate Y represents nonlabor income T represents total time available U(C, L) represents the individual's utility function MUC denotes the marginal utility of consumption MUL denotes the marginal utility of leisure Unless otherwise instructed, assume that consumption and leisure are normal goods. Whenever graphi the model, put C on the vertical axis and L on the horizontal axis. What is the slope of the budget line? -(MUC/MUL) O-(MUL/MUC) O-W O -(w/p) O-(w+Y)/p
John works in a shoe factory. He can work as many hours per day as he wishes at a wage rate w. Let C be the amount of dollars he spends on consumer goods and R. be the number of hours of leisure that he chooses. John's preferences are represented by U(C, R) = CR utility function Question 2 Part a John earns $8 an hour and has 18 hours per day to devote to labor or leisure, and he has $16 of nonlabor income per day. Draw John's indifference curves, budget constraints and solve for his optimal consumption and leisure choices.
Because Income depends on work effort and work effort depends on nutrition, suppose the relationship between income (Y) and total food availability (F) in a poor household is given by: Y = 10F + 20F2 – 0.6F3 a) If food availability in a two-person household is 20, would it be “rational” to share the food? Explain. b) If food availability in a two-person household is 30, would it be “rational” to share the food? Explain.
QUESTION 7: Budget constraints Everyone is endowed with 168 hours in a week (24X7). If you work 40 hours or less, you w=$20 per hour. If you work overtime, you earn w-$25. Assume the worker has M= non-labor income and that the price of the consumption good is p. Draw the budget constraint. Label the intercepts and the slopes in both the overtime and non-overtime region.
Can you help me with part b please?