Consider a utility function defined over hours of leisure and consumption expenditure: U(c, h) ch. The after-tax wage rate is given by w and the amount of nonwage income, by N. Assume the number of hours of leisurein a year is 8000. Potential annual income, I, is given by1-8000wN.It is allocated over hours of leisure, which cost wh, and consumption expenditure, c. The budget constraint isthus8000wN-cwh 0.1. Find the demand functions for leisure and consumption.a. Write the Lagrangean function for this problem.b. Find the first order conditions.c. Solve the first order conditions to obtain the condition that the MRS wage rate. Show your steps inthe solution.d. Use the results from c to obtain the expansion path

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ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Jack's marginal utility of consumption is MUc = L - 6, and the marginal utility of leisure is MUL=C-40. Jack does not have any nonlabor income, i.e., V = 0. Jack faces a $48 an hour wage rate. Jack's total number of hours available per week is 150. What is Jack's optimal choice of consumption? (calculate to 2 decimal places)
An agent lives for 2 periods and gains utility only by consuming. Future consumption is discounted at rate θ where 0<θ<1. Agent consumes c, saves s at interest rate r in first period of life from income y. In second period agent consumes from savings plus interest earned but must pay a flat fixed tax. Find the Euler equation for this agent and what it shows.
The consumer's utility function for Consumption (C) and Leisure (L) is given as U(C,L) = √CLHis hourly wage is $10, non-labor income is $20; and he has a total of 16 hours to allocate between labor and leisureBased on this information, the consumer's total utility at the optimal level (or optimal C,L combination) is:a. 57.0 utilsb. 28.5 utilsc. 99.75 utilsd. 114.5 utilse. Cannot be determined with the information given I prefer typed answers.
Assume you can work as many hours you wish at £12 per hour (net of tax). If you do not work, you have no income. You have no ability to borrow or lend, so your consumption, c, is simply equal to your income. Derive and plot the feasible set, between daily values of consumption c, and “leisure”, l. Label the values at the intercepts (the points where the feasible frontier cuts the two axes).
Economics Summer break is approaching! Suppose you derive utility from days spent traveling on vacation domestically, D, and days spent traveling on vacation in a foreign country, F. Your utility function over these two “goods” is: U(D, F) : 4D0.25F 0.75 Let your budget constraint be I(D, F) = pDD + pF F; where I is your income, pD is the price of domestic travel per day, and pF is the price of foreign travel per day. a. Determine the demand functions for domestic travel and foreign travel. Make sure you show your work – show the steps used. b. Suppose that you’ve saved $800 for your summer travel, the price of domestic travel per day is $25 and the price of foreign travel per day is $100. How many days of each type of travel will you embark on? c. Illustrate the indifference curve, budget constraint, and the utility maximizing bundle associated with (b). Make sure you show the level of utility, the budget constraint intercepts, and the optimizing equilibrium. Your answer
2nd attempt See Hint A consumer faces a tradeoff between labor (L) and leisure (R). She consumes a composite good (C). When the consumer works, she earns an hourly wage of $15.00, and she spends a maximum of 24 hours on labor and leisure, but she chooses to work 10.00 hours. Whatever time she does not spend working, she spends on leisure. She starts with an initial endowment of 11.00 units of the composite good, which she can buy and sell freely at a market price of $4.00. Given this information, what is the consumer's real wage? $ 194
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.
In any given week, Anne receives satisfaction only from the consumption of goods and from the consumption of leisure L, which is measured in hours. Obviously, Anne consumes many different types of goods, but for simplicity we aggregate the dollar value of all the goods that she consumes during the week and call it C. Assume that if Anne chooses to work, the hourly wage rate is w=9 and she has to sleep 8 hours per day. (Sleeping time is not considered leisure.) Potentially, if she wants, she can work up to 7 days a week.
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Tim is buying pizza and salad for a company lunch. Suppose that a slice of pizza costs $4.00, and a bowl of salad costs $5.00. Let ♬ be the amount in dollars that Tim spends on pizza and salad. If Tim buys P slices of pizza and S bowls of salad, then the total amount of money he spends (B) can be represented by the equation Now rearrange the equation you wrote above so that S is written in terms of E and P. The quantity of salad he buys can be represented by the equation Suppose Tim has $40.00 to spend on pizza and salad; that is, E = $40.00. Complete the following table with the values of P or S that make the equation true. Hint: To complete the first row, determine the number of salad bowls Tim can purchase with $40.00, when the number of pizza slices he purchases is 0. Budget Pizza (Dollars) (Slices) 40.00 0 40.00 5 40.00 Use the black line (plus symbols) to plot the line illustrating the combinations of pizza and salad that Tim can purchase with a budget of $40.00. SALAD (Bowis) 14…
Mia is a registered nurse. She has 18 hours per day to devote to labor or leisure, and has $20 nonlabor income per day. She is paid $10 per hour for the first 8 hours of work and $15 per hour for overtime (for hours worked over 8 hours). Mia's preferences are represented by U(C, R) = CR utility function, where Cis the amount of dollars she spends on consumer goods and R be the number of hours of leisure that she chooses. Question 1 Part a Assuming she can work as many hours per day as she wishes, draw Mia's indif- ference curves, budget constraints and solve for her optimal consumption and leisure choices. Question 1 Part b Suppose that Mia's wage rate rises to $11 an hour for the first 8 hours. She is still paid $15 per hour for overtime. Again, find her optimal choice. Decompose the total change in demand due to a price change into a substitution effect, ordinary income effect and endowment income effect and graphically demonstrate each effect.

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