1. An individual derives utility from the consumption of a basket of goods, c and leisure time, & given by U(c₂l) = cºl(¹-a) where 0 < a < 1, is a constant; and must decide how to allocate her time between work, L and leisure to maximize her utility. The individual has a total of 24 hrs in a day (L+= 24) and total consumption is constrained by her income; i.e., c = wL, where w the real per hour, is taken as given.

1. An individual derives utility from the consumption of a basket of goods, c and leisure time, & given by U(c₂l) = cºl(¹-a) where 0 < a < 1, is a constant; and must decide how to allocate her time between work, L and leisure to maximize her utility. The individual has a total of 24 hrs in a day (L+= 24) and total consumption is constrained by her income; i.e., c = wL, where w the real per hour, is taken as given.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter4: Utility Maximization And Choice

Section: Chapter Questions

Problem 4.12P

See similar textbooks

Similar questions

Katie Kwasi's utility function is U(x₁, x₂)=5(In x₁)+x₂. Given her current income and the current relative prices, she consumes 10 units of x₁ and 15 units of x₂. If her income doubles, while prices stay constant, how many units of x₁ will she consume after the change in income? a)10 b)20 c)15 d)5
Given the utility function: U = ln c + l + ln c’ + l’ and the budget constraint: w(ℎ−l)+(w′(ℎ−l′))/(1+r)=c+(c′)/(1+r) (see pictures of function and constraint) where c = current consumption, c' = future consumption, l = current leisure, l' = future leisure, and r is the market interest rate.Suppose that the current wage, w = 20 and the future wage w' = 22. a) What is the optimal value of current consumption, c? b) What is the optimal valueof future consumption, c’*?
Answer the question on the basis of the following two schedules, which show the amounts of additional satisfaction (marginal utility) that a consumer would get from successive quantities of products J and K. Units of J MUj Units of K MUk 1 56 1 32 2 48 2 28 3 32 3 24 4 24 4 20 5 20 5 12 6 16 6 10 7 12 7 8 What level of total utility is realized from the equilibrium combination of J and K, if the consumer has a money income of $28 and the prices of J and K are $8 and $4, respectively? Multiple Choice a. 172 utils b. 168 utils c. 188 utils d. 72 utils Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.
Juan is currently working in a job that pays $25 an hour and he chooses to work 8 hours per day. Assume that Juan can work a maximum of 16 hours a day, and he has complete flexibility in how many hours a day he works. Illustrate Juan’s budget constraint and his optimal choice of consumption and leisure. What is the slope of his budget constraint? What does this slope represent? (As on any graph you draw, make sure that you label the axes, the intercepts and the optimal choice.) Juan begins receiving a government transfer payment of $100 per day. Add his new budget constraint to your graph in (a) and show his new optimal choice. Does he choose more or less consumption? More or less leisure? Explain why for both goods. The government imposes a tax of 25% on Juan’s earnings from work and increases his government transfer to $150 per day (the government transfer payment is not taxed.) Redraw the budget constraint from part (b) (omit the part (a) budget constraint), and add a new budget…
Suppose you have a monthly income of $1000, $850 in monthly expenses, and you can put money in a savings account that yields a monthly interest rate of 4%. Create a budget constraint showing the trade-off between present consumption (horizontal axis) and future consumption (vertical axis). How much will you have in the future if you choose to consume $850 now? Show this point on your budget constraint.
Henry's utility function is u(x,y)=max{x+3y,3x+y}. (a) Suppose Henry's current consumption bundle is (2,1.5), what is his current utility level? If he consumes the bundle (1.5,2), will his utility change from the current utility level?
(Short Answers) 1. Jie works in a university. He can work as many hours as he wishes at a wage rate of w. Let C be the number of dollars he has to spend on consumption and let R be the number of hours of leisure that he chooses. Assume that Jie has the utility function U(C, R) = In(C) + In (R). He carms $4 per hour and has 80 hours per week to devote to labor or leisure, and has no income from sources other than labor. a) How many consumptions does he choose? How many hours of leisure does he choose? b) Suppose that Jie's wage rate will rise to $6 per hour from next year. How many hours of leisure per week will he choose next year? You are required to decompose his change in demand into the substitution effect, ordinary income effect and endowment income effect. c) Suppose that Jie will get $4 per hour for the first 35 hours that he works and $6 per hour for every hour beyond 35 hours a week from next year. How many hours of leisure per week will he choose next year?
What is the optimal number of work hours for the student whose utility function for other goods (X) and leisure (L) is U (C,L) = CL, and who has $50 of nonlabor income per week and the possibility to work at $5 per hour. Assume that after studying for class & other activities, the student has only 50 hours per week remaining to choose between work and leisure.
The utility derived by a consumer from the consumption of two commodities is given by the function U (A, B) = 0.5In (A) + 0.5 In (B) where A are the number of units of the first commodity consumed and B are the number of units of the second commodity consumed each month. A unit of the first commodity costs $8 and a unit of the second commodity costs $ 4 using the Lagrange multiplier method determine the optimal quantity of each of the commodities consumed each month given that consumer has $32 to spend on both commodities each month
Aisha is considering how to allocate the next 6 hours of her free time. She could choose between leisure (L) and helping her neighbour with the house chores. If she decides to help her neighbour, she is going to get paid at £25 per hour, which she can then spend on her favourite pizza (P). Suppose the price of pizza is £12.50. Aisha’s preferences for leisure and pizza are given by the following utility function: . U(L,P)= 3L + P MU(L)= 3 MU(P)=1 Write down Aisha’s budget equation and draw the corresponding budget line. Clearly label the axes and calculate the coordinates of the points of intersection of the budget line with each axis. Calculate Aisha’s marginal rate of substitution between leisure and pizza. Explain the concept of MRS and interpret the figure obtained. Find Aisha’s optimal consumption bundle, both algebraically and graphically. Explain your reasoning. Would Aisha’s optimal choice change if she could get a discount on her pizza purchases so that each pizza would cost…
Question 1 Consider a person with the utility function U (C, L) = (1 − α) log C + α log L, where L is leisure time and C is consumption of other goods measured in dollars. The person has V dollars of non-labor income and a wage of w. There are T hours available for either working or leisure. 1. Write down the person’s budget constraint. Draw a graph representing this constraint, taking care to label the axes and key points. 2. What are the person’s marginal utilities for consumption and leisure? What is her marginal rate of substitution between leisure and consumption in terms of C, L, and α? 3. Write down a condition involving the person’s marginal rate of substitution that characterizes her optimal choice. Represent this condition graphically and interpret in words. 4. Solve for the person’s optimal choices of leisure and consumption, L ∗ and C ∗ , in terms of T, V , w, and α. 5. How does L ∗ change as you increase wage w and non-labor income V ? 6. How does C ∗ change as you…
1) Suppose that a person consumes two goods, x and y, in fixed proportions. He or she always consumes 1 unit of x together with 3 units of y no matter what the relative prices are.a) What is the mathematical form for this person's utility function?b) Calculate the Marshallian demand functions for both goods for this person.c) Calculate the indirect utility function and the expenditure function for this person.d) In class we discussed why expenditure functions are concave in prices. Is the expenditure function you calculated in part (c) concave in ???