2. Suppose Jill derives utility from not only consuming goods, but also from enjoying leisure time. Let her utility function be defined as follows: U=C.25.R.75 where C is a consumption good that can be bought at a price of $1 and R is hours of leisure (relaxation) consumed per day. There are 24 hours in a day and leisure is defined as time spent not working. Jill has a job that pays $w per hour, a trust fund that pays her $M per day, and she can work any number of hours per day, L, she desires. C, consumption good; R, Leisure (relaxation); L, labor M, non-wage income; w, wage rate. a. Derive her labor supply function? b. Assume M = $100, at what wage is her quantity supplied of hours = 0?

2. Suppose Jill derives utility from not only consuming goods, but also from enjoying leisure time. Let her utility function be defined as follows: U=C.25.R.75 where C is a consumption good that can be bought at a price of $1 and R is hours of leisure (relaxation) consumed per day. There are 24 hours in a day and leisure is defined as time spent not working. Jill has a job that pays $w per hour, a trust fund that pays her $M per day, and she can work any number of hours per day, L, she desires. C, consumption good; R, Leisure (relaxation); L, labor M, non-wage income; w, wage rate. a. Derive her labor supply function? b. Assume M = $100, at what wage is her quantity supplied of hours = 0?

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
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.
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…
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’*?
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…
John likes Coca-Cola. After consuming one Coke, John has a total utility of 10 utils. After two Cokes, he has a total utility of 25 utils. After three Cokes, he has a total utility of 50 utils. Does John show diminishing marginal utility for Coke, or does he show increasing marginal utility for Coke? Supposethat John has $3 in his pocket. If Cokes cost $1 each and John is willing to spend one of his dollars on purchasing a first can of Coke, would he spend his second dollar on a Coke, too? What about the third dollar? If John’s marginal utility for Coke keeps on increasing no matter how many Cokes he drinks, would it be fair to say that he is addicted to Coke?
7. A consumer has preferences for coffee and pancakes that are complete, continuous, transitive, monotonic, and convex. At her current consumption bundle on the budget line, you could take away a maximum of 2 cups of coffee if you give her 5 extra pancakes without changing her utility. The price of a cup of coffee is $4, and the price of a pancake is $1. Assume you graph pancakes on the X-axis and coffee on the Y-axis. At the current consumption bundle, the bang per buck is higher for pancakes than coffee, and the consumer’s indifference curve is flatter than her budget line. a. True b. False 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.
Katie’s preferences for consumption and leisure can be expressed as U(C, L) = (C – 80) x (L – 40) This utility function implies that Katie’s marginal utility of leisure is C – 80 and her marginal utility of consumption is L – 40. There are 110 hours in the week available to split between work and leisure. Katie earns $15 per hour after taxes. She also receives $200 worth of assistance benefits each week regardless of how much she works. Graph Katie’s budget line. What is Katie’s marginal rate of substitution when L = 70 and she is on her budget line? What is Katie’s reservation wage? Find Katie’s optimal amount of consumption and leisure.
Given an individual’s current consumption patterns, we know that the person is consuming in such a manner that he is maximizing his satisfaction. Given a decrease in the price of one of the goods he normally purchases, what will happen to the consumer’s total satisfaction and to the marginal utilities connected with the consumption of this particular good. a) His overall satisfaction will increase, but his satisfaction from the last unit consumed of the good with a decreased price will decrease. b) His overall satisfaction will decrease and his satisfaction from the last unit consumed of the good with a decreased price will decrease. c) His overall satisfaction will increase and his satisfaction from the last unit consumed of the good with a decreased price will increase. d) His overall satisfaction will decrease and his satisfaction from the last unit consumed of the good with a decreased price will increase. e) We cannot tell about the changes in his total utility or his marginal…
During any year, I can consume any amount that doesnot exceed my current wealth. If I consume c dollars duringa year, I earn ca units of happiness. By the beginning of thenext year, the previous year’s ending wealth grows by afactor k.a Formulate a recursion that can be used to maximizetotal utility earned during the next T years. Assume Ioriginally have w0 dollars.b Let ft(w) be the maximum utility earned during years t, t 1, . . . , T, given that I have w dollars at the be-ginning of year t; and ct(w) be the amount that should be consumed during year t to attain ft(w). By workingbackward, show that for appropriately chosen constantsat and bt,ft(w) btwa and ct(w) atwInterpret these results.
. Suppose that initially, bread is $2 per loaf,and cake is $2 per slice. Marie Antoinettehas $18 to spend on these items each week.At this income and those prices, Marie consumes 5 loaves of bread and 4 slices of cake.Then, the price of bread DECREASES to$1 per loaf. (The price of cake is still $2.)IF Marie’s budget had also fallen to $13so that she could still just afford her original bundle, she WOULD choose to spendthose $13 on 7 loaves of bread and 3 slicesof cake.But since Marie still has her original $18budget, she actually chooses to buy 4loaves of bread and 7 slices of cake afterthe price change.When the price of bread fell from $2 to $1,what was the substitution effect on Marie’sdemand for bread?
Anna is a Vancouverite who starts off her day drinking either a coffee or a bubble tea. From her part-time job, she has earned P15 that she can spend on either coffee or bubble tea over a month. A coffee costs P1, and a bubble tea costs P1. Draw her budget line, with bubble tea on the y-axis. If she chooses to drink only coffee or only bubble tea for one month, how many of each can she drink?