Let us denote Ben’s daily hours of work by H, and his hours of leisure by N = 24 − H. Suppose that Ben’s only source of income is wages for hours worked. He derives utility from leisure, N, and from the consumption of a composite good, Y. The price of Y is 1. Ben’s utility function is U(Y, N) = ln(Y) + ln(N). (a) Suppose the wage rate is $60 per hour. Write down Ben’s constraint with Y and N as the choice variables.

Let us denote Ben’s daily hours of work by H, and his hours of leisure by N = 24 − H. Suppose that Ben’s only source of income is wages for hours worked. He derives utility from leisure, N, and from the consumption of a composite good, Y. The price of Y is 1. Ben’s utility function is U(Y, N) = ln(Y) + ln(N). (a) Suppose the wage rate is $60 per hour. Write down Ben’s constraint with Y and N as the choice variables.

Micro Economics For Today

10th Edition

ISBN:9781337613064

Author:Tucker, Irvin B.

Publisher:Tucker, Irvin B.

Chapter6: Consumer Choice Theory

Section6.A: Indifference Curve Analysis

Problem 1SQP

See similar textbooks

Similar questions

Terry’s utility function over leisure (L) and other goods (Y ) is U(L, Y ) = Y + LY. The associated marginal utilities are MUY = 1 + L and MUL = Y. He purchases other goods at a price of $1, out of the income he earns from working. Show that, no matter what Terry’s wage rate, the optimal number of hours of leisure that he consumes is always the same. (a)   What is the number of hours he would like to have for leisure?  Determine the MRS of leisure for labour (b) Draw a leisure-influenced labor curve
Terry’s utility function over leisure (L) and other goods (Y) is U (L, Y) = Y + LY. The associated marginal utilities are MUY = 1 + L and MUL = Y. He purchases other goods at a price of $1, out of the income he earns from working. Show that, no matter what Terry’s wage rate, the optimal number of hours of leisure that he consumes is always the same. (a)  What is the number of hours he would like to have for leisure? (b)  Determine the MRS of leisure for labour (c)  Draw a leisure-influenced labor curve
Terry’s utility function over leisure (L) and other goods (Y ) is U(L, Y ) = Y + LY. The associated marginal utilities are MUY = 1 + L and MUL = Y. He purchases other goods at a price of $1, out of the income he earns from working. Show that, no matter what Terry’s wage rate, the optimal number of hours of leisure that he consumes is always the same. (a)   What is the number of hours he would like to have for leisure? (b)  Determine the MRS of leisure for labour Draw a leisure-influenced labor curve
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.
The utility that Elena receives by consuming food F and clothing C is given by U(F,C) = FC + F. Food costs £1 per unit, and clothing costs £2 per unit. Elena's income is£22. MUF = C+1 and MUc = F.(i) Define the term Marginal Rate of Substitution (MRS). (ii) Find the utility maximizing values of C and F for the numerical values given above(Hint: You can assume interior solution). (ili) Now suppose that price of C and Elena's income remain unchanged at £2 per unitand £22, respectively, while the price of F varies. Find the equation of the demand forF as a function of the unit price of F (PF).
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.
An individual values both consumption and leisure. Suppose the individual has 1600 hours per week they can allocate between leisure and work. IF the individual works, they make a wage of $25 per hour. The individual's utility function is given as a function of leisure time, L and consumption, c: U(L, c) = L^(1/2)c ^ (1/2) a) Draw the individual's budget constraint for leisure and consumption. b) How much leisure time will the individual have when utility maximizing? c) Consider a Universal Basic Income policy like the one proposed by Andrew Yang that would give all individuals a lump -sum, unconditional cash transfer of $1,000 each month. How much leisure time will the individual have when utility maximizing with the cash transfer? d) Now suppose, instead of a cash transfer, a minimum wage of $40 per hour is implemented. How much leisure time will the individual have when utility maximizing with the cash transfer? e) What change in leisure time can be attributed to the substitution…
An individuals utility function is given by U = 340x1 + 960x2 + 2x, x2 - 2x – x3/2, when the weekly amount of leisure is x = 132 and earned income is x2 = 760 answer the following 1. The marginal utility of x is 2. The marginal utility of x2 is 3. Use the small increments formula to estimate the change in the utility when x decreases by 1 and x2 increases by 4. The change= 4. Does the law of diminishing marginal utility hold? 5. The MRCS at a given values is Enter non-integer numerical values as decimals to at least 3 decimal places. Note: you must use a . and not, for a decimal point.
Find the marginal utility of an additional unit of good z for a consumer with utility function u (a, y) = zi yi when their current consumption level is 2 and y = 16.
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. (MUL = 3, MUp = 1). a) 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. d) Would Aisha's optimal choice change if she could get a discount on her pizza purchases so that each pizza would cost £5? Explain. e) Would Aisha's optimal choice change (as compared to c), if she could get a discount on her pizza purchases so that each additional pizza beyond the first two, cost £5? (In other words, the first two pizzas need to…
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. (MUL = 3, MUp = 1). a) 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. b) Calculate Aisha's marginal rate of substitution between leisure and pizza. Explain the concept of MRS and interpret the figure obtained. c) Find Aisha's optimal consumption bundle, both algebraically and graphically. Explain your reasoning. d) Would Aisha's optimal choice change if she could get a discount on her pizza purchases so that each…
Suppose Vivi’s utility function over tea and crumpets are given by U(T, C) = min(T, 3C). (a) Graphically derive Vivi’s demand for tea when her income is $60 and the price of crumpets is $2. Do this by showing her optimal consumption (exact numbers) at three different values for the price of tea. (b) What is the formula for Vivi’s demand function for crumpets when her income is $60, the price of crumpets is pC, and the price of tea is pT ? 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.