Two individuals, Sam and Barb, derive utility from the hours of leisure (L) they consumeand from the amount of goods (G) they consume. In order to maximize utility, they needto allocate the 24 hours in the day between leisure hours and work hours. The price of agood is equal to $1.00 and the price of leisure is equal to the hourly wage. We observethe following information about the choices that the two individuals make:Q16-14-12-SamBarbSamBarbPrice of Price10-LLof L (hours) (hours) G ($)G ($)G8-713107798113211110121541157142551506-Graphically, illustrate Sam's leisure demand curve and Barb's leisure demand curve.4-1.) Using the line drawing tool, draw Sam's leisure demand curve. Label this line D'2-2) Using the line drawing tool, draw Barb's leisure demand curve. Label this line D'0-04в8101214Leisure (hours)Carefully follow the instructions above, and only draw the required objects.Wage (S)

To determine how there can be fewer leisure activities spend would be associated with the more hours…

Answered: Two individuals, Sam and Barb, derive…

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter6: Demand Relationships Among Goods

Section: Chapter Questions

Problem 6.9P

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Recent research confirms that the demand for cigarettes is not only inelastic, but it also indicates that smokers with incomes in the lower half of all incomes respond to a given price increase by reducing their purchases by amounts that are more than four times as large as the purchase reductions made by smokers in the upper half of all incomes. How can the income and substitution effects of a price change help explain this finding?
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 increase wage…
Janie works for an accounting firm. Her wage increased from $30 per hour to $40 per hour. She can work up to 50 hours each week. The table below shows her utility from different levels of leisure and income. Before her raise, if Janie decreases her hours of work from 30 to 20 hours per week, the marginal utility gain from having more leisure is: Hours of Leisure Total Utility from Leisure Income Total Utility from Income 0 0 0 0 10 29 300 40 20 54 400 72 30 75 600 96 40 86 800 108 50 92 900 116 1200 120 1500 122 1600 124 2000 125 Question 4 options: 29 21 13 7
4. Two individuals, Amir and Budi, consume two goods, clothes (X) and shoes (Y). The utility functions for the two individuals are given as: Utility function of Amir, UA = 15X0.25Y0.75Utility function of Budi, UB = 25X0.5Y0.5 The current price for clothes (Px) is Rp 100,000 and the current price for shoes (PY) is Rp 150,000 a. Determine marginal rate of substitution (MRSXY)between clothes (X) and shoes (Y) for Amir and Budi! Please explain. b. Amir is currently consuming 5 units of clothes (X) and 10 units of shoes (Y), whereas Budi is consuming 12 units of clothes (X) and 8 units of shoes (Y). At this current consumption, have Amir and Budi reached the efficient allocation of clothes and shoes? If they have, explain why. If they have not, calculate the optimal allocation and explain. c. Considering the relative price between of clothes and shoes, at the current consumption, have Amir and Budi reached exchange equilibrium? Please explain d. Use the Edgeworth Box to illustrate the…
4. Two individuals, Amir and Budi, consume two goods, clothes (X) and shoes (Y). The utility functions for the two individuals are given as: Utility function of Amir, UA = 15X0.25Y0.75Utility function of Budi, UB = 25X0.5Y0.5 The current price for clothes (Px) is Rp 100,000 and the current price for shoes (PY) is Rp 150,000 a. Determine marginal rate of substitution (MRSXY)between clothes (X) and shoes (Y) for Amir and Budi! Please explain. b. Amir is currently consuming 5 units of clothes (X) and 10 units of shoes (Y), whereas Budi is consuming 12 units of clothes (X) and 8 units of shoes (Y). At this current consumption, have Amir and Budi reached the efficient allocation of clothes and shoes? If they have, explain why. If they have not, calculate the optimal allocation and explain. c. Considering the relative price between of clothes and shoes, at the current consumption, have Amir and Budi reached exchange equilibrium? Please explain d. Use the Edgeworth Box to illustrate the…
Suppose that each week Fiona buys 16 peaches and 4 apples at her local farmer's market. Both kinds of fruit cost $1 each. From this we can infer that: If Fiona is maximizing her utility, then her marginal utility from the 16th peach she buys must be greater than her marginal utility from the 4th apple she buys. Fiona is not maximizing her utility. If Fiona is maximizing her utility, then her marginal utility from the 16th peach she buys must be equal to her marginal utility from the 4th apple she buys. The law of diminishing marginal utility does not hold for Fiona.
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…
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.
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 attends college and works part-time in a drug store. She can work up to 40 hours per week and is paid $9 per hour. With her schoolwork and other responsibilities, she only has 40 hours per week total to devote to work and leisure. The following table shows her utility from different levels of leisure and income. Hours of Leisure Total Utility from Leisure Marginal Utility of Leisure Work Hours Income Total Utility from Income Marginal Utility from Income 5 18 5 45 35 10 34 10 90 59 15 48 15 135 77 20 56 20 180 86 25 60 25 225 92 30 65 30 270 98 35 69 35 315 103 40 72 40 360 107 Terry decides to decrease her work hours from 20 to 10. What will be her total utility from both leisure and income when working 10 hours per week?
Terry attends college and works part-time in a drug store. She can work up to 40 hours per week and is paid $9 per hour. With her schoolwork and other responsibilities, she only has 40 hours per week total to devote to work and leisure. The following table shows her utility from different levels of leisure and income. Hours of Leisure Total Utility from Leisure Marginal Utility of Leisure Work Hours Income Total Utility from Income Marginal Utility from Income 5 18 5 45 35 10 34 10 90 59 15 48 15 135 77 20 56 20 180 86 25 60 25 225 92 30 65 30 270 98 35 69 35 315 103 40 72 40 360 107 Terry decides to decrease her work hours from 20 to 10. 8. What would be marginal utility loss from less income?
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…

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