How would you demonstrate part c) diagramatically 6. 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. b) Assume that your optimal choice of consumption and leisure is to work 8 hours per day. Illustrate this choice diagrammatically using the feasible set and indifference curves. c) Use indifference curves and the feasible set to show why, given the properties of the optimal choice in part b), it is not optimal to work, say, 10, or 6 hours per day.

How would you demonstrate part c) diagramatically 6. 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. b) Assume that your optimal choice of consumption and leisure is to work 8 hours per day. Illustrate this choice diagrammatically using the feasible set and indifference curves. c) Use indifference curves and the feasible set to show why, given the properties of the optimal choice in part b), it is not optimal to work, say, 10, or 6 hours per day.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter4: Utility Maximization And Choice

Section: Chapter Questions

Problem 4.14P

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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. b) Assume that your optimal choice of consumption and leisure is to work 8 hours per day. Illustrate this choice diagrammatically using the feasible set and indifference curves.
Answer please with added diagrams b) Assume that your optimal choice of consumption and leisure is to work 8 hours per day. Illustrate this choice diagrammatically using the feasible set and indifference curves. c) Use indifference curves and the feasible set to show why, given the properties of the optimal choice in part b it is not optimal to work, say, 10, or 6 hours per day.
Q3. Consider a utility function with one consumption good q1 and one type of leisure q2 c) Show mathematically and diagrammatically the decomposition of totaleffect.
Q11. Consider a utility function: U (F,C) = FC so MU_F = C and MU_C = F. Suppose as Case A, Total income is $120 and per unit prices of Food (F) and Cloth (C) are $2 and $10, respectively. a. What is the value of MRS at the optimal point and what does this value mean? b. What is the optimal consumption bundle i.e (F*,C*)? c. Plot the budget line and clearly depict the point of optimality in the F (x-axis)-C (y-axis) space.
Suppose a person can work up to 80 hours per week at a pre-tax wage of $20 per hour but faces a constant 20% payroll tax. Assume that under these conditions the person maximizes utility by choosing to work 50 hours each week. The government proposes a negative income tax so that everyone receives $300 per week regardless of how much they work. To pay for the negative income tax, the payroll tax would be increased to 50%. Using the labor-leisure model, graphically show whether a person would be better off if the negative income tax is adopted and indicate whether hours worked increases or decreases due to the policy.
How would you demonstrate part b) diagramatically 6. 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. a) 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). b) Assume that your optimal choice of consumption and leisure is to work 8 hours per day. Illustrate this choice diagrammatically using the feasible set and indifference curves.
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.
Q9. Consider a utility function: U (F,C) = FC so MU_F = C and MU_C = F.Suppose as Case X, Total income is $100 and per unit prices of Food (F) and Cloth (C) are $2 and $15, respectively. a. What is the value of MRS at the optimal point and what does this value mean? b. What is the optimal consumption bundle i.e (F*,C*)? c. Plot the budget line and clearly depict the point of optimality in the F (x-axis)-C (y-axis) space. d. Now assume a new Case Y, Pc' = $10, holding all else the same, do the same analysis (parts a-c) and contrast your answers to Case X. For part c, you should draw old (Case X) and new (Case Y) budget lines/point of optimality.
The graph below shows David’s preferences for leisure and consumption. Draw three budget constraints in the graph below. One if David’s wage is $10 per hour (BC1), another if his wage is $20 per hour (BC2) and a third for if his wage is $30 per hour (BC3). Show the optimal combination of leisure and consumption for each of the three budget constraints. Label the optimal amount of Leisure, L1, L2 & L3, and label the optimal amounts of consumption C1, C2 & C3.
2. Utility maximization - Trading off labor and leisure The indifference curves on the following graph show Simone’s preferences for leisure and consumption for increasing levels of utility, such that her utility increases in both consumption and leisure. Assuming that Simone spends 68 hours each week sleeping, she has a maximum of 100 hours available to her for leisure if she does not work at all. Initially, she works 50 hours (and thus has 50 hours of leisure) and earns $400 per week. Use the grey point (star symbol) to indicate Simone’s initial leisure/consumption bundle. Dashed drop lines will automatically extend to both axes. [Please see the image attached] Now, suppose that Simone is laid off, but she is eligible to collect unemployment benefits of $350 per week. Use the black point (cross symbol) to represent Simone’s unemployment point on the previous graph when she consumes $350 per week and has 100 hours of leisure. Suppose that after a month of…
Q6. Consider a utility function: U (F,C) = FC so MU_F = C and MU_C = F. Suppose as Case 1, Total income is $100 and per unit prices of Food (F) and Cloth (C) are $2 and $10, respectively. a. What is the value of MRS at the optimal point and what does this value mean? b. What is the optimal consumption bundle i.e. (F*,C*)? c. Plot the budget line and clearly depict the point of optimality in the F (x-axis)-C (y-axis) space. d. Now suppose Case 2, where assuming if income increases to $120, holding all else the same, do the same analysis (parts a-c) and contrast your answers to Case 1. For part c, you should draw old (Case 1) and new (Case 2) budget lines/point of optimality.
Consider an individual who receives utility from consumption, c, and leisure, l. The individual has L time to allocate to work, n, and leisure. The individual’s consumption is a function of how much he works. In particular, c = root n. The individual’s maximization problem is max U =ln(c)+θl subject to c = √n n+l=L where θ > 0. Solve the maximization problem. Hint: Substitute both constraints into the objective function.