Suppose that there are, at most, 112 hour of leisure each week. In a fully labeled diagram in leisure-income space, depict graphically the following situation:
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Suppose that there are, at most, 112 hour of leisure each week. In a fully labeled diagram in leisure-income space, depict graphically the following situation:
a) if the wage rate is $10/hour, the optimal work-week would be 40 hours;
b) if the wage rate is $15/hour, the optimal work-week would be 80 hours;
c) if the wage rate is $20/hour, the optimal work-week would be 60 hours.
d) from the above information, does it appear that the worker has a target income? Explain what the term “target income” means and indicate what does it appears to be in this example.
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- 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.Illustrate (using a labor-leisure choice diagram) how a firm may induce a typical employee to lengthen his work week voluntarily by paying him premium wage rates for overtime hours.Consider the problem of a consumer who chooses between consuming goods and enjoying leisure in the current and future periods. Denote the consumption and leisure in the current period as C and l, and the consumption and leisure in the future period as C′ and l′, respectively. The preference is summarized by the following utility function: U(C,C′,l,l′)=lnC+ψlnl+β(lnC′ +ψlnl′). This individual is endowed with h units of time in each period. Wage rate per unit of labour time is w and w′ in the current and future period. In addition, the consumer receives profit transfer π and π′ and pays lump-sum taxes T and T′ in the current and future periods. Denote the saving in the current period as Sp. Answer the following questions. Derive the life-time budget constraint of this consumer. Set up the consumer’s problem. Solve for consumption (C and C′), leisure (l and l′), and saving (Sp). How does an increase in wage rate w affect C, Sp, and l?
- 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.Refer to the labor–leisure budget constraint shown to answer the questions. This curve shows trade-offs between income and leisure that must be made over the course of one day. How much does this person earn per hour? $ At point A, how many hours of labor are selected? hourshours At point A, how many hours of leisure are selected? hoursWhat is the budget line for consumption (C) and leisure (L) if a person faces a constant wage of $12 per hour, there are 110 hours in the week to work, and she receives nonlabor income of $300 per week?
- 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.An individual's decision to supply her labor or to spend her time in leisure activity is known as the labor-leisure tradeoff. True or false?Susan obtains utility by consuming carrots C and enjoying leisure L. Suppose that she has a daily non-wage income Y of £100 and is paid a fixed hourly wage rate of £10 for every hour she works in a local coffee shop. Assume that Susan is a utility maximiser and is free to choose x hours of work per day where 0 ≤ x ≤ 10. Assume also that the unit price of C is £1. a) Suppose that L is measured on the horizontal axis and C on the vertical axis. Use these axes to draw the set of all C and L combinations that Susan can choose from. Write down Susan’s budget equation. b) Suppose that Susan’s preferences over carrots and leisure are expressed by the following utility function: U(C,L) = min{C, 10L}. Calculate Susan’s optimal consumption bundle, both algebraically and graphically. Calculate the value of MRS at the optimal choice. c) Suppose instead that Susan’s preferences are such that indifference curves in the L-C space are strictly convex to the origin, and that she chooses to work 5…
- 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.Consider a couple (a husband and a wife) that jointly represents their collective preferences between combinations of household production time (X) and purchased goods and services (Y) according to the formula W = X2Y, where W represents the level of welfare. Suppose the maximum time available in a day is 16 hours and currently the wife devotes 6 hours to market work (H) at a wage of $16 per hour. a. What is the level of welfare associated with the wife’s current situation? b. How much additional purchasing power would the wife contribute if her market work hours increased to 8? c. How much of an increase in purchased goods and services would be necessary to compensate for the additional 2 hours of lost household production? d. Should this couple choose to have the wife increase her market work by 2 hours? e. If this couple is raising a child, suppose that combinations of household production and purchased goods are now ranked according to the formula U = X3Y. Would the additional 2…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.