3. A consumer has 16 hours to allocate a day (8 hours for sleep). She may use L hours for leisure and 16-L hours for work. The wage per hour is W dollars. (a) The consumer values leisure L and money M. Write down her budget constraint. Hint: The amount of money she can get is less or equal to the total wage, which is determined by the time allocated to work and leisure. (b) Suppose the utility function is U(M, L) = min{M, 10L}. What is the demand for leisure L as a function of wage W? If the wage W increases from 6 to 10, what will be the change in the demand for leisure?
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- James has a wage income of $50.000 in the present and $200.000 in the future. His utility is given as U = min (2Cp, Cr) - that is, his utility is the lesser of twice the dollars spent on present consumption or the dollars spent on future consumption. The interest rate is 30%. (A) What is the minimum amount of money James would be willing to accept today to have the interest rate at 40% rather than 30%? Explain and show work (B) What is the maximum amount of money James would pay today to have the interest rate at 30% rather than 40%? Explain and show workJack's marginal utility of consumption is MUc = L - 6, and the marginal utility of leisure is MUL=C-40. Jack does not have any nonlabor income, i.e., V = 0. Jack faces a $48 an hour wage rate. Jack's total number of hours available per week is 150. What is Jack's optimal choice of consumption? (calculate to 2 decimal places)(Short Answers) 1. Jie works in a university. He can work as many hours as he wishes at a wage rate of w. Let C be the number of dollars he has to spend on consumption and let R be the number of hours of leisure that he chooses. Assume that Jie has the utility function U(C, R) = In(C) + In (R). He carms $4 per hour and has 80 hours per week to devote to labor or leisure, and has no income from sources other than labor. a) How many consumptions does he choose? How many hours of leisure does he choose? b) Suppose that Jie's wage rate will rise to $6 per hour from next year. How many hours of leisure per week will he choose next year? You are required to decompose his change in demand into the substitution effect, ordinary income effect and endowment income effect. c) Suppose that Jie will get $4 per hour for the first 35 hours that he works and $6 per hour for every hour beyond 35 hours a week from next year. How many hours of leisure per week will he choose next year?
- An example of income earned but not received is O a. welfare payments. O b. consumption. Ocundistributed profits. O d. Social Security payments.Suppose there are two goods, co ee (C) and tea (T). The consump-tion set is R2+, so both goods can be consumed in arbitrary non-negativequantities.Abdul owns 2000 grams of co ee but does not own any tea. He hasno other wealth. The price of co ee is pC = 2 (in Dhs per gram) andthe price of tea is pT > 0 (in Dhs per gram). Abdul can sell co ee toearn income, which he can then use to buy tea or co ee. He can alsothrow co ee away (at no cost).Abdul's preferences can be represented by the utility functionu(c; t) = -(800 - c)2 - (800 - t)2;where c is the quantity of co ee (in grams) and t is the quantity of tea(in grams).(a) In separate diagrams, illustrate (i) the map of Abdul's indi erencecurves, (ii) Abdul's constraint set.(b) How much co ee and tea does Abdul decide to consume when (i)pT = 2, (ii) pT = 3, and (iii) pT = 4?(c) Illustrate Abdul's demand for co ee as a function of the price of tea (pT > 0) in an appropriate diagram.Question 1 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…
- 5. Rhoda’s preferences for consumption and leisure can be expressed as U(C, L) = (C - 100) × (L - 40). There are 110 (non-sleeping) hours in the week available to split between work and leisure. Rhoda earns 10 GHS per hour after taxes. She also receives 320 GHS worth of support from her parents each week regardless of how much she works.a. What will be Rhoda’s marginal utility of leisure and her marginal utility of consumption?b. What is Rhoda’s marginal rate of substitution when L = 100 and she is on her budget line? c. Find Rhoda’s optimal amount of consumption.5. Rhoda’s preferences for consumption and leisure can be expressed as U(C, L) = (C - 100) × (L - 40). There are 110 (non-sleeping) hours in the week available to split between work and leisure. Rhoda earns 10 GHS per hour after taxes. She also receives 320 GHS worth of support from her parents each week regardless of how much she works.a. What will be Rhoda’s marginal utility of leisure and her marginal utility of consumption?b. What is Rhoda’s marginal rate of substitution when L = 100 and she is on her budget line?c. Find Rhoda’s optimal amount of consumptionTerry’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
- What 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?Monthly income = salary of 1200 and a gov welfare payment of 800 Y= 2000 Needs to use this income for food and goods quantity of food = qf quantity of goods= qd Price of food = 1 Price of goods = 2 1) Draw budget line, qf on vertical axis and qd on horizontal one 2) The welfare payment is now given in the form of food stamps. 1200 can be spent on food and other goods, food stamps can only be used to purchase food. The prices of food and other goods remain the same. budget line with the food stamps, measuring on the vertical axis and on the horizontal axis. Label all critical points on the budget line. Show you are at least as well off under the cash welfare payment as under the food stamps. Here is how: Depict the budget lines in 1. and 2a. in a single diagram and superimpose indifference curve(s) to show the optimal consumption bundle(s). You will need two such diagrams to illustrate two different cases: optimal consumption bundle is the same under the cash welfare…A worker views leisure and income as “goods” and has an opportunity to work at an hourly wage of $15 per hour. a. Illustrate the worker’s opportunity set in a given 24-hour period. b. Suppose the worker is always willing to give up $11 of income for each hour of leisure. Do her preferences exhibit a diminishing marginal rate of substitution? How many hours per day will she choose to work?