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- 4. A consumer’s utility function over leisure and consumption is given by u(L, Y) =LY. Wage rate is w and the price of the composite consumption good is p = 1. (a) Suppose w = 10. Find the optimal leisure - consumption combination. (b) Suppose the overtime wage law is passed so that the firm must pay 1.5 times the normal wage for hours worked beyond the first 8 hours. Find the effect on the hours worked. Decompose the effect into substitution effect and income effect4. Steve's utility funetion over leisure and consumption is given by u(L,Y) = min (3L, Y). Wage rate is w and the price of the composite consumption good is p = 1. (a) Suppose w = 5. Find the optimal leisure - consumption combination. What is the amount of hours worked? (b) Suppose the overtime law is passed so that every worker needs to be paid 1.5 times their current wage for hours worked beyond the first 8 hours. Will this law induce Steve to work more hours? If so, how many? If not, explain.5. Cindy gains utility from consumption C and Leisure L. Then most leisure she can consume in any given week is 110 hours. Her utility function is U (C, L) = C × L. Cindy receives $660 each week from her great-grandmother. (a) Find her marginal rate of substitution |M RS|. (b) Find her reservation wage. (c) Interpret the reservation wage.
- 3. John's utility function is U(C, L) = C1/2L!/2. The most leisure time he can consume is 110 hours. His wage rate is $10. Find John's optimal amount of consumption and hours for leisure and work.(5) Steven has non-labor income each week of $500. He can work up to 100 hours per week foran hourly wage of $10 per hour. His utility for recreation (R) and consumption (C) is given byU(R, C) = 2R2C. What is Steven’s reservation wage if the price of consumption is unity?(a) $30(b) $40(c) $50(d) $60(e) None of the aboveThis problem considers the decisions of a consumer whose preferences are given by u(C,1)=C+4 lnl, in which C' is the quantity of consumption and I is the quantity of leisure. The consumer faces two constraints. The time constraint is given by 1 + N³ = 1 with NS as the time spent working (or the labor supply). The main advantage of working is the wages consumers receive. Consumers take wages as given (outside of their control) and obtain wage income equal to wN³. The budget constraint is C wNsT, with π as real dividend income and T as the real = lump-sum taxes paid to government.
- a) Chika has calculated the marginal utility that she derives from her paid employment and from leisure. This is presented in table below. In her ideal world, where she could work as few or as many hours as she wished, how would she allocate her sixteen waking hours? (She does need to sleep.) Hours 1 2 3 4 5 6 7 8 9 10 MU Paid Employment 105 95 85 75 65 55 45 35 25 15 MU Leisure 100 90 80 70 60 50 40 30 20 10 hours working and b) Unfortunately, Chika begins to realize that unless she gets an education she will not enjoy a high salary and therefore, will not be able to afford more leisure time. She therefore decides to spend six hours each day studying (in addition to her eight hours of sleep). How will she now divide the remaining hours between work and leisure? hours working and hours leisure. hours leisure.cook -int ences a) Chika has calculated the marginal utility that she derives from her paid employment and from leisure. This is presented in table below. In her ideal world, where she could work as few or as many hours as she wished, how would she allocate her sixteen waking hours? (She does need to sleep.) Hours 1 2 3 4 5 6 7 8 9 10 MU Paid Employment 80 75 70 65 60 55 50 45 40 35 MU Leisure 120 110 100 90 80 70 60 50 40 30 9 hours working and 40 hours leisure. b) Unfortunately, Chika begins to realize that unless she gets an education she will not enjoy a high salary and therefore, will not be able to afford more leisure time. She therefore decides to spend six hours each day studying (in addition to her eight hours of sleep). How will she now divide the remaining hours between work and leisure?! hours working and hours leisure. Help Save C(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?
- Suppose your weekly allowance from your parents is $100 and your part-time job pays $10 per hour. The slope of the line plotting the relationship between the hours worked per week (the horizontal axis) and the income per week (the vertical axis) is $. (Enter your response as an integer.) Suppose you start with 10 hours of part-time work and then decide to increase your time working by 3 hour(s). By how much will your weekly income increase? $. (Enter your response as an integer.) Suppose you start with 10 hours of work and then decide you need additional income of $20 per week. How many additional hours would you have to work? hours. (Enter your response as an integer.)7. An individual's utility function is given by U =1000x, +450x, +5 x,x, -2x - x where x, is the amount of leisure measured in hours per week and x, is income earned measured in cedis per week. Determine the value of the marginal utilities, when x, = 138 and x, = 500. Hence estimate the change in utility if the individual works for an extra hour, which increases earned income by GH¢15 per week. Does the law of diminishing utility hold for this function?1) Sharon spends her time (20h) between leisure (L) and work and he consume Y product from his working income (Py=1). Assume that she gets W$ per hour of working and has the following utility function: U (L, Y) =LY+2L C. vv). e. VS What will happen to L, Y and H if the wage per hour (W) will decrease? d. How would your answer to the previous question (c) will change if Sharon has a fixed amount of money (Wo) that is not connected to W? If Sharon has the following utility function: U= L³+ Y², is it possible that she will choose not to work at all? Explain and show the condition for your result if exists. |||