Robinson Crusoe's preferences over coconut consumption, C, and leisure, R, are represented by the utility function U(C, R) = CR. There are 48 hours available for Robinson to allocate between labor and leisure. Let Robinson's production function be C = √L. Find Robinson's L.
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- (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?Elsa lives alone on an island with two goods, bananas and fresh water. Her utility function is U = 4BW where B is the amount of bananas she consumes and Wthe amount of water. Her production function for bananas is B=Lg where Lg is the amount of labour time she devotes to bananas. Her production function for water is W = Lwwhere Lwis the amount of labour time she devotes to water. If the total time she has available is 70, what should she do to maximize her utility? (Enter your answers in whole numbers.) LB= Lw=[John works in a shoe factory. He can work as many hours per day as he wishes at a wage rate w. Let C be the amount of dollars he spends on consumer goods and R. be the number of hours of leisure that he chooses. John's preferences are represented by U(C, R) = CR utility function Question 2 Part a John earns $8 an hour and has 18 hours per day to devote to labor or leisure, and he has $16 of nonlabor income per day. Draw John's indifference curves, budget constraints and solve for his optimal consumption and leisure choices.
- An individual values both consumption and leisure. Suppose the individual has 1600 hours per week they can allocate between leisure and work. IF the individual works, they make a wage of $25 per hour. The individual's utility function is given as a function of leisure time, L and consumption, c: U(L, c) = L^(1/2)c ^ (1/2) a) Draw the individual's budget constraint for leisure and consumption. b) How much leisure time will the individual have when utility maximizing? c) Consider a Universal Basic Income policy like the one proposed by Andrew Yang that would give all individuals a lump -sum, unconditional cash transfer of $1,000 each month. How much leisure time will the individual have when utility maximizing with the cash transfer? d) Now suppose, instead of a cash transfer, a minimum wage of $40 per hour is implemented. How much leisure time will the individual have when utility maximizing with the cash transfer? e) What change in leisure time can be attributed to the substitution…Elsa lives alone on an island with two goods, bananas and fresh water. Her utility function is U = BW where B is the amount of bananas she consumes and W the amount of water. Her production function for bananas is B = 6LB where LB is the amount of labour time she devotes to bananas. Her production function for water is W = 2LW where LW is the amount of labour time she devotes to water. If the total time she has available is 10, what should she do to maximize her utility?Consider Bundle A: (B, M) = (12 loaves, 16 gallons). If bread is the horizontal axis good, what is Rhea's marginal rate of substitution at bundle A?
- John is trying to decide how to divide his time between his job as a stocker in the local grocery store, which pays $7/hr for as many hours as he chooses to work, and cleaning windows for the businesses in downtown. He makes $2 for every window he cleans. John is indifferent between the two tasks, and the number of windows he can clean depends on how many hours he cleans a day, as shown in the table below: Cleaning time (hr/day) Total numbers of windows cleaned 0 0 1 7 2345 11 14 16 17 What is John's per-window reservation price to justify the 4th and 5th hours of cleaning windows? A. $7 and $7.5 respectively B. $2 and $3.5 respectively C. $3.5 and $7 respectively D. $11 and $14 respectivelyIf the consumer's non-labor income increases while wages remain unchanged, what will happen to the budget line? A) The budget line shifts inward without a change in slope. B) The budget line rotates inward from the intercept on the horizontal axis. C) The budget line rotates outward from the intercept on the vertical axis. D) The budget line shifts outward without a change in slope. An optimum labor-leisure that occurs as a corner solution A) can be an equilibrium in the aggregate economy. B) includes the consumption of only one good. C) cannot exhaust the budget constraint. D) includes the exact same amounts of each good. ) If a firm is a price taker in both the labor market and the output market, it will A) hire labor until the marginal product of labor equals the output price. B) hire labor until the marginal product of labor equals zero. C) earn zero economic profit in the short run. D) hire labor until the marginal product of labor equals the wage rate.Trey works as a waiter for Puff & Stuff catering for a wage of w 11. In addition to his %3D labor income from waiting, Trey makes supplemental income with his household production time by streaming video games on Twitch. He doesn't have any unearned income (V=0). Trey's preferences over consumption and household production are given by the utility function below: u (H, C) = 2\H + VC Assume Trey has 16 hours each day to split between household production and consumption, if he spends 10% of his time at home streaming and earns an hourly rate of P = 7, what will be his optimal allocation of household production? (hint: assume that Trey's utility-max condition remains unchanged and his supplemental income will only impact his budget constraint)
- A college football coach says that given any two linemen A and B, he always prefers the one who is bigger and faster. Is this preference relation transitive? Is it complete? The production function for puffed rice is given by q , where q is the number of boxes produced per hour, K is the number of puffing guns used each hour, and L is the number of workers hired each hour. Calculate the q = 1,000 isoquant for this production function and show it on a graph. If K = 10, how many workers are required to produce q = 1,000? What is the average productivity of puffed-rice workers? Suppose technical progress shifts the production function to , answer parts a and b for this new situation.Ana decides every day how many hours to work and how much beef to consume. She spends all income earned from work each day on consumption of beef. Her utility function for free time (t, 24 hours minus hours worked) and consumption (y) is: U(t,y)=2t^1/2 + y The price per unit of beef consumed is 4 and her hourly wage is 1. Using a diagram and appropriate algebra, explain what Ana’s optimal number of hours work and units of beef consumed are each day. Ana reads a book about the impact of beef consumption on climate change and realises that there is a cost to society of her beef consumption. She takes account of this impact on society in her own decisions, incorporating a disutility of -0.03y per unit of beef consumed. She still only consumes beef and spends all income earned each day on this consumption. Explain, using a diagram and appropriate algebra, how recognition of the impact of her consumption choice on climate change impacts on Ana’s daily free time and beef…An economy is endowed with 100 units of labor, and the production functions x = 2Lx and y = 4Ly. The utility function for this economy is u(x,y) xy. What is the optimal basket (x,y) for this economy %3D to produce? O (10, 380) O (50, 100), O (100, 200) O (150, 150)