Q1 A representative household receives utility from consumption c and supplying labor l: u(c, 1) = √c+y√√1-1 As usual, is the share of time that the household spends working. The household owns an exogenously determined amount of capital, earns the nominal rental rate R on each unit of its capital holdings, earns the nominal wage W on each unit of labor it supplies, and pays the price P per unit of consumption.. The household's budget constraint is: Pc Wl+ Rk Solve the household's utility maximization problem and select which of the following represents the household's labor supply equation: 1-2 (WP)k +4P 1-2-() 1= 01= l= 1-4(wk) 1+4 W-²(WP) Save Answer
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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?A) 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 + 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 consumption…Suppose the wage rate for labor is $20 an hour and the rental rate for capital is $50 per hour. Based on this information, please answer the questions appearing below the graph. 80 70 60 50 40 30 20 10 10 20 30 40 50 60 70 80 1,000 cases Labor Draw an (approximate) is-cost line associated with an hourly budget of $1,000. Hint: Find the intercept points first. If you were to shift this line out, what is the approximate least-cost combination of labor and capital when packaging 1,000 cases of fruit juice?
- 1) Sharon spends her time (20h) between leisure (L) and work and he consume Y product from his working income (Py=1). Assume that she gets W$ per hour of working and has the following utility function: U (L, Y)=LY+2L a. b. C. Calculate the demand function for L and show it on a graph (L vs W). Calculate the labor supply (H) and show it on a graph (H vs W). What will happen to L, Y and H if the wage per hour (W) will decrease? =Emma is employed at a contract where he can vary his labour supply between 0 and 40 hours per week. She derives utility from consumption, c, and leisure, L. Her preferences are represented by the following utility function: U(c,L) = min(c, L). The unit price of consumption is p, and the hourly wage rate is w. (a) Derive an expression for Emma's labour supply. (b) The government contemplates introducing a consumption boosting policy including a monthly transfer of money for which Emma is eligible. At what size of the transfer will Emma decide to not work? Assume that the unit price of consumption is 30 and the hourly wage rate is 50- Find the marginal revenue function for the total revenue function given by 1 TR(Q) = 500Q Q3 - - 3 Find the marginal cost function for the total cost function given by TC(Q) = Q3 – 90Q² + 7,500Q
- Ivan faces a labor supply decision. His well-behaved preferences over the two goods "hours of leisure' L and 'consumption' c can be represented by u= 4(L)1/2 +c. He has no non-labor income and can choose how many hours to work at the wage rate u per hour. The price per unit of consumption is p, and his available free time is T hours .a) Sketch Ivan's budget set, with axes, intercepts, and slope labeled (these will depend on the parameters w, p, and T) .b) Use the tangency method to find Ivan's demand functions for leisure and consumption (as functions of u, p. and T) .c) Let's think about Ivan's "time expansion path" (that is, the analog of the income expansion path a.k.a. income-consumption loci but for changes in T). Sketch it and explain why it has this shape. with reference to Ivan's demand functions.d) In terms of parameters from the model, what is the most that Ivan would be willing to pay to have an extra hour of free time (that is, to increase T by 1)? Why?Ivan faces a labor supply decision. His well-behaved preferences over the two goods "hours of leisure' L and 'consumption' c can be represented by u= 4(L)1/2 +c. He has no non-labor income and can choose how many hours to work at the wage rate u per hour. The price per unit of consumption is p, and his available free time is T hours .a)Sketch Ivan's budget set, with axes, intercepts, and slope labeled (these will depend on the parameters w, p, and T) .b)Use the tangency method to find Ivan's demand functions for leisure and consumption (as functions of u, p. and T) .c) Let's think about Ivan's "time expansion path" (that is, the analog of the income expansion path a.k.a. income-consumption loci but for changes in T). Sketch it and explain why it has this shape. with reference to Ivan's demand functions.d) (3 points) In terms of parameters from the model, what is the most that Ivan would be willing to pay to have an extra hour of free time (that is, to increase T by 1)? Why?In any given week, Anne receives satisfaction only from the consumption of goods and from the consumption of leisure L, which is measured in hours. Obviously, Anne consumes many different types of goods, but for simplicity we aggregate the dollar value of all the goods that she consumes during the week and call it C. Assume that if Anne chooses to work, the hourly wage rate is w=9 and she has to sleep 8 hours per day. (Sleeping time is not considered leisure.) Potentially, if she wants, she can work up to 7 days a week.
- Ms Katrina has eighteen hours available per day to allocate between Leisure and work. She has N$100 non - labour income and her wage rate per hour is N$25.00. a) Contract budget constraint equation b) Draw a budget line and make sure to include intercepts c) Calculate the slope of the budget line d) If Ms Katrina's utility function is , what combination of Leisure hour and income that will help to maximize her utility?In any given week, Anne receives satisfaction only from the consumption of goods and from the consumption of leisure L, which is measured in hours. Obviously, Anne consumes many different types of goods, but for simplicity we aggregate the dollar value of all the goods that she consumes during the week and call it C. Assume that if Anne chooses to work, the hourly wage rate is w =9 and she has to sleep 8 hours per day. (Sleeping time is not considered leisure.) Potentially, if she wants, she can work up to 7 days a week. If Anne chooses to devote 0 hours to leisure during the week, how much can she consume? C = If Anne chooses to devote all available hours (except those she has to sleep) to leisure during the week, how much can she consume? C = If Anne chooses to devote 27 hours to leisure during the week, how much can she consume? C =If 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.