Consider a utility function with one consumption good qi and one type of leisure q2 U(q1, 92) = qi 1/3 1/3 92 a) Derive complete labour supply function. b) Under what condition the labour supply curve will be negatively sloped.
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Q3. Consider a utility function with one consumption good q1 and one type of leisure q2
a) Derive complete labour supply function.
b) Under what condition the labour supply curve will be negatively sloped.
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- 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 50In a standard consumer optimization problem in microeconomics, a consumer purchases any pair of goods untilU1U2=p1p2(?), at an interior solution, where Ux is the marginal utility of good x for the consumer and px is the price of good x, where x={1,2}. What is the corresponding optimality condition for a worker-consumer in his labour-leisure optimization problem and why is it just a variation on the standard optimality condition (?)?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…
- According to The Wall Street Journal, Mitsubishi Motors recently announced a major restructuring plan in an attempt to reverse declining global sales. Suppose that as part of the restructuring plan Mitsubishi conducts an analysis of how labor and capital are used in its production process. Prior to restructuring Mitsubishi’s marginal rate of technical substitution is 0.12 (in absolute value). To hire workers, suppose that Mitsubishi must pay the competitive hourly wage of ¥1,800. In the study of its production process and markets where capital is procured, suppose that Mitsubishi determines that its marginal productivity of capital is 0.8 small cars per hour at its new targeted level of output and that capital is procured in a highly competitive market. The same study indicates that the average selling price of Mitsubishi’s smallest car is ¥1,200,000. Determine the rate at which Mitsubishi can rent capital and the marginal productivity of labor at its new targeted level of output. To…(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?Using the model developed in The Economy Unit 3, Section 3.7, consider an individual who is facing a wage (w) of $20 per hour. Assume that their spending on goods and services cannot exceed their earnings per day. Maximum consumption (c) per day is: c = w(24 – t) where t = hours of free time per day. a) Initially when facing w = $20 per hour the individual chooses to work 10 hours per day and have 14 hours of free time per day. In a fully labelled diagram show the individual’s optimal combination of free time and consumption. (Fully labelled means that you must label both axes, correctly determine the vertical axis and horizontal axis intercepts, label the slope of the budget constraint and show the optimal amount of free time and consumption associated with it.) b) Assume that the wage increases to $30 per hour. Show the new utility maximizing combination of free time and consumption in your diagram from a). c) On your diagram decompose the overall change in hours of free time in…
- Cindy gains utility from consumption C and leisure L. The most leisure she can consume in any given week is 168 hours. Her utility function is U ( C, L) = C x L. This functional form implies that Cindy’s marginal rate of substitution is C/L. Cindy receives $630 each week from her great-grandmother—regardless of how much Cindy works. What is Cindy’s reservation wage?According to the Wall Street Journal, Mitsubishi Motors recently announced a major restructuring plan in an attempt to reverse declining global sales. Suppose that as part of the restructuring planMitsubishi conducts an analysis of how labour and capital are used in its production process. Prior to restructuring Mitsubishi’s marginal rate of technical substitution is 0.15 ( in absolute value). To hire workers. Suppose that Mitsubishi must pay the competitive hourly wage of US$ 15. In thestudy of production process and markets where capital is procured, suppose that Mitsubishi determine that its marginal productivity of capital is 0.5 small cars per hour at its new targeted level of output and that capital is procured in a highly competitive market. The same study indicates that the average selling price of Mitsubishi’s smallest car is US$ 9500. Determine the rate at which Mitsubishi can rent capital and marginal productivity of labour at its new targeted level of output. To minimize…Suppose that a firm's estimated production is: Q = K³/411/4 What is the marginal rate of technical substitution (MRTS) equal to?
- 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?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 Use the tangency method to find Ivan's demand functions for leisure and consumption (as functions of u, p. and T)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.