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- According to the Wall Street Journal, Mitsubishi Motors recently announced a major restructuringplan 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. Priorto restructuring Mitsubishi’s marginal rate of technical substitution is 0.15 ( in absolute value). Tohire 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 Mitsubishidetermine that its marginal productivity of capital is 0.5 small cars per hour at its new targetedlevel of output and that capital is procured in a highly competitive market. The same studyindicates that the average selling price of Mitsubishi’s smallest car is US$ 9500. Determine therate at which Mitsubishi can rent capital and marginal productivity of labour at its new targetedlevel of output. To minimize costs…Suppose Jenny has 16 hours per day to allocate between work and leisure and she earns a wage rate of $25 per hour. If at the utility-maximizing level of employment (i.e., MRSy; = w), Jenny's MUy is 20 utils, what is her MUl? O A. 1.25 utils O B. 0.8 utils O C. 500 utils O D. Cannot be determined with the information provided.Shelly’s preferences for consumption and leisure can be expressed as U(C, L) = (C - 200) * (L - 80) This utility function implies that Shelly’s marginal utility of leisure is C - 200 and her marginal utility of consumption is L - 80. There are 168 hours in the week available to split between work and leisure. Shelly earns $5 per hour after taxes. She also receives $320 worth of welfare benefits each week regardless of how much she works. a. Graph Shelly’s budget line. b. What is Shelly’s marginal rate of substitution when L = 100 and she is on her budget line? c. What is Shelly’s reservation wage? d. Find Shelly’s optimal amount of consumption and leisure.
- According to the Wall Street Journal, Mitsubishi Motors recently announced a major restructuring plan in an attempt to reverse declining global sales. Suppose that as part of the restructuring planMitsubishi conducts an analysis of how labour and capital are used in its production process. Prior to restructuring Mitsubishi’s marginal rate of technical substitution is 0.15 ( in absolute value). To hire workers. Suppose that Mitsubishi must pay the competitive hourly wage of US$ 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…Cowles Foundationfor Research in Economicsat Yale UniversityCowles Foundation Discussion Paper No. 2021ARE WE APPROACHING AN ECONOMIC SINGULARITY?INFORMATION TECHNOLOGY AND THE FUTUREOF ECONOMIC GROWTHWilliam D. NordhausSeptember 2015An author index to the working papers in theCowles Foundation Discussion Paper Series is located at:http://cowles.yale.edu/This paper can be downloaded without charge from theSocial Science Research Network Electronic Paper Collection:http://ssrn.com/abstract=2658259Electronic copy available at: http://ssrn.com/abstract=2658259Are We Approaching an Economic Singularity?Information Technology and the Future of Economic GrowthWilliam D. Nordhaus1September 1, 2015AbstractWhat are the prospects for long-run economic growth? The presentstudy looks at a recently launched hypothesis, which I label Singularity.The idea here is that rapid growth in computation and artificialintelligence will cross some boundary or Singularity after whicheconomic growth will…Imagine a firm that employs two types of workers – some with computer skills and others withno technology related skills. (i) Explain how a firm’s production function is related to its marginal product of labour, howa firm’s marginal product of labour is related to the value of its marginal product and how afirm’s value of marginal product is related to its demand for labour. (ii) Explain how the wage can adjust to balance the supply and demand for labour whilesimultaneously equalling the value of the marginal product of labour.
- Y5 If a firm uses n inputs (n > 2), what inequality does the theory of revealed cost mini- mization imply about changes in factor prices (∆wi) and the changes in factor demands (∆xi) for a given level of output?Show the profit function is convex in (p, c). Provide an intuitionfor this result. hint: Consider (p, c), (p', c') and (pα, cα) = α(p, c) + (1 −α)(p', c'). Let w, w' and wα denote the corresponding factor demands. What do you know about the relation between (the size of) pf(w)−cw and pf(wα)−cwα, as required by the definition of profit-maximizing?In a perfectly competitive labor market, a profit maximizing firm will hire labor up to the point at which the:O. wage rate >marginal revenue productO. wage rate= marginal resource costO. wage rate =marginal productO. wage rate = marginal revenue productO. wage rate <marginal revenue product
- Consider a manufacturing firm in a labor market that isperfectly competitive. There are two kinds of workers: productiveworkers whose marginal revenue product is $48,000 per year, andlazy workers whose marginal revenue product is $40,000 per year. Itis difficult for the firm to differentiate between productive andlazy workers. A local college offers a new yearlong astronomy course. Althoughthe cost of tuition is the same for both types of workers, thepsychic cost of having to work hard and get a passing grade islower for productive workers because they are able to learn morequickly than lazy workers. Therefore, the cost of taking the class(including the cost of tuition as well as the psychic cost) is$5,000 per year for a productive worker and $10,000 per year for alazy worker. Because astronomy has little relevance tomanufacturing, taking the class does not increase or decrease aworker's productivity. The firm uses the class as a way to differentiate betweenproductive and lazy…Illustrate and examine how the individual supply of labor curve demonstrate the way an individual divides his/her time between work and leisurePatty’s Pizza has the production function per hour shown in the table below. The hourly wage rate for each worker is $10. Each pizza sells for $2. Quantity of workers - 0, 1, 2, 3, 4, 5. Quantity of pizza - 0, 9, 15, 19, 22, 24. Now, let’s assume that Patty buys a new high-tech pizza oven that allows her workers to become twice as productive as before. That is, the first worker now produces 18 pizzas per hour instead of 9, and so on. e) Calculate the new MPL and the new VMPL at the original price of $2 per pizza using the new information above. f) Using answer (e) determine how Patty’s hiring decision responds to this increase in the productivity of her workforce when the wage rate is $10, i.e., will she hire more workers or less workers than before or not change the number of workers? (use a diagram)