MGEB06宏观经济理论

考虑具有三个输入的Cobb–Douglas生产函数。K是资本（机器的数量），L是劳动力（工人的数量），H是人力资本（大学学位的数量工人）。生产功能是Y=K1/3 L1/3 H1/3a） 推导出劳动的边际产品的表达式。人的数量是如何增加的资本影响劳动的边际产品？b） 推导人力资本边际产品的表达式。金额如何增加人力资本的边际产品会影响人力资本吗？c） 支付给劳动力的收入份额是多少？支付给人力资本的收入份额是多少？在这个经济体的国民收入账户，你认为工人在总收入中占多大份额似乎收到了？（提示：考虑一下人力资本的回报在哪里。）d） 非技术工人赚取的是边际劳动成果，而技术工人赚取边际劳动成果劳动的产品加上人力资本的边际产品。使用您对（a）和（b）部分的回答，找出熟练工资与非熟练工资的比例。人的数量是如何增加的资本会影响这个比率吗MGEB06 Assignment 1 (WINTER 2023) 1MGEB06 – WINTER 2023Macroeconomic Theory and PolicyAssignment 1Due: On (or before) Friday, March 3rd 11pm(Note: Assignments submitted after 11pm on March 3rd WILL NOT BE accepted under ANYcircumstance.)The table below should be the cover page of each question submitted for your assignment.Group members: Student number

1.Instructions

You can submit an individual or group assignment. If you submit a group assignment, theremust be no more than FIVE students in your group (coming from any one of the sections ofMGEB06 this term) and you must submit ONE copy.A PENALTY OF 10% OF THE TOTAL MARKS will be imposed if you FAIL TO DO THEFOLLOWING: Submit the filled-in table as your cover page (for EACH answer uploaded) Label your graph(s); otherwise, marks will be subtracted. No credit will be given if you do not show your work (i.e., don’t simply say the answer is 3 writedown enough of the steps you used to arrive at this answer).Your answer should be structured in a way such that those that know little about economicswill have no difficulty understanding your argument/answer.DO NOT USE any notations that are not used in lectures. If you use your own notations and/orabbreviations that are not being used in lectures, you will receive a grade of zero for thatquestion.MGEB06 Assignment 1 (WINTER 2023) 2Question 4 (20 points) – Chapter 3/8/9Consider a Cobb–Douglas production function with three inputs. K is capital (the number of machines),L is labor (the number of workers), and H is human capital (the number of university degrees among theworkers). The production function isY = K1/3 L1/3 H1/3a) Derive an expression for the marginal product of labor. How doesan increase in the amount of humancapital affect the marginal product of labor?b) Derive an expression for the marginal product of human capital. How does an increase in the amountof human capital affect the marginal product of human capital?c) What is the income share paid to labor? What is the income share paid to human capital? In thenational income accounts of this economy, what share of total income do you think workers wouldappear to receive?(Hint: Consider where the return to human capital shows up.)d) An unskilled worker earns the marginal product of labor, whereas a skilled worker earns the marginalproduct of labor plus the marginal product of human capital. Using your answers to parts (a) and (b),find the ratio of the skilled wage to the unskilled wage. How does an increase in the amount of humancapital affect this ratio? Explain.e) Some people advocate government funding of university scholarships as a way of creating a fairersociety. Others argue that scholarships help only those who are able to go to university. Do youranswers to the preceding questions shed light on this debate?
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