劳动的边际产量(marginal product of labor, MPL)
劳动的边际产量(marginal product of labor, MPL)
劳动的边际产量(marginal product of labor, MPL)
第1题
The marginal product of labor in the production of computer chips is 50 chips per hour. 'The marginal rate of technical substitution of hours of labor for hours of machine-capital is 1/4. What is the marginal product of capital?
第2题
Suppose that labor is the only variable input to the production process. If the marginal cost of production is diminishing as more units of output are produced, what can you say about the marginal product of labor?
第3题
第4题
(这个题要求运用微积分)考虑有三种投入的柯布—道格拉斯生产函数。K是资本(机器数量),L是劳动(工人人数),H是人力资本(工人中持有大学学历的人数)。生产函数是:Y=K1/3L1/3H1/3
a.推导出劳动的边际产量。人力资本量的增加怎样影响劳动的边际产量?
b.推导出人力资本的边际产量的表达式。人力资本量的增加怎样影响人力资本的边际产量?
c.支付给劳动的收入份额是多少?支付给人力资本的收入份额是多少?在这个经济的国民收入核算中,你认为工人会得到多大份额的总收入?(提示:考虑人力资本的收益体现在哪里。)
d.一个无技术工人赚到劳动的边际产量,而一个技术工人赚到劳动的边际产量加人力资本的边际产量。用(a)与(b)的答案,找出技术工人与无技术工人工资的比率。人力资本量增加如何影响这个比率?请解释。
e.一些人倡议把政府融资的大学奖学金作为创造一个更加平等的社会的途径。另一些人认为,大学奖学金只能帮助那些能上大学的人。你能用前面问题的答案来讨论这种争论吗?
(This problem requires the use of calculus) Consider 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 college degrees among the workers). The production function is Y=K1/3L1/3H1/3
a.Derive an expression for the marginal product of labor. How does an increase in the amount of human capital affect the marginal product of labor?
b.Derive an expression for the marginal product of human capital. How does an increase in the amount of 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 the national income accounts of this economy, what share of total income do you think workers would appear 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 marginal product of labor plus the marginal product of human capital. Using your answers to (a) and (b), find the ratio of the skilled wage to the unskilled wage. How does an increase in the amount of human capital affect this ratio? Explain.
e.Some people advocate government funding of college scholarships as a way of creating a more egalitarian society. Others argue that scholarships help only those who are able to go to college. Do your answers to the preceding questions shed light on this debate?
第7题
总产量、平均产量和边际产量(total,average,and marginal product)
第8题
假设坎塔布雷吉亚(Cantabrigia)是一个很小的经济体,共有20名工人。这些工人可以生产两种产品,即制造品和粮食。在制造业的生产中,边际劳动产量取决于就业人数。关系如下:
工人数 | 最后一个工人的际产出 |
1 | 20 |
2 | 18 |
3 | 16 |
4 | 14 |
5 | 12 |
6 | 11 |
7 | 10 |
8 | 9 |
9 | 8 |
10 | 7 |
在粮食部门,边际劳动产量与就业人数无关,恒等于9。制造品与粮食的世界价格都是每单位10美元。
a.假设不存在劳动市场扭曲现象,求工资率、制造业和粮食业的劳动配置,以及每种产品的产量。
b.现在假设由于某种原因,制造业部门的最低工资是150美元。同时,该经济仍然保持充分就业状态。求这种情形下整个经济的产出以及市场扭曲带来的成本。
c.最后,假设工人从农村向城市迁移,直至城市工人的工资与被雇佣的概率的乘积等于农村工人的工资。求产出水平和失业人数。
The very small economy of Cantabrigia has a total labor force of 20 workers.These workers can produce two goods,manufactures and food.in production of manufactures,the marginal product of labor depends on employment as follows:
Number of workers | Marginal product of last worker |
1 | 20 |
2 | 18 |
3 | 16 |
4 | 14 |
5 | 12 |
6 | 11 |
7 | 10 |
8 | 9 |
9 | 8 |
10 | 7 |
In the food sector the marginal product of labor is independent of employment,and is 9. The world price of a unit of manufactures is $10,so is the world price of a unit of food.
a.Suppose there were no distortion in the labor market;find the wage rate,the allocation of labor between manufactures and food,and the output of each good.
b.Now suppose that for some reason the minimum wage in the manufactures sector is $150. Full employment,however,is maintained.Find the output of the economy in this case.How large is the cost of the distortion?
c.Finally,suppose that workers migrate from the country to the city until the wage of city workers multiplied by the probability of being employed equals the rural wage.Find the level of output and unemployment.
第9题
To encourage an industry to produce at the socially optimal level, the government should impose a unit tax on output equal to the marginal cost of production. True or false? Explain.
第10题
Do the following functions exhibit increasing, constant, or decreasing returns to scale? What happens to the marginal product of each individual factor as that factor is increased and the other factor held constant?