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考虑用以下生产函数描述的一个经济:Y=F(K,L)=K0.3L0.7’。求解: (1)人均生产函数是什么?
考虑用以下生产函数描述的一个经济:Y=F(K,L)=K0.3L0.7’。求解: (1)人均生产函数是什么? (2)假定没有人口增长或技术进步,找出稳定状态的人均资本存量、人均产出,以及作为储蓄率和折旧率函数的人均消费。 (3)试用微积分找出资本的边际产量。
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考虑用以下生产函数描述的一个经济:Y=F(K,L)=K0.3L0.7’。求解: (1)人均生产函数是什么? (2)假定没有人口增长或技术进步,找出稳定状态的人均资本存量、人均产出,以及作为储蓄率和折旧率函数的人均消费。 (3)试用微积分找出资本的边际产量。
A.生产可能性集合给定了一个多产出、多部门的分析框架
B.生产可能性集合假设了经济体内的技术性质
C.生产可能性集合是一种实物生产函数和经营函数的统称
D.生产可能性集合给出了投入产出的界限性分析的基本条件
考虑一个有以下柯布一道格拉斯生产函数的经济:Y=K1/3L2/3。这个经济有1000单位资本和1000个工人的劳动力。
a.求出描述这个经济中劳动力需求作为实际工资和资本存量函数的方程式。
b.如果实际工资可以调整到使劳动力供求均衡,那么,实际工资是多少?在这一均衡状态,就业量、产出和工人所赚到的总工资量是多少?
c.现在假设国会关注工人阶级的福利,通过一项法律要求企业向工人支付l单位产品的实际工资。这种工资与均衡工资相比如何?
d.议会不能指定企业以规定的工资雇佣多少工人。给定这一事实,这种法律有什么影响?特别地,就业、产出以及工人赚到的总收入会发生什么变动?
e.国会能成功地实现帮助工人阶级的目标吗?请解释。
f.你认为这种分析为考虑最低工资法提供了一种好方法吗?为什么是或不是?
Consider an economy with the following Cobb-Douglas production function:Y=K1/3L2/3. The economy has 1,000 units of capital and a labor force of 1,000 workers.
a.Derive the equation describing labor demand in this economy as a function of the real wage and the capital stock.
b.If the real wage can adjust to equilibrate labor supply and labor demand. what is the real wage? In this equilibrium, what are employment, output, and the total amount earned by workers?
c.Now suppose that Congress concerned about the welfare of the working class, passes a law requiring firms to pay workers a real wage of 1 unit of output. How does this wage compare to the equilibrium wage?
d.Congress cannot dictate how many workers firms hire at the mandated wage. Given this fact, what are the effects of this law? Specifically, what happens to employment, output, and the total amount earned by workers?
e.Will Congress succeed in its goal of helping the working class? Explain.
f.Do you think that this analysis provides a good way of thinking about a minimum-wage law? Why or why not?
A国与B国的生产函数都是:
Y=F(K,L)=K1/2L1/2
a.这个生产函数是规模收益不变吗?请解释。
b.人均生产函数y=f(k)是什么?
c.假设没有一个国家经历了人口增长或技术进步,并且资本折旧为每年5%。再假设A国每年储蓄为产出的10%,而B国每年储蓄为产出的20%。用你对(b)的答案和投资等于折旧的稳定状态条件,找出每个国家稳定状态的人均资本水平。然后找出稳定状态的人均收入水平和人均消费水平。
d.假定两国都从人均资本存量为2开始。人均收入水平和人均消费水平是多少?记住资本存量的变动是投资减折旧,用计算器来计算这两个国家的人均资本存量随时间推移将如何变动。计算每一年的人均收入和人均消费。B国的消费会在多少年后高于A国的消费?
Country A and country B both have the production function Y=F(K,L)=K1/2L1/2.
a.Does this production function have constant returns to scale? Explain.
b.What is the per-worker production function,y=f(k)?
c.Assume that neither country experiences population growth or technological progress and that 5 percent of capital depreciates each year. Assume further that country A saves 10 percent of output each year and country B saves 20 percent of output each year. Using your answer from part (b) and the steady-state condition that investment equals depreciation, find the steady-state level of capital per worker for each country. Then find the steady-state levels of income per worker and consumption per worker.
d.Suppose that both countries start off with a capital stock per worker of 2. What are the levels of income per worker and consumption per worker? Remembering that the change in the capital stock is investment less depreciation, use a calculator to show how the capital stock per worker will evolve over time in both countries. For each year, calculate income per worker and consumption per worker. How many years will it be before the consumption in country B is higher than the consumption in country A?
考虑二元函数f(x,y)的下面四条性质:
(1)f(x,y)在点(x0,y0)连续;
(2)fx(x,y),fy(x,y)在点(x0,y0)连续;
(3)f(x,y)在点(x0,y0)可微分;
(4)fx(x0,y0),fy(x0,y0)存在.
A.可以使用lambda函数定义列表的排序原则
B.f=lambdax,y:x+y执行后,f的类型为数字类型
C.lambda函数是匿名函数
D.lambda用于定义简单的能够在一行内表示的函数
A.lambda用于定义简单的、能够一行内表示的函数
B.可以使用lambda函数定义列表的排序原则
C.f=lambdax,y:x+y执行后,f的类型为数字类型
D.lambda函数将函数名作为函数结果返回
设V是对于非退化对称双线性函数f(α,β)的n维准欧氏空间,V的一组基ε1,...,εn如果满足
则称为V的一组正交基。如果V上的线性变换满足
则称为V的一个准正交变换。试证:
1)准正交变换是可逆的,且逆变换也是准正交变换;
2)准正交变换的乘积仍是准正交变换;
3)准正交变换的特征向量α,若满足f(α,α)≠0,则其特征值等于1或-1;
4)准正交变换在正交基下的矩阵T满足