小麦的生产函数为q=100K0.8L0.2。
(1)开始时资本投入为4单位,劳动投入为49单位,请证明劳动和资本的边际产量都下降。
(2)该生产函数显示的规模报酬是递增、递减,还是不变?
In Example 6.3,wheat is produced according to the production function g= 100(K0.8L0.2).
a. Beginning with a capital input of4 and a labor input of 49,show that the marginal product of labor and the marginal product of capital are both decreasing.
b. Does this production function exhibit increasing, decreasing, or constant returns to scale?
A、参数A反映广义的技术进步水平
B、资本要素的产出弹性Ek=β
C、劳动要素的产出弹性EL=α
D、α+β必定等于1
某移动电话公司的某种产品有下面的生产函数
(1)求由125个人力单位和64个资本单位生产的产品数量;
(2)求边际生产力;
(3)计算在x=125和y=64时的边际生产力.
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?
(1)计算该生产函数下劳动的平均产量和边际产量;
(2)该生产函数是否显示了劳动的边际报酬递减,请解释;
(3)请直观地解释劳动边际产量为负的原因?
Suppose a chair manufacturer is producing in the short run (with its existing plant and equipment). The manufacturer has observed the fallowing levels of production corresponding to different numbers of workers:
a. Calculable the marginal and average product of labor for this production function.
b. Does this production function exhibit diminishing returns to labor? Explain.
e. Explain intuitively what might cause the marginal product of labor to become negative,
A、若α+β=1,则生产函数规模报酬不变
B、边际生产力,可以是正也可以是负
C、α是产出Y关于资本K的弹性
D、替代弹性等于零
E、若0﹤α﹤1,0﹤β﹤1时,则边际生产率递减
对于生产函数
(1)推导出短期总成本、平均成本、平均可变成本及边际成本函数;
(2)证明:当短期平均成本最小时,短期平均成本和边际成本相等。