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更多“对于长期生产函数来说，劳动对资本的边际替代率随着劳动投入量增…”相关的问题
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？
(1)企业目前的产量为100单位，成本最小化的劳动和资本分别为20和5。在图上用等产量线和等成本线表示出来。
(2)企业想将产量扩大为140单位，如果资本在短期固定，需要多少劳动？在图形上表示出来，并计算企业新的成本。
(3)在图形上表示出企业在长期生产140单位产品的成本最小化劳动和资本投入。
(4)如果边际技术替代率为K/L,计算生产140单位产品的最优劳动和资本投入。
Suppose that a firm' s production is q= 10L1/2K1/2. The cost of a unit of labor is $ 20 and the cost of a unit of capital is $ 80. a The firm is currently production 100 unis of output and has determined that the cost - mini-mizing quantities of labor and capital are 20 and 5, respectively. Graphically illustrate this using isoquants and isocost lines.
b，The firm now wants to increase output to 140 units. If capital is fixed in the short run, how much labor will the firm require？ Illustrator this graphically and find the firms new total cost.
c. Graphically identify the cost - minimizing level of capital and labor in the long run if the firm wants to produce 140 units.
d. If the marginal rate of technical substitution is K/L, find the optimal level of capital and labor required to produce the 140 units of output.
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
已知生产函数Q=f(L，K)=2KL-0.5L2-0.5K2，假定厂商目前处于短期生产，且K=10。
(1)写出在短期生产中该厂商关于劳动的总产量TPL函数、劳动的平均产量APL函数和劳动的边际产量MPL函数。
(2)分别计算当劳动的总产量TPL劳动的平均产量APL和劳动的边际产量MPL各自达到极大值时的厂商的劳动投入量。
(3)什么时候APL=MPL？它的值又是多少？
(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,
