考虑用以下生产函数描述的一个经济：Y=F（K，L)=K0.3L0.7。 a．人均生产函数是什么？ b．假定没有人口增长或技术

考虑用以下生产函数描述的一个经济：Y=F(K，L)=K^0.3L^0.7。

a．人均生产函数是什么？

b．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。

c．假定折旧率是每年10%。作一个表，表示储蓄率分别为0、10%、20%、30%等时，稳定状态的人均资本、人均产出和人均消费。(你需要用一个有指数键的计算器来计算这个问题。)使人均产出最大化的储蓄率是多少？使人均消费最大化的储蓄率是多少？

d．用微积分找出资本的边际产量。在你的表上增加一项——每种储蓄率下的资本的边际产量减折旧。你的表说明了什么？

Consider an economy described by the production function Y=F(K，L)=K^0.3L^0.7.

a．What is the per-worker production function？

b．Assuming no population growth or technological progress, find the steady-state capital stock per worker, output per worker, and consumption per worker as functions of the saving rate and the depreciation rate.

c．Assume that the depreciation rate is 10 percent per year. Make a table showing steady-state capital per worker, output per worker, and consumption per worker for saving rates of 0 percent, 10 percent, 20 percent, 30 percent, and so on. (You will need a calculator with an exponent key for this.) What saving rate maximizes output per worker？ What saving rate maximizes consumption per worker？

d．(Harder) Use calculus to find the marginal product of capital. Add to your table the marginal product of capital net of depreciation for each of the saving rates. What does your table show？