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=

A国与B国的生产函数都是：

Y=F(K，L)=K^1/2L^1/2

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)=K^1/2L^1/2.

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？