生产函数（production function)

此题为判断题(对，错)。

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?

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?

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According to the traditional view of government debt, how does a debt-financed tax cut affect public saving, private saving, and national saving？

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Describe four problems affecting measurement of the government budget deficit.

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