考虑赫克索尼亚经济。 a．消费函数是：C=200＋0.75（Y－T)；投资函数是：I=200－25r：政府购买和税收都是100，针对这

考虑赫克索尼亚经济。

a．消费函数是：C=200+0.75(Y-T)；投资函数是：I=200-25r：政府购买和税收都是100，针对这个经济体，画出r在0～8之间的IS曲线。

b．在赫克索尼亚，货币需求函数是：(M/P)^d=Y-100r：货币供给M是1000，物价水平P是2，针对这个经济，画出r在0～8之间的LM曲线。

c．找出均衡利率r和均衡收入水平Y。

d．假定政府购买从：100增加到150，IS曲线会移动多少？新的均衡利率和收入水平是多少？

e．假设货币供给从1000增加到1200，LM曲线会移动多少？新的均衡利率和收入水平是多少？

f．使用货币和财政政策的初始值，假设物价水平从2上升到4，会发生什么变化？新的均衡利率和收入水平是多少？

g．推导并画出总需求方程式。如果财政或货币政策像(d)和(e)部分那样变动，这条总需求曲线会发生什么变动？

Consider the economy of Hicksonia.

a．The consumption function is given by C=200+0.75(Y-T). The investment function is I=200-25r. Government purchases and taxes are both 100. For this economy, graph the IS curve for r ranging from 0 t0 8.

b．The money demand function in Hicksonia is (M/P)^d=Y-100r. The money supply M is 1,000 and the price level P is 2. For this economy, graph the LM curve for r ranging from 0 to 8.

c．Find the equilibrium interest rate r and the equilibrium level of income Y.

d．Suppose that government purchases are raised from 100 to 150. How much does the IS curve shift？ What are the new equilibrium interest rate and level of income？

e．Suppose instead that the money supply is raised from 1,000 to 1,200. How much does the LM curve shift？ What are the new equilibrium interest rate and level of income？

f．With the initial values for monetary and fiscal policy, suppose that the price level rises from 2 to 4. What happens？ What are the new equilibrium interest rate and level of income？

g．Derive and graph an equation for the aggregate demand curve. What happens to this aggregate demand curve if fiscal or monetary policy changes, as in parts (d) and (e)？

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？

考虑失业会如何影响索洛增长模型。假定产出是根据生产函数Y=K^a[(1-u＜sup＞*＜/sup＞)L]^1-a而生产的。式中，K为资本；L为劳动；u＜sup＞*＜/sup＞为自然失业率。国民储蓄率为s，劳动力增长率为n。资本折旧率为δ。
a．把人均产出(y=Y/L)表示为人均资本(k=K/L)和自然失业率的函数。描述该经济的稳定状态。
b．假定政府政策的某些变化降低了自然失业率。描述这一变化随时间的推进如何影响产出。对产出的稳定状态的影响大于还是小于立即的影响？请解释。
Consider how unemployment would affect the Solow growth model. Suppose that output is produced according to the production function Y=K^α[(1-u＜sup＞*＜/sup＞)L]^1-α，where K is capital, L is the labor force, and u＜sup＞*＜/sup＞ is the natural rate of unemployment. The national saving rate is s, the labor force grows at rate n, and capital depreciates at rate δ.
a．Express output per worker (y=Y/L) as a function of capital per worker (k=K/L) and the natural rate of unemployment. Describe the steady state of this economy.
b．Suppose that some change in government policy reduces the natural rate of unemployment. Describe how this change affects output both immediately and over time. Is the steady-state effect on output larger or smaller than the immediate effect？ Explain.