上财罗大庆高宏作业2
上财金融学院高宏课件(谭继军) (2)
— Again, we are interested in the properties of s. This time we use implicit function theorem to find
∂st ∂st ∂w1 , ∂w2
rief review of implicit function theorem (see Appendix ) — Define H (st , w1 , w2 , rt ) ≡ −U1 (w1 − st ) + rt U2 (wt + rt st ) = 0, where st is endogenous variable, and w1 , w2 and rt are parameters. If U is additive separable, which ensures c1 and c2 are normal goods, then 1> U11 ∂st 1 = − ∂w = > 0, 2U ∂H ∂w1 U11 + rt 22 ∂s
∂H rU2 ∂s ∂τ = − ∂H = < 0. 2 ∂τ U11 + r (1 − τ )U22 ∂s
From
∂s ∂τ ,
only substitute effect exists, no income effect.
— Because τ only changes gross real interest rate, real income doesn’t change at all (rsi (1 − τ ) + w2 + a and τ rsi = a ⇒ rsi + w2 ). Income is compensated. — Another word: Though people’s real income doesn’t change, they still response to the tax by decreasing saving. Another word: No neutral tax on price (interest rate), even if real income doesn’t change.
上财金融学院高宏课件(谭继军) (3)
Graphically (insert a graph) How can the government solve this problem?
— Using less centralized methods, short of taking over the entire economy as done in the G.R. administration.
— Transfers from young to old, which is called social security.
—
Look at
U1(w1−k) U2(w2+f (k))
.
Such transfers mean
U1(w1−k−τ ) U2(w2+f (k)+σ)
.
— For a given k, these transfers increase c2 and lower c1.
— The C.E. tells us the best that individuals can do for a given budget.
— It may not be the best possible allocation. The key to understanding these models is to distinguish between the decision of individuals and those of the social planner.
A social planner’s problem: maximizing utility of future generations, ignoring the initial old (Golden Rule of Phelps (AER, 1965)).
上财高级计量经济学朱东明作业2
Econometrics I,Fall2012Assignment2The due date for this assignment is Monday Nov.5.1.The…le consumption.txt contains data on real personal disposable income and con-sumption expenditures in Canada,seasonally adjusted in1986dollars,from the…rst quarter of1947until the last quarter of1996.The layout of the data is explained at the end of the…le.(a)The simplest imaginable model of the Canadian consumption function would haveconsumption expenditures as the dependent variable,and a constant and personaldisposable income as explanatory variables.Run this regression for the period1953:1to1996:4.What is your estimate of the marginal propensity to consumeout of disposable income?(b)Plot a graph of the OLS residuals for the consumption function regression againsttime.All modern regression packages will generate these residuals for you onrequest.Does the appearance of the residuals suggest that this model of theconsumption function is well speci…ed?(c)Simulate the consumption function model you have just estimated in(a)for thesame sample period,using the actual data on disposable income.For the para-meters,use the OLS estimates obtained in(a).For the error terms,use drawingsfrom the N(0;s2)distribution,where s2is the estimate of the error variance pro-duced by the regression package.(d)Run a regression using the simulated consumption data as the dependent vari-able and the constant and disposable income as explanatory variables.Are theparameter estimates the same as those obtained using the real data?Why or whynot?(e)Plot the residuals from the regression with simulated data.Does the plot looksubstantially di¤erent from the one obtained using the real data?It should!2.The…le tbrate.txt contains data for1950:1to1996:4for three series:r t,the interestrate on90-day treasury bills, t,the rate of in‡ation,and y t,the logarithm of real GDP.For the period1950:4to1996:4,run the regression4r t= 1+ 2 t 1+ 34y t 1+ 44r t 1+ 5r t 2+u t;(1) where4is the…rst-di¤erence operator,de…ned so that4r t=r t r t 1.(a)Plot the residuals and…tted values against time.Then regress the residuals on the…tted values and on a constant.What do you learn from this second regression?Now regress the…tted values on the residuals and on a constant.What do youlearn from this third regression?(b)For the same sample period,regress4r t on a constant,4y t 1,4r t 1and4r t 2.Save the residuals from this regression,and call them b e t.Then regress t 1on aconstant,4y t 1,4r t 1and4r t 2.Save the residuals from this regression,andcall them b v t .Now regress b e t on b v t .How are the estimated coe¢cient and the residuals from this last regression related to anything that you obtained when you estimated regression (1)?(c)Calculate the diagonal elements of the hat matrix P X for regression (1)anduse them to calculate a measure of leverage,h t X 0t [X 0X ] 1X t ,where X i =(x t;1;:::;x t;k )0.We say that observations for which h t is large have high leverage or are leverage points.A leverage point is not necessarily in‡uential,but it has the potential to be in‡uential.Plot this measure against time.On the basis of this plot,which observations seem to have unusually high leverage?3.Consider the following linear regression:y =X +"=X 1 1+X 2 2+",where y is n 1,X 1is n k 1,X 2is n k 2,X =[X 1;X 2]is n k (k 1+k 2=k <n ),and 0=[ 01; 02].Suppose that X ,X 1and X 2are of full column rank.The OLS estimator b = b 01;b 020are expressed as b = b 1b 2 =(X 0X ) 1X 0y = X 01X 02 [X 1;X 2] 1 X 01X 02 y = X 01X 1X 01X 2X 02X 1X 02X 2 1 X 01y X 02y:(a)Use the formula of partitioned inverse (see A-74,page824)to show thatb 1=[X 01M 2X 1] 1X 01M 2y =[X 01X 1] 1X 01y b 2=[X 02M 1X 2] 1X 02M 1y =[X 02X 2] 1X 02y whereP i X i (X 0i X i ) 1X 0i ,M i I P i ,i =1;2X 1=M 2X 1;y =M 2y ;X 2=M 1X 2;y =M 1y :(b)Note that a square matrix is an orthogonal projection if and only if it is symmetricand e this result to show that P X P 1is an orthogonal projection matrix.What is the trace of P X P 1?(c)Show that any n 1vector z of the form M 1X 2 ,for an arbitrary k 2 1vec-tor ,is left unchanged when premultiplied by P X P 1;that is,show that(P X P 1)M 1X 2 =M 1X 2 .(d)Why do the above results prove that P X P 1=P M 1X 2,where this last matrix denotes the orthogonal projection on to S (M 1X 2)?(e)Consider the following regressions,all to be estimated by OLS:(a)y =X 2 2+u ;(b)P 1y =X 2 2+u ;(c)P 1y =P 1X 2 2+u ;(d)P X y =X 1 1+X 2 2+u ;(e)P X y =X 2 2+u ;(f)M 1y =X 2 2+u ;(g)M 1y =M 1X 2 2+u ;(h)M 1y =X 1 1+M 1X 2 2+u ;(i)M 1y =M 1X 1 1+M 1X 2 2+u ;(j)P X y =M 1X 2 2+u :For which of these regressions are the estimates of 2the same as for the original regression?Why?For which are the residuals the same?Why?。
上财罗大庆高级宏观作业3
上财罗大庆高级宏观作业3Advanced Macroeconomics IInstructor:Luo DaqingAssignment3Note:You may use either English or Chinese to answer the questions.Question1(5points)Consider the Overlapping Generations framework we discussed in classes.Suppose there are two countries where individuals di?er in their endowment streams.The characteris-tics of the two countries are summarized in the following table: Home Country Foreign CountryN t=60,t≥0N?t=40,t≥0{y1t,y2t+1}={1,1.25},t≥0{y?1t ,y?2t+1}={1,1},t≥0u(c1t,c2t+1)=ln c1t+0.95ln c2t+1,t≥0u(c?1t ,c?2t+1)=ln c?1t+0.95ln c?2t+1,t≥0(1)(4points)Find the sequence of equilibrium interest rate and the consumption allo-cation for this economy,and thenindividual savings in the equilibrium.(The derivation of the consumption and saving functions is not a must for this problem.However,you are de?nitely supposed to know how to derive these functions.)(2)(1points)Verify whether free trade is superior to autarky by comparing the welfare of home and foreign agents in free trade and in autarky.Question2(5points)Consider an Overlapping Generations economy with government.Suppose that in each period,100identical individuals are born(i.e.N t=100for t=0,1,2,...).The utility of an individual born in period t is given byu(c1t,c2t+1)=ln c1t+0.95ln c2t+1.. An individual born in period t has the following endowment stream{y1t,y2t}={1,1.25}∞t=1 In addition,assume the government announces the following policy.In period1,the government borrows5units of the time1good and transfers those units to the old in-dividuals alive in period1.The government will payo?its debt by taxing the members of generation1in their old age and will issue no debt after that.Find the sequence of equilibrium interest rate and the consumption allocation for this economy.(Again,the derivation of the consumption and saving functions is not a must for this problem.)。
上财罗大庆高宏课件 (9)
• Since all periods are identical, the competitive equilibrium prices and consumption allocation are
∞ {r t }∞ t=1 = {0.01}t=1 , ∞ {c 1 t , c 2 t }∞ t=1 = {2.2, 2}t=1 .
• Optimization problem solved by an individual born in period t is to maximize u(c1t , c2t+1 ) subject to the Present Value budget constraint. • Logarithmic utility example: – Maximize u(c1t , c2t+1 ) = ln c1t + β ln c2t+1 subject to c 1t + c2t+1 y2t+1 = y 1t + . 1 + rt 1 + rt
(II) Heterogeneity within Cohorts
• Heterogeneity creates incentives for trade. • Assume there are two types of agents born in each period. • Type 1 (group 1) – Nt individuals of type 1 are born in period t – they have utility function u(c1t , c2t+1 ) – and an endowment stream {y1t , y2t+1 }. • Type 2 (group 2) – Nt∗ individuals of type 2 are born in period t
高宏(08)2014年11月17日§2.1§2.2(纯白)
•第三次作业：第117页：•2.8 —2.11•11月24日交第3次作业2014-11-17 高宏（8）《高宏》讲义，张延著。
版权所有2•四、家庭的最大化问题•1、家庭最大化问题的一阶条件•家庭的问题是，在预算约束条件下选择c(t)的路径以最大化一生效用。
尽管这涉及选择每一时点上的c(而非像标准的最大化问题那样，仅选择有限的一组变量)，传统的最大化方法仍可使用。
2014-11-17 高宏（8）《高宏》讲义，张延著。
版权所有3•由于消费的边际效用总为正，所以家庭满足其预算约束的等号形式。
因此，我们可用目标函数(2.14)和预算约束(2.7)来构造拉格朗日函数：•目标函数：∞[ e -βt c(t)1-θ／(1-θ) ] dt (2.14)•U ≡ B∫t=02014-11-17 高宏（8）《高宏》讲义，张延著。
版权所有4•约束条件：•∫t=0∞e -R(t) c(t) e(n+g)t dt•≤ k(0) + ∫t=0∞e -R(t) w(t) e(n+g)t dt (2.7)•L= B∫t=0∞[e -βt c(t) 1-θ／(1-θ)]dt +λ[ k(0) +•∫t=0∞e -R(t) e(n+g)t w(t)dt -∫t=0∞e -R(t) e(n+g)t c(t)dt ]•(2.15)2014-11-17 高宏（8）《高宏》讲义，张延著。
版权所有5•c(t)：选择变量，政策可控制。
如何选择，以最大化一生的效用。
•k(t)：状态变量。
•t ：时间变量。
2014-11-17 高宏（8）《高宏》讲义，张延著。
版权所有6•即以某一时期t为例，写出某一时期t的拉格朗日函数：•L = B e -βt c(t)1-θ／(1-θ) +•λ [ k(0) +e -R(t)e(n+g)t w(t) -e -R(t)e(n+g)t c(t) ]•存在极值的一阶条件为：•∂L ／∂c=B e-βt c(t)-θ-λe -R(t)e(n + g)t= 0 2014-11-17 高宏（8）《高宏》讲义，张延著。
管理方法与艺术第二次作业参考答案.doc
管理方法与艺术第二次作业参考答案--单选--0(本题2分) 领导方格理论是由( )提出的布莱克和穆顿费德勒坦南鲍姆施密特1(本题2分) ( )是组织文化最直观的部分潜层次的精神层表层的制度系统显现层的组织文化载体组织价值观2(本题2分) 下列不能作为管理人员考评的目的是（）确定薪酬的依据人事调整提供依据为管理人员培训提供依据进行惩罚的标准3(本题2分) 组织规模一定的条件下，管理幅度较大、管理层次较少的组织形态为（）。
扁平结构直线型结构矩阵结构锥形结构4(本题2分) （）是一种传统的、普遍的组织形式。
矩阵组织产品部门化职能部门化区域部门化5(本题2分) 一些大公司喜欢采取内部提升的选拔制度。
你认为以下哪些是它的弊病（）可能造成“近亲繁殖” 的现象有利于保证选聘工作的正确性。
有利于吸引人才。
有利于鼓舞士气6(本题2分) 下行沟通是指( )组织中的上层领导按指挥系统从上而下的情报沟通下级的意见、信息向上级反映下级之间的意见交流通过上级组织明文规定的渠道进行信息传递7(本题2分) 对于组织的看法，你认为哪种正确（）正式组织中不存在非正式组织。
正式组织中也存在非正式组织非正式组织中通常会传递小道消息，因此应尽量消除非正式组织。
非正式组织是由企业管理者用非正式的方式建立的。
8(本题2分) 一般说来，管理层次所拥有的能够确定集权或分权程度的是( )。
审批权计划权组织权决策权9(本题2分) 组织结构设计中，划分管理层次的主要原因是( ) 组织高层领导的偏好法律的规定组织规模管理幅度10(本题2分) 不利于分权的因素主要有（）。
组织规模的扩大组织活动的分散较多受过良好训练的管理人员政策的统一性11(本题2分) 距阵式组织的主要缺点是（）。
分权不充分多头领导对项目经理要求高组织稳定性差12(本题2分) 下列不是组织分权的标志（）决策的频度决策的幅度决策的重要性组织的规模13(本题2分) 下列不属于委员会制的优点的是（）责任明确集体决策可以产生更多的方案集思广益14(本题2分) 关于沟通，下列说法正确的是（）。
上海财经大学附属中学2012届高三10月月考数学试卷
上海财经大学附属中学2012届高三10月月考数学试卷2011.10.9（满分100分，时间90分钟） 成绩___________________一、填空题（每题4分，满分56分）1、已知{}{}R x x y y B R x x y y A ∈==∈==,,,22，则=B A I _________。
[0,)+∞2、函数y =___________。
(]0,93、已知幂函数()y f x =的图象过点12⎛ ⎝⎭，则2log (2)f = 。
12 4、下面给出四个命题：①直线l 与平面a 内两直线都垂直，则l a ⊥； ②棱柱的侧棱都相等，侧面都是平行四边形；③圆锥的侧面展开图为扇形，这个扇形的半径等于圆锥底面的半径；④函数2()2log xf x x =-的零点有1个；⑤函数2()1,(0)f x x x =+≤的反函数是1()1)f x x -=≥。
其中正确的命题序号是 。
②⑤5、有五位同学报名参加两个课外活动小组，每位同学限报其中的一个小组，则不同的报名方法共有___________种。
326、如果函数23(0)()(0)x x y f x x ->⎧=⎨<⎩是奇函数，则()f x =____________。
23x +7、在北纬45o圈上有甲、乙两地，它们分别在东经50o与东经140o圈上，地球半径为R ，则甲、乙两地的球面距离是___________。
13R π8、在一个水平放置的底面半径为3的圆柱形量杯中装有适量的水，现放入一个半径为R 的实心铁球，球完全浸没于水中且无水溢出，若水面高度恰好上升R ，则R = 。
329、已知0,1a a >≠有两个命题：①函数log a y x =是减函数；②关于x 的不等式210ax +>的解集为R ，如果这两个命题中有且只有一个是真命题，则实数a 的取值范围是 。
()1,+∞10、一个盒子中装有4张卡片，上面分别写着四个函数：31()f x x =，42()f x x =，||3()2x f x =，41()f x x x=+，现从盒子中任取2张卡片，将卡片上的函数相乘得到一个新函数，所得函数为奇函数的概率是_________。
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Advanced Macroeconomics I
Instructor:Luo Daqing
Assignment2
Note:You may use either English or Chinese to answer the questions.
Question1(5points)
Suppose there is a large number of identical agents with preferences represented by
E0
∞
t=0
βt ln c t
where c t is consumption in period t.Agents can trade one-period real bonds.The gross return on a bond purchased in period t,denoted R t,is known at the time of purchase (i.e.the bonds are risk-free).Therefore,the price of a bond is R−1t.
The constraints faced by a representative agent are
c t+L t R−1
t
=A t,A t+1=L t,A0given
where A t is wealth at the beginning of period t and L t is the holding of one-period bonds.Assume that R t is identically and independently distributed and is such that E R t<1/β.
(a)(1pts)Using L t as the control variable,write down Bellman equation corresponding to the representative agent’s optimization problem.
(b)(2pts)Use dynamic programming to derive the Euler equation corresponding to the representative agent’s problem.Interpret this Euler equation.
(c)(2pts)Use the guess L t=γR t A t to solve for the policy function for bond holdings L t(and consumption).
Question2(5points)
Consider a simple“real business cycles”model where a planner maximizes utility
E0
∞
t=1
βt[ln c t+γln(1−n t)],0<β<1,γ>0
where c t denotes consumption and n t hours worked.The maximization is subject to the resource constraint
c t+x t=z t kα
t n1−α
t
,0<α<1
and the transition equation for capital
k t+1=(1−δ)k t+x t0≤δ<1.
k t denotes the capital stock installed at the beginning of period t and z t is a stochas-tic disturbance interpreted as a productivity shock.δis the capital depreciation rate. Assume that
ln z t∼iid(0,σ2
z
).
(a)(1pts)What are the state variables and the control variables for this problem? What is Bellman equation corresponding to this problem?
(b)(2pts)Using dynamic programming,derive the Euler equation for capital and the first-order condition for hours worked(substitute out any Lagrange multiplier).Interpret these equations.
(c)(1.5pts)Now assume thatδ=ing the guess and verify method,show that the policy function for hours worked is time-invariant and that the policy function for
investment is linear in output.(Hint:Guess k t+1=ηz t kα
t n1−α
t
=ηy t.)
(d)(0.5pts)In light of the results found in part(b),discuss the ability of this model to generate realisticfluctuations in hours worked.。