上财金融学院高宏课件(谭继军) (10)

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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.

高宏课件CHAPTER(1)

8.6 不确定性
8.7 金融市场的不完全性
h
11
f)
pK
(t)
其中: f为公司所得税减税比率
h
(8.5)
5
4.模型的不足之处
(1)假定资本存量调整是完全有弹性的，无成本的，无限制的，实际上投资受限于产出规模，因此投资和资本不可能无限连续(infinite)变动；
(2)未考虑预期因素: 当预期需求上升或资本成本下降时，K↑；
(3)对模型的修正: 引入资本存量的调整成本
1）内部调整成本：如安装新机器设备的成本，训练工人操纵新机器设备的成本，利率变动的成本等。
2）外部成本：资本h品价格的变化。
6
8.2 Q Theory Model of Investment
with Adjustment Cost
1.假定：
一产业有N个同质厂商
(1)一个典型厂商的实际利润与其资本存量(k(t))成正比（若规模报酬不变、产品市场完全竞争、
K(t) I(t) 2. 厂商的利润函数(8.6) 即利润=收益－I－调整成本若用离散时间，则(8.7)
h
8
预算约束 : kt1 kt It
最优化 : (8.8) t : 资本的边际收益
令 q t (1 r ) t , 变成 (8 .9 )
L : (8.10) I
为总收益, Xs:产品价格和要素成本等假定:K 0,KK0
2.合意的资本存量的确定
K P K (K ,X 1 ,X h2 ,X 3 , ,X n ) r K 0 3
K()rK (8.1)
厂商合意的资本存量 Kf(rK,X's)
对 (8.1)式对 rk求导 :

上财金融学院高宏课件(谭继军) (9)

— Introduce ﬁat money, a constant nominal money stock M . — Denote Pt as the price level at t, $/goods. — Two–period agents with endowment (w1 , w2 ) when young and old. — When young: Pt (w1 − c1t ) = mt , where mt is quantity of money acquired by a young agent. So w1 − c1t = which is called real money balance. Note that $/($/goods)=goods, so real money balance means how many goods are held. When old: Pt+1 c2t+1 = Pt+1 w2 + mt , or c2t+1 = w2 + mt m t Pt = w2 + · . Pt+1 Pt Pt+1 mt , Pt
which means real money balance demand/capita equals real money balance supply/capita. ⇒ Pt M = f (w1 , w2 , ), Pt N t Pt+1 where both M and Nt are exogenous. — Deﬁne zt =
— The agent max U (c1t , c2t+1 ), s.t. w1 − c1t = c2t+1 ⇔ max U (w1 −

上财金融学院高宏课件(谭继军) (3)

— This is less than the maximum sustainable production.
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。

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。

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。

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。

高宏课件3 lecture_OK

7
5 Stationary paths,interest rates and golden rules
• Pro 20.E.2 r>0 or r<0; • Golden Rule
8
6 Dynamics
• Forms of Dynamics (see figure20.F1-4) • Shocks:Transitory or Permanent (fig 20.F.7)
3
1 Introduction
• Structure of Time • Dynamic Aspects • Dynamics Equilibrium
4
2 Intertemporal Utility
• Comsumption stream c=(c0,…ct…),Bounded,||ct||<infinite
第三章宏观经济学中的微观经济学基础——时间与均衡
掌握动态一般均衡的基础知识；了解动态宏观经济学的微观基础；
从微um and Time， Chapter 20；in Mas-Colell, Whinston, Green, Microeconomics Theory,Oxford University Press,1995
2
Outline
• Introduction • Intertemporal Utility • Intertemporal Production and Effeciency • Equilibrium:One-Comsumer Case • Stationary Paths,Interest Rates and Golden Rules • Dynamics • Equilibrium:Several Consumers • Overlapping Generations • Remarks on Nonequilibrium Dynamics

上财金融学院高宏课件(谭继军) (5)

Case 2: r < n, government debt/GNP falls over time. (insert a graph)
— The government’s budget constraint: total government expenses equal total government revenues.
or
r
1
பைடு நூலகம்gt + n bt−1 = τ1 + n τ2 + bt.
— Consider a cut in taxes of 5 units per young person in period t but no
change in g.
So there must be an increase of 5 goods in government debt per young
Now in equilibrium,
U1 U2
= r = f (k∗).
So if r = n, the golden rule
conditions
are
meet
(
U1 U2
=
n
and
f
(k)
=
n).
All the government needs to know to implement this is the long run
3
3 The Eﬀect of the National Debt on Capital and Saving
Assume a tax of τ1 goods on each young person and τ2 goods on each old person and f (k) = x = r. Incorporating these taxes into individuals’ budget constraint:

债券培训基教材本资料-高老师

7、转股价格修正条款约定：如果股票在连续30个交易日中有20日的收盘价不高于当期转股价格的90%，公司董事会必须在上情况出现后看个工作日内向下修正幅度不低于当期转股价格10% 。
上海财经大学金融学院
30
例：新钢钒转债（续）
8、赎回条款：发行6个月至60个月期间，在可转债公司债到期之前，若公司A股股票在连续40个交易日中，至少30个交易日的收盘价不低于该30个交易日生效转股价的130%，公司有权赎回未赎回的可转债，每年当赎回条件首次满足时，公司有权按面值的105%（含当期利息）的价格赎回全部或者部分仍未转股的可转债。
收益性。债券的收益率通常比银行存款高，且比股票的收益率要稳定。
债券的返还性、流动性、安全性与收益性之间存在着一定的转换关系。
如果某种债券流动性强，安全性高，在市场上供不应求，价格会上涨，
其收益率也就随之降低;反之，如果某种债券风险大，流动性差，供过
于求，价格必然下降，上其海财收经益大率学随金融之学上院升。
24
可转换债券的性质
基本属性: 债券性期权性
隐含属性：股票性
上海财经大学金融学院
25
赎回条款的要素
• 赎回期 • 赎回条件 • 赎回价格
上海财经大学金融学院
26
赎回条款的特点
• 赎回条款是一种偿还方式 • 有利于发行人 • 限制了投资人可能取得的收益
上海财经大学金融学院
27
回售条款的要素：
• 在美国，中长期国债的利息收入正常缴纳联邦收入
税，但是部分州和地方可以豁免收入税。在我国，
国债免收利息税。上海财经大学金融学院
19
政府机构债券
• 政府机构债券是指某些政府机构为了筹措资金而发行的债券。在美国，许多政府机构发行债券，例如：联邦住房贷款银行、住房贷款抵押公司、联邦农业信贷体系、小企业管理局、学生贷款市场协会、全国抵押贷款协会等。政府机构债券与国库债券很相似，但是，这些债券不是财政部门的债务，财政部门不负责偿还。我国不允许政府机构发债。

高宏北大课件11

高级宏观经济学教师：张延北大经济学院硕博士生课程2012年11月26日2012-11-26 高宏（11）《高宏》讲义，张延著。

2012-11-26 高宏（11）《高宏》讲义，张延著。

就泰勒级数近似是否为有限变化提供好的指导这一问题，尚无一个普遍适用的答案。

对于多数值的不大变化而言，泰勒级数近似一般是相当可靠的。

2012-11-26 高宏（11）《高宏》讲义，张延著。

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zt+1 = 1 − δ + f (kt+1) · · · (∗∗).
zt
1+n
— Steady state:
1. k = 0 and z = 0 (trivial steady state).
2.
z
= 0 ⇒ kt+1
=
1 1+n
s(kt,
kt+1
).
So
any
non–trivial
steady–state
λ
c2
:
U2
=
1
+
. n
⇒ U1 = 1 + n. U2
So R¯GR = 1 + n = U1 . U2
While the C.E.:
U1 = R = 1 − δ + f (k∗). U2
Normally, k∗ > kGR, f (k∗) < f (kGR). People save two much. ⇒ Dynamic
— There are ﬁrms with production function, F (K, L), (CRS and F =
K FK
+ LFL).
Denote
k
=
K L
,
so
f (k)
=
F (k, 1).
— Firms: F.O.C.:
max F (Kt, Lt) − rtKt − wtLt.
By the ﬁrst order condition of the problem,
st = s(wt, 1 − δ + rt+1).
— Saving market clearing condition:
M Kt+1 + Pt = Nts(w(kt), 1 − δ + f (kt+1)).
Divided by Ntd model are still steady–state values here.
3. z = 0 ⇒ zt+1 = zt = z. From (**),
(kt)
= lim f (kt) − lim f (kt) = 0(Inada)
kt→∞
kt→∞
So we get kt+1 − kt graph as follows. (insert a graph) There exists at least a non–trivial steady state. It is not certain how many there are. If getting a steady state below, it must get one steady state upper.
⇒
max L
c1t ,c2t+1 ,zt ,it
= U (c1t, c2t+1) + λ1(wt − it −
mt Pt
− c1t)
+
λ2
(
mt Pt
Pt Pt+1
+
it(1
−
δ
+
rt+1)
−
c2t+1).
zt(
mt Pt
)
:
−λ1
+
λ2
Pt Pt+1
= 0,
it : −λ1 + λ2(1 − δ + rt+1) = 0.
— We still have wt = w(kt) and rt = f (kt). No change.
— But young:
max U (c1t, c2t+1),
5
s.t.
Ptc1t ≤ Ptwt − Ptit − mt, Pt+1c2t+1 ≤ mt + it(1 − δ + rt+1)Pt+1. v.s.
or
c1
+
1
c2 +
n
+
(1
+
n)kt+1
≤
f (kt)
+
(1
−
δ)kt.
⇔
max
U (c1,
c2)
+
λ(f (kt)
+
(1
−
δ)kt
−
c1
−
1
c2 +
n
−
kt+1(1
+
n)).
F.O.C.:
k : f (kGR) = n + δ, R¯GR = 1 − δ + f (kGR) = 1 + n,
c1 : U1 = λ,
c1t ≤ wt − st, (st = it)
c2t+1 ≤ stRt.
⇒
c1t
≤
wt
−
it
−
mt , Pt
c2t+1
≤
mt Pt
Pt Pt+1
+ it(1 − δ
+ rt+1),
where
Pt Pt+1
is
real
gross
rate
of
return
of
real
money
balance
and
1−
δ + rt+1 is rate of investment.
st
=
mt Pt
+
it,
⇒
Rtst
=
Pt ( mt Pt+1 Pt
+ it)
=
(1 − δ
+
rt+1)(
mt Pt
+ it).
So the budget constraints become:
c1t ≤ wt − st, c2t+1 ≤ Rtst.
6
So max U (wt − st, (1 − δ + rt+1)st).
growth), less capital/capita.
(insert a graph)
3.1 Steady state welfare
Social planner:
max U (c1, c2),
c1,c2,k
4
s.t. Ntc1 + Nt−1c2 + Kt+1 ≤ F (Kt, Nt) + (1 − δ)Kt,
)
dkt+1 dkt
)
⇒
dkt+1 (1 − s2f (kt+1) ) = s1w (kt) ,
dkt
1+n
1+n
where s1 > 0, s2 > 0, w (kt) > 0 and f (kt+1) < 0.
So dkt+1 > 0. dkt
3
–
Claim:
kt+1 kt
→ 0 as kt → ∞.
— F.O.C.:
s = s(w(kt), 1 − δ + f (kt+1)).
So Kt+1 = Nts(w(kt), 1 − δ + f (kt+1)),
⇒
Kt+1 Nt+1
=
Nt Nt+1
s(w(kt),
1
−
δ
+
f
(kt+1)),
⇒ 1
kt+1 = 1 + n s(w(kt), 1 − δ + f (kt+1)).
kt+1 +
M PtNt
·
Nt Nt+1
=
Nt Nt+1
s(w(kt),
1
−
δ
+
f
(kt+1)),
or
1
1
kt+1 + zt · 1 + n = 1 + n s(w(kt), 1 − δ + f (kt+1)) · · · (∗).
Also, ⇒
zt+1 = Pt ·
1 .
zt Pt+1 1 + n
If n ↑, look at the graph, mathematically keep kt+1, then w(k(kt)) need
to increase ⇒ kt need to increase. So the curve shifts right and the
steady state capital decrease. That is, higher 1 + n (higher population
0 ≤ kt+1 = s(wt, Rt) ≤ w(kt) kt (1 + n)kt (1 + n)kt
If w → constant, done; if not,
lim
kt→∞
w(kt) kt
=
lim ( f (kt) kt→∞ kt
−
f
(kt))
=
lim
kt→∞
f (kt) kt
−
lim f
kt→∞
— Then, from good market clearing,
Nt(w(kt) − st) + (1 − δ + rt)Kt + Kt+1 = F (Kt, Lt) + (1 − δ)Kt.

上财金融学院高宏课件(谭继军) (10)

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上财金融学院高宏课件(谭继军) (2)

高宏课件CHAPTER(1)

上财金融学院高宏课件(谭继军) (9)

上财金融学院高宏课件(谭继军) (3)

上财罗大庆高宏课件 (9)

高宏(08)2014年11月17日§2.1§2.2(纯白)

高宏课件3 lecture_OK

上财金融学院高宏课件(谭继军) (5)

债券培训基教材本资料-高老师

高宏北大课件11

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