高宏课件Chapter1SolowGrowthModel
合集下载
高宏课件Chapter 1 Solow Growth Model
Conditions
• These conditions imply each input is essential: F(0, L) = F(K, 0) = 0. • An example of a neoclassical production function is the Cobb-Douglas one: • Y = AKαL1-α, A > 0; 0 < α < 1. • This form implies unit elasticity of substitution between K and L. If factors paid marginal products, factor shares of income are constant at α for K and 1-α
Labor
• L = labor supply (market clears with full employment). Labor supply = population (or proportional to population). No labor leisure choice and labor-force-participation rate is constant. Can extend model to make these endogenous. • Population grows exogenously at rate n ≥ 0: (1/L)· (dL/dt) = n L(t) = L(0)· exp(nt) • Can extend model to make fertility, mortality, immigration endogenous—then n is endogenous.
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 :
高级宏观经济学索洛斯旺模型ppt课件
•.
•2
1 模型的假设
1、投入与产出：①生产函数的形式为Y(t)=F[K(t), A(t)L(t)]。资本K、劳动L、知识A(或称“劳动有效性”) 为投入，将各种投入结合在一起，即可以生产出产品Y。
②时间不直接进入生产函数，仅当投入随时间发生变化 时，产量才随时间发生变化。
③AL可称为有效劳动，以此种形式引入的技术称为 “哈罗德中性”技术。本模型采用“哈罗德中性”技术。
中的规模报酬不变假设.将生产函数改写为密集形式.
FcK,cAL cK cAL1 cc1K AL 1 cFK, AL
f
k
f
AKL,1
K AL
k.
容易验证: f 'k0, f ''k0
•.
•5
1 模型的假设
3、三种投入品变动的假设： ①劳动和知识以不变速度增长，L(t)= L(0)ent或
dL(t)/dt= nL(t)， A(t)= A(0)ent或dA(t)/dt= gA(t) 。 ②储蓄率s是外生的，现存资本的折旧率为б ，于
•.
•8
2 k的动态方程
将有效劳均总投资与持平投次 表示为k的函数。可得右上图。
右上图中，由于f(0)=0，因此， 当k=0时，实际投资与持平投 资相等。
稻田条件意味着当k=0时， f‘(k)很大，因而，实际投资曲 线陡于持平投资曲线。
稻田条件也意味着k很大时， k
f‘(k)趋近于0。 随着实际投资曲线变得平坦，
•.
•12
4 储蓄率变化的影响
如果f 'k * n g ,那么0
4 储蓄率变化的影响
1、对产量的影响：储蓄率s的增加会使实际投资 曲线向上移动,因此k*上升，但到达新的k*值后， 它又将保持不变。
高级宏观经济学索洛斯旺模型ppt课件
高级宏观经济学索洛斯旺模型ppt 课件
contents
目录
• 索洛-斯旺模型概述 • 索洛-斯旺模型中的经济增长 • 储蓄、投资与资本积累 • 劳动生产率、技术进步与经济增长 • 政策因素对索洛-斯旺模型的影响 • 索洛-斯旺模型在现实世界的应用 • 总结与展望
01 索洛-斯旺模型概述
模型背景与意义
03 储蓄、投资与资本积累
储蓄函数及影响因素
01
储蓄函数的定义与性质
02
储蓄是可支配收入减去消费的部分
储蓄函数描述了储蓄与可支配收入之间的关系
03
储蓄函数及影响因素
收入越高，储蓄倾向越大
收入水平
影响因素
01
03 02
储蓄函数及影响因素
利率水平 利率上升，储蓄增加；利率下降，储蓄减少
储蓄函数及影响因素
经济增长路径的特点
经济增长路径具有收敛性、稳定性和 动态性等特点。其中收敛性是指不同 经济体在长期中趋向于相同的稳态均 衡状态；稳定性是指经济增长路径在 受到外部冲击时能够保持相对稳定； 动态性是指经济增长路径随着技术进 步和制度变迁等因素的变化而不断调 整。
经济增长路径的政策 含义
经济增长路径的政策含义在于，政府 可以通过调整经济政策来影响经济增 长的路径和速度。例如，通过提高投 资率、促进技术进步、优化产业结构 等措施来加快经济增长；同时，也需 要关注经济增长带来的资源环境压力 和社会公平问题，实现可持续发展。
03
加强教育和科技创新投入，提高人力资本 积累水平。
04
推进产业结构调整和升级，优化资源配置 效率。
04 劳动生产率、技术进步与 经济增长
劳动生产率提升途径
教育和培训
通过提高劳动者的知识和技能水平，提升劳动 生产率。
contents
目录
• 索洛-斯旺模型概述 • 索洛-斯旺模型中的经济增长 • 储蓄、投资与资本积累 • 劳动生产率、技术进步与经济增长 • 政策因素对索洛-斯旺模型的影响 • 索洛-斯旺模型在现实世界的应用 • 总结与展望
01 索洛-斯旺模型概述
模型背景与意义
03 储蓄、投资与资本积累
储蓄函数及影响因素
01
储蓄函数的定义与性质
02
储蓄是可支配收入减去消费的部分
储蓄函数描述了储蓄与可支配收入之间的关系
03
储蓄函数及影响因素
收入越高，储蓄倾向越大
收入水平
影响因素
01
03 02
储蓄函数及影响因素
利率水平 利率上升，储蓄增加；利率下降，储蓄减少
储蓄函数及影响因素
经济增长路径的特点
经济增长路径具有收敛性、稳定性和 动态性等特点。其中收敛性是指不同 经济体在长期中趋向于相同的稳态均 衡状态；稳定性是指经济增长路径在 受到外部冲击时能够保持相对稳定； 动态性是指经济增长路径随着技术进 步和制度变迁等因素的变化而不断调 整。
经济增长路径的政策 含义
经济增长路径的政策含义在于，政府 可以通过调整经济政策来影响经济增 长的路径和速度。例如，通过提高投 资率、促进技术进步、优化产业结构 等措施来加快经济增长；同时，也需 要关注经济增长带来的资源环境压力 和社会公平问题，实现可持续发展。
03
加强教育和科技创新投入，提高人力资本 积累水平。
04
推进产业结构调整和升级，优化资源配置 效率。
04 劳动生产率、技术进步与 经济增长
劳动生产率提升途径
教育和培训
通过提高劳动者的知识和技能水平，提升劳动 生产率。
L3_Solow_augmenting_technology
Consumption per unit of effective labor: c (t ) = (1 − s )y (t ) Investment per unit of effective labor: i (t ) = sy (t ) Output per unit of effective labor: y (t ) = f [k (t )] The fundamental law of motion of the Solow model: ˙ (t ) = sf [k (t )] − (n + g + δ )k (t ) k
A Permanent Increase in the Saving Rate
∗ ] − (n + g + δ ) ≤ 0 Case 1: snew f [kold
0.16 0.14 0.12
Small Increase in the Saving Rate
ሶ
0.1 0.08 0.06 0.04 0.02 0
Essentiality: f (0) = 0
f (0) = F [0, 1] = 0
Unboundedness: lim f [k ] = ∞
k →∞
K →∞ K lim F [K , AL] = AL lim F [ AL , 1] = AL lim f [k ]
K AL →∞
k →∞
Equilibrium
+δ − n+g =0 s
(k ∗ )2
Using Implicit Function Theorem, we can obtain
Q /∂ s n+g +δ = − ∂∂Q /∂ k ∗ = − s 2
A Permanent Increase in the Saving Rate
∗ ] − (n + g + δ ) ≤ 0 Case 1: snew f [kold
0.16 0.14 0.12
Small Increase in the Saving Rate
ሶ
0.1 0.08 0.06 0.04 0.02 0
Essentiality: f (0) = 0
f (0) = F [0, 1] = 0
Unboundedness: lim f [k ] = ∞
k →∞
K →∞ K lim F [K , AL] = AL lim F [ AL , 1] = AL lim f [k ]
K AL →∞
k →∞
Equilibrium
+δ − n+g =0 s
(k ∗ )2
Using Implicit Function Theorem, we can obtain
Q /∂ s n+g +δ = − ∂∂Q /∂ k ∗ = − s 2
高级宏观经济学 02 The Solow growth model
( ) ( ) ⇒ sf ' k∗ ∂k∗ + f k∗ = (n + g + δ ) ∂k∗
∂s
∂s
⇒
∂k ∗ ∂s
=
(n +
g
f (k∗ )
+ δ )− sf
'(k∗ )
⇒
∂y∗ ∂s
=
f '(k∗ )f (k∗ ) (n + g + δ )− sf '(k∗ )
( ) k∗ f ' k∗
( )( ( ) ) ( ( ) ) ⇒
z f (0) = 0, f '(k) > 0, f "(k) < 0
z Inada (1964) conditions: lim f '(k) = ∞, lim f '(k) = 0
k →0
k →∞
To ensure that the path of the economy does not diverge
z The saving rate is exogenous in the Solow model z The impact on output:
z The long-run effect
k The effect of an increase in the saving rate on
investment
∂y∗ ∂s
s y∗
= 1−k∗ f '
f k∗
k∗ f k∗
=
1
αK −α
k
K
∗
k
∗
4
( ) z
Empirical evidence shows: αK k∗
高宏课件Chapter 1 Solow Growth Model
高宏课件Chapter 1 Solow Growth Model
# 高宏课件Chapteห้องสมุดไป่ตู้ 1 Solow Growth Model
简介
描述S olow增长模型的意义和应用，解释其重要组成部分。 Introduce the significance and applications of the Solow Growth Model and explain its important components.
总结
S olow模型的优缺点，S olow模型在经济增长研究中的价值，S olow模型的未来应用和发展趋势。 Summary: strengths and weaknesses of the Solow Model, its value in economic growth research, and future applications and development trends.
Solow模型概述
S olow模型的基本假设，生产函数和边际产出，稳态状态和收敛性。 Overview of the Solow Model: assumptions, production function and marginal output, steady state and convergence.
模型应用
S olow模型在各种经济系统中的应用，特定假设下的计算，政策建议的制定。 Applications of the Solow Model: its use in various economic systems, calculations under specific assumptions, formulation of policy recommendations.
# 高宏课件Chapteห้องสมุดไป่ตู้ 1 Solow Growth Model
简介
描述S olow增长模型的意义和应用，解释其重要组成部分。 Introduce the significance and applications of the Solow Growth Model and explain its important components.
总结
S olow模型的优缺点，S olow模型在经济增长研究中的价值，S olow模型的未来应用和发展趋势。 Summary: strengths and weaknesses of the Solow Model, its value in economic growth research, and future applications and development trends.
Solow模型概述
S olow模型的基本假设，生产函数和边际产出，稳态状态和收敛性。 Overview of the Solow Model: assumptions, production function and marginal output, steady state and convergence.
模型应用
S olow模型在各种经济系统中的应用，特定假设下的计算，政策建议的制定。 Applications of the Solow Model: its use in various economic systems, calculations under specific assumptions, formulation of policy recommendations.
最新高宏课件Chapter 1 Solow Growth Model精品资料
• Y = F(K, L, t). • Common assumption to get nice steady-state
results, when n = (1/L)·(dL/dt) is constant, is that technical progress takes labor augmenting, Kaldor form. Y depends on K and effective labor, • Lˆ = L·φ(t) Y = F(K, Lˆ ).
• An example of a neoclassical production function is the Cobb-Douglas one:
• Y = AKαL1-α, A > 0; 0 < α < 1. • This form implies unit elasticity ond Model Structure
• Production:Neoclassical production function: Y = F(K, L, A).
• A: non-rival, non-excludible technology. • One-sector technology: Y goes for C or ΔK (gross investment). • K, capital, is cumulated net investment. Can interpret K to include human capital. K depreciates at rate δ > 0 (exogenous).
extend model to make these endogenous.
• Population grows exogenously at rate n ≥ 0:
results, when n = (1/L)·(dL/dt) is constant, is that technical progress takes labor augmenting, Kaldor form. Y depends on K and effective labor, • Lˆ = L·φ(t) Y = F(K, Lˆ ).
• An example of a neoclassical production function is the Cobb-Douglas one:
• Y = AKαL1-α, A > 0; 0 < α < 1. • This form implies unit elasticity ond Model Structure
• Production:Neoclassical production function: Y = F(K, L, A).
• A: non-rival, non-excludible technology. • One-sector technology: Y goes for C or ΔK (gross investment). • K, capital, is cumulated net investment. Can interpret K to include human capital. K depreciates at rate δ > 0 (exogenous).
extend model to make these endogenous.
• Population grows exogenously at rate n ≥ 0:
- 1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
- 2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
- 3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。
• An example of a neoclassical production function is the Cobb-Douglas one:
• Y = AKαL1-α, A > 0; 0 < α < 1. • This form implies unit elasticity of substitution
between K and L. If factors paid marginal products, factor shares of income are constant at α for K and 1-α
Technological progress
• Basic model assumes exogenous technological progress—A depends only on time, t:
• Y = F(K, L, t). • Common assumption to get nice steady-state
results, when n = (1/L)·(dL/dt) is constant, is that technical progress takes labor augmenting, Kaldor form. Y depends on K and effective labor, • Lˆ = L·φ(t) Y = F(K, Lˆ ).
Chapter1SolowGrowthModel
Factsabouteconomicgrowth; Assumptionandmodelstructure; Dynamics;Comparativestatic;Conver gence;Dataandgrowthaccounting;Ho
meworkandpaper
About A
• If technical change takes place at constant rate
• x ≥ 0, Lˆ= L exp(xt), • Lˆ grows at rate n + x. • Technology might instead augment K
(Solow) or F(K, L) overall (Hicks). If production function is Cobb-Douglas, the three forms are indistinguishable.
Properties of neoclassical
production function
• Constant returns to scale (CRS) in K, L: F(λK, λL, A) =λ·F(K, L, A) for allλ >0
• Positive and diminishing marginal products: FK , FL > 0; FKK, FLL < 0.
• L = labor supply (market clears with full employment). Labor supply = population (or proportional to population). No labor leisure choice and labor-force-participation rate is constant. Can extend model to make these endogenous.
• Limiting (Inada) conditions:
• Lim (FK) = ∞, Lim (FFK) = 0, Lim (FL) = 0;
• K→∞
L→∞
Conditions
• These conditions imply each input is essential: F(0, L) = F(K, 0) = 0.
1 Facts and key questions
• Growth rates differ: as China,US, Africa; • Productivity growth slowdown; • See Pictures • Key question: what drives economic growth • Key question 2:why it differ so much? • Now we start with Solow model • Question:Why starts with Solow?
• Population grows exogenously at rate n ≥ 0:
• (1/L)·(dL/dt) = n
L(t) = L(0)·exp(nt)
• Can extend model to make fertility, mortality, immigration endogenous—then n is endogenous.
Model Structure
• Standard model has labor-augmenting technical change at constant rate, x.
2Assumptions and Model Structure
• Production:Neoclassical production function:
•
Y = F(K, L, A).
• A: non-rival, non-excludible technology.
• One-sector technology: Y goes for C or ΔK
• (gross investment).
• K, capital, is cumulated net investment. Can
• interpret K to include human capital. K
• depreciates at rate δ > 0 (exogenous).
Labor
• Y = AKαL1-α, A > 0; 0 < α < 1. • This form implies unit elasticity of substitution
between K and L. If factors paid marginal products, factor shares of income are constant at α for K and 1-α
Technological progress
• Basic model assumes exogenous technological progress—A depends only on time, t:
• Y = F(K, L, t). • Common assumption to get nice steady-state
results, when n = (1/L)·(dL/dt) is constant, is that technical progress takes labor augmenting, Kaldor form. Y depends on K and effective labor, • Lˆ = L·φ(t) Y = F(K, Lˆ ).
Chapter1SolowGrowthModel
Factsabouteconomicgrowth; Assumptionandmodelstructure; Dynamics;Comparativestatic;Conver gence;Dataandgrowthaccounting;Ho
meworkandpaper
About A
• If technical change takes place at constant rate
• x ≥ 0, Lˆ= L exp(xt), • Lˆ grows at rate n + x. • Technology might instead augment K
(Solow) or F(K, L) overall (Hicks). If production function is Cobb-Douglas, the three forms are indistinguishable.
Properties of neoclassical
production function
• Constant returns to scale (CRS) in K, L: F(λK, λL, A) =λ·F(K, L, A) for allλ >0
• Positive and diminishing marginal products: FK , FL > 0; FKK, FLL < 0.
• L = labor supply (market clears with full employment). Labor supply = population (or proportional to population). No labor leisure choice and labor-force-participation rate is constant. Can extend model to make these endogenous.
• Limiting (Inada) conditions:
• Lim (FK) = ∞, Lim (FFK) = 0, Lim (FL) = 0;
• K→∞
L→∞
Conditions
• These conditions imply each input is essential: F(0, L) = F(K, 0) = 0.
1 Facts and key questions
• Growth rates differ: as China,US, Africa; • Productivity growth slowdown; • See Pictures • Key question: what drives economic growth • Key question 2:why it differ so much? • Now we start with Solow model • Question:Why starts with Solow?
• Population grows exogenously at rate n ≥ 0:
• (1/L)·(dL/dt) = n
L(t) = L(0)·exp(nt)
• Can extend model to make fertility, mortality, immigration endogenous—then n is endogenous.
Model Structure
• Standard model has labor-augmenting technical change at constant rate, x.
2Assumptions and Model Structure
• Production:Neoclassical production function:
•
Y = F(K, L, A).
• A: non-rival, non-excludible technology.
• One-sector technology: Y goes for C or ΔK
• (gross investment).
• K, capital, is cumulated net investment. Can
• interpret K to include human capital. K
• depreciates at rate δ > 0 (exogenous).
Labor