| Type: | Package |
| Title: | Computing General Equilibrium |
| Version: | 0.3.3 |
| Author: | LI Wu <liwu@staff.shu.edu.cn> |
| Maintainer: | LI Wu <liwu@staff.shu.edu.cn> |
| Description: | Developing general equilibrium models, computing general equilibrium and simulating economic dynamics with structural dynamic models in LI (2019, ISBN: 9787521804225) "General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press". When developing complex general equilibrium models, GE package should be used in addition to this package. |
| License: | GPL-2 | GPL-3 |
| Encoding: | UTF-8 |
| LazyData: | true |
| BugReports: | https://github.com/LiWuR/CGE/issues |
| RoxygenNote: | 7.1.0 |
| NeedsCompilation: | no |
| Packaged: | 2020-05-24 01:50:01 UTC; 86189 |
| Repository: | CRAN |
| Date/Publication: | 2020-05-24 05:00:11 UTC |
Cobb-Douglas Demand Structure Matrix
Description
This function computes the Cobb-Douglas demand structure matrix.
Usage
CD_A(alpha, Beta, p)
Arguments
alpha |
a nonnegative numeric m-vector or m-by-1 matrix. |
Beta |
a nonnegative numeric n-by-m matrix whose each column sum equals 1. |
p |
a nonnegative numeric n-vector or n-by-1 matrix. |
Value
A demand coefficient n-by-m matrix is computed which indicates the demands of agents (firms or consumers) for obtaining unit product or utility with Cobb-Douglas production functions or utility functions under the price vector p.
Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Examples
CD_A(1, c(0.5, 0.5), c(1, 2))
#####
alpha <- c(5, 3, 1)
Beta <- matrix(c(
0.6, 0.4, 0.2,
0.1, 0.4, 0.7,
0.3, 0.2, 0.1
), 3, 3, TRUE)
p <- 1:3
CD_A(alpha, Beta, p)
Cobb-Douglas Monetary Demand Structure Matrix
Description
This function computes a Cobb-Douglas monetary demand structure matrix in a monetary economy.
Usage
CD_mA(alpha, Beta, p)
Arguments
alpha |
a nonnegative numeric m-vector or m-by-1 matrix. |
Beta |
nonnegative numeric n-by-m matrix whose each column sum equals 1. |
p |
a nonnegative numeric n-vector or n-by-1 matrix. |
Details
Some elements of Beta corresponding to money equal -1.
Value
A n-by-m matrix is computed which indicates the (monetary) demand structure of agents (firms or consumers) with Cobb-Douglas production functions or utility functions under the price vector p.
Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Examples
alpha <- c(1, 1, 1)
Beta <- matrix(c(
0.5, 0.5, 0.5,
0.5, 0.5, 0.5,
-1, -1, -1
), 3, 3, TRUE)
p <- c(1, 2, 0.1)
CD_mA(alpha, Beta, p)
CES Demand Coefficient Matrix
Description
This function computes the CES demand coefficient matrix.
Usage
CES_A(sigma, alpha, Beta, p, Theta = NULL)
Arguments
sigma |
a numeric m-vector or m-by-1 matrix. |
alpha |
a nonnegative numeric m-vector or m-by-1 matrix. |
Beta |
a nonnegative numeric n-by-m matrix. |
p |
a nonnegative numeric n-vector or n-by-1 matrix. |
Theta |
null or a positive numeric n-by-m matrix. |
Value
A demand coefficient n-by-m matrix is computed which indicates the demands of agents (firms or consumers) for obtaining unit product or utility with CES production functions or utility functions (e.g. alpha*(beta1*x1^sigma+beta2*x2^sigma)^(1/sigma) or alpha*(beta1*(x1/theta1)^sigma+beta2*(x2/theta2)^sigma)^(1/sigma)) under the price vector p.
Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Examples
CES_A(-1, 2, c(0.2, 0.1), c(1, 2))
#####
sigma <- c(-1, -1, -1)
alpha <- c(1, 1, 1)
Beta <- matrix(c(
0, 1, 1,
1, 0, 0,
1, 0, 0
), 3, 3, TRUE)
p <- 1:3
CES_A(sigma, alpha, Beta, p)
#####
sigma <- -1e-10
alpha <- 1
Beta <- c(0.8, 0.2)
Theta <- c(2, 1)
p <- c(1, 1)
CES_A(sigma, alpha, Beta, p, Theta)
CD_A(alpha * prod(Theta^(-Beta)), Beta, p)
CES_A(sigma, alpha, Beta, p, Beta)
CD_A(alpha * prod(Beta^(-Beta)), Beta, p)
CES_A(-1e5, alpha, Beta, p, Theta)
CES Monetary Demand Coefficient Matrix
Description
This function computes a CES monetary demand coefficient matrix in a monetary economy.
Usage
CES_mA(sigma, alpha, Beta, p, Theta = NULL)
Arguments
sigma |
a numeric m-vector or m-by-1 matrix. |
alpha |
a nonnegative numeric m-vector or m-by-1 matrix. |
Beta |
a nonnegative numeric n-by-m matrix whose each column sum equals 1. |
p |
a nonnegative numeric n-vector or n-by-1 matrix. |
Theta |
null or a positive numeric n-by-m matrix. |
Details
Some elements of Beta corresponding to money equal -1.
Value
A n-by-m matrix is computed which indicates the (monetary) demand structure of agents (firms or consumers) with CES production functions or utility functions under the price vector p.
Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Examples
alpha <- matrix(1, 6, 1)
Beta <- matrix(c(
0, 1, 1, 0, 1, 1,
0.5, 0, 0, 0, 0, 0,
-1, -1, -1, 0, 0, 0,
0.5, 0, 0, 0.5, 0, 0,
0, 0, 0, 0.5, 0, 0,
0, 0, 0, -1, -1, -1
), 6, 6, TRUE)
p <- c(1, 2, 0.1, 4, 5, 0.1)
CES_mA(rep(-1, 6), alpha, Beta, p)
A CGE Model of China based on the Input-Output Table of 2012 (Unit: Ten Thousand RMB)
Description
This data set gives parameters of a CGE model of China based on the input-output table of 2012.
Usage
ChinaCGE2012Format
A list containing the following components:
| A(state) | function | a function which returns a demand structure 41-by-38 matrix under a given price 41-vector. |
| B | numeric | a supply structure 41-by-38 matrix. |
| S0Exg | numeric | an exogenous supply 41-by-38 matrix. |
| z0 | numeric | an initial exchange levels (i.e. activity levels, production levels or utility levels) 38-vector. |
| subject.names | character | names of 41 subjects (or commodities). |
| sector.names | character | names of 38 sectors. |
Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Examples
ChinaCGE2012$A(list(p = rep(1, 41)))
#####
cge <- function(GRExg = 0) {
sdm(
A = ChinaCGE2012$A,
B = ChinaCGE2012$B,
S0Exg = ChinaCGE2012$S0Exg,
GRExg = GRExg,
z0 = ChinaCGE2012$z0,
priceAdjustmentVelocity = 0.03
)
}
#####
ge0 <- cge()
names(ge0$p) <- ChinaCGE2012$subject.names
ge0$p
names(ge0$z) <- ChinaCGE2012$sector.names
ge0$z
#####
ge6 <- cge(GRExg = 0.06)
names(ge6$p) <- ChinaCGE2012$subject.names
ge6$p
names(ge6$z) <- ChinaCGE2012$sector.names
ge6$z
Example 15.B.1 in MWG (1995)
Description
This is Example 15.B.1 in MWG (1995, P519), which is a pure exchange Cobb-Douglas 2-by-2 economy.
Usage
Example.MWG.15.B.1(
a = 0.1,
S0Exg = matrix(c(
1, 2,
2, 1
), 2, 2, TRUE)
)
Arguments
a |
Each consumer has the Cobb-Douglas utility function x1^a*x2^(1-a). |
S0Exg |
exogenous supply matrix which will be passed to the function sdm. |
Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Mas-Colell, Andreu and Whinston, Michael Dennis and Green, Jerry R. (1995, ISBN: 0195073401) Microeconomic Theory. Oxford University Press (New York).
Examples
Example.MWG.15.B.1()
#####
Example.MWG.15.B.1(a = 0.2)
#####
S <- matrix(c(
18, 72,
40, 20
), 2, 2, TRUE)
ge <- Example.MWG.15.B.1(a = 0.2, S0Exg = S)
ge$p / ge$p[1]
Example 15.B.2 in MWG (1995)
Description
This is Example 15.B.2 in MWG (1995, P521), which is a pure exchange 2-by-2 economy with quasilinear utility functions.
Usage
Example.MWG.15.B.2(p0 = c(1, 0.3))
Arguments
p0 |
an initial price 2-vector, which will be passed to the function sdm. |
Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Mas-Colell, Andreu and Whinston, Michael Dennis and Green, Jerry R. (1995, ISBN: 0195073401) Microeconomic Theory. Oxford University Press (New York).
Examples
ge <- Example.MWG.15.B.2()
ge$p
#####
ge <- Example.MWG.15.B.2(p0 = c(0.3, 1))
ge$p
#####
ge <- Example.MWG.15.B.2(p0 = c(1, 1))
ge$p
Exercise 15.B.6 in MWG (1995)
Description
This is Exercise 15.B.6 in MWG (1995, P541), which is a pure exchange CES 2-by-2 economy.
Usage
Example.MWG.Exercise.15.B.6(p0 = c(1, 2))
Arguments
p0 |
an initial price 2-vector, which will be passed to the function sdm. |
Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Mas-Colell, Andreu and Whinston, Michael Dennis and Green, Jerry R. (1995, ISBN: 0195073401) Microeconomic Theory. Oxford University Press (New York).
Examples
ge <- Example.MWG.Exercise.15.B.6()
ge$p / ge$p[2] # (3/4)^3
#####
ge <- Example.MWG.Exercise.15.B.6(p0 = c(2, 1))
ge$p / ge$p[2] # (4/3)^3
#####
ge <- Example.MWG.Exercise.15.B.6(p0 = c(1, 1))
ge$p
Exercise 15.B.9 in MWG (1995)
Description
This is Exercise 15.B.9 in MWG (1995, P541), which is a pure exchange 2-by-2 economy.
Usage
Example.MWG.Exercise.15.B.9(
S0Exg = matrix(c(
30, 0,
0, 20
), 2, 2, TRUE)
)
Arguments
S0Exg |
an exogenous supply matrix, which will be passed to the function sdm. |
Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Mas-Colell, Andreu and Whinston, Michael Dennis and Green, Jerry R. (1995, ISBN: 0195073401) Microeconomic Theory. Oxford University Press (New York).
Examples
Example.MWG.Exercise.15.B.9()
#####
S <- matrix(c(
5, 0,
0, 20
), 2, 2, TRUE)
Example.MWG.Exercise.15.B.9(S0Exg = S)
Example in Section.3.1.2 of Li (2019)
Description
This is the example in Section.3.1.2 of Li (2019), which is a Leontief-type two-sector corn economy.
Usage
Example.Section.3.1.2.corn()
Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Exercise 18.2 in Varian (1992)
Description
This is Exercise 18.2 in Varian (1992, P357), which is a Cobb-Douglas 3-by-4 economy.
Usage
Example.Varian.Exercise.18.2()
Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Varian, Hal R. (1992, ISBN: 0393957357) Microeconomic Analysis. W. W. Norton & Company.
Examples
ge <- Example.Varian.Exercise.18.2()
ge$A %*% diag(ge$z) #input matrix
Example on Page 352 in Varian (1992)
Description
This is the example on page 352 in Varian (1992) (see also Example 15.C.2. in MWG, 1995, P542), which is a decreasing-returns-to-scale Cobb-Douglas 3-by-2 economy and can be transformed into a constant-returns-to-scale 3-by-3 (or 3-by-2) economy.
Usage
Example.Varian.P352(agent.number = 3)
Arguments
agent.number |
agent.number can be set to 3 or 2. |
Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Mas-Colell, Andreu and Whinston, Michael Dennis and Green, Jerry R. (1995, ISBN: 0195073401) Microeconomic Theory. Oxford University Press (New York).
Varian, Hal R. (1992, ISBN: 0393957357) Microeconomic Analysis. W. W. Norton & Company.
Examples
Example.Varian.P352()
#####
Example.Varian.P352(agent.number = 2)
Example 2.2 in Li (2019)
Description
This is Example 2.2 in Li (2019), which is a Cobb-Douglas pure production economy.
Usage
Example2.2()
Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Example2.3 in Li (2019)
Description
This is Example 2.3 in Li (2019), which is a von Neumann economy.
Usage
Example2.3()
Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Example 3.1 in Li (2019)
Description
This is Example 3.1 in Li (2019),which is a two-sector corn economy with a non-homothetic utility function.
Usage
Example3.1()
Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Example 3.10 in Li (2019)
Description
This is Example 3.10 in Li (2019),which is a Leontief corn economy with three primary factors.
Usage
Example3.10()
Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Example 3.12 in Li (2019)
Description
This is Example 3.12 in Li (2019),which is an economy with decreasing returns to scale.
Usage
Example3.12()
Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Example 3.14 in Li (2019)
Description
This is Example 3.14 in Li (2019),which illustrates the relationship between a regular economy and a pure exchange economy.
Usage
Example3.14()
Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Example 3.2 in Li (2019)
Description
This is Example 3.2 in Li (2019),which is a Cobb-Douglas two-sector corn economy.
Usage
Example3.2()
Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Example 3.4 in Li (2019)
Description
This is Example 3.2 in Li (2019),which is a Lontief three-sector economy with one primary factor.
Usage
Example3.4()
Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Example 3.8 in Li (2019)
Description
This is Example 3.8 in Li (2019),which is a Cobb-Douglas three-sector economy with one primary factor.
Usage
Example3.8()
Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Example 3.9 in Li (2019)
Description
This is Example 3.9 in Li (2019),which is a Cobb-Douglas three-sector economy with two primary factors.
Usage
Example3.9()
Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Example 4.10 in Li (2019)
Description
This is Example 4.10 in Li (2019),which illustrates the tax.
Usage
Example4.10()Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
First Part of Example 4.11 in Li (2019)
Description
This is the first part of Example 4.11 in Li (2019),which illustrates the tax.
Usage
Example4.11.1()Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Second Part of Example 4.11 in Li (2019)
Description
This is the second part of Example 4.11 in Li (2019),which illustrates the tax.
Usage
Example4.11.2()Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Example 4.12 in Li (2019)
Description
This is Example 4.12 in Li (2019),which illustrates the tax.
Usage
Example4.12()Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Example 4.13 in Li (2019)
Description
This is Example 4.13 in Li (2019),which illustrates the divident.
Usage
Example4.13()Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Example 4.15 in Li (2019)
Description
This is Example 4.15 in Li (2019),which illustrates over-investment.
Usage
Example4.15()Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Example 4.16 in Li (2019)
Description
This is Example 4.16 in Li (2019),which illustrates technology monopoly.
Usage
Example4.16()Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Example 4.2 in Li (2019)
Description
This is Example 4.2 in Li (2019), which illustrates the non-sufficient supply of the primary factor.
Usage
Example4.2()
Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Example 4.8 in Li (2019)
Description
This is Example 4.8 in Li (2019),which illustrates the increasing returns to scale.
Usage
Example4.8()Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Example 4.9 in Li (2019)
Description
This is Example 4.9 in Li (2019),which illustrates the price signal.
Usage
Example4.9()Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Example 5.1 in Li (2019)
Description
This is Example 5.1 in Li (2019),which illustrates fixed assets.
Usage
Example5.1()Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Example 5.10 in Li (2019)
Description
This is Example 5.10 in Li (2019),which illustrates pollution.
Usage
Example5.10()Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
First Part of Example 5.11 in Li (2019)
Description
This is the first part of Example 5.11 in Li (2019),which illustrates pollution.
Usage
Example5.11.1()Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Second Part of Example 5.11 in Li (2019)
Description
This is the second part of Example 5.11 in Li (2019),which illustrates pollution.
Usage
Example5.11.2()Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Example 5.2 in Li (2019)
Description
This is Example 5.2 in Li (2019),which illustrates fixed assets.
Usage
Example5.2()Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
First Part of Example 5.3 in Li (2019)
Description
This is the first part of Example 5.3 in Li (2019),which illustrates fixed assets.
Usage
Example5.3.1()Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Second Part of Example 5.3 in Li (2019)
Description
This is the second part of Example 5.3 in Li (2019),which illustrates fixed assets.
Usage
Example5.3.2()Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Example 5.4 in Li (2019)
Description
This is Example 5.4 in Li (2019),which illustrates fixed assets.
Usage
Example5.4()Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Example 5.5 in Li (2019)
Description
This is Example 5.5 in Li (2019),which illustrates fixed assets.
Usage
Example5.5()Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Example 5.6 in Li (2019)
Description
This is Example 5.6 in Li (2019),which illustrates fixed assets.
Usage
Example5.6()Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Example 6.10 in Li (2019)
Description
This is Example 6.10 in Li (2019),which illustrates a two-country economy.
Usage
Example6.10()Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Example 6.11 in Li (2019)
Description
This is Example 6.11 in Li (2019),which illustrates a two-country economy.
Usage
Example6.11()Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Example 6.13 in Li (2019)
Description
This is Example 6.13 in Li (2019),which illustrates a two-country economy.
Usage
Example6.13()Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Examples
ge <- Example6.13()
matplot(ge$ts.p, type = "l")
matplot(ge$ts.z, type = "l")
First Part of Example 6.2 in Li (2019)
Description
This is the first part of Example 6.2 in Li (2019),which illustrates a two-country economy.
Usage
Example6.2.1()Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Second Part of Example 6.2 in Li (2019)
Description
This is the second part of Example 6.2 in Li (2019),which illustrates a two-country economy.
Usage
Example6.2.2()Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Example 6.3 in Li (2019)
Description
This is Example 6.3 in Li (2019),which illustrates a two-country economy.
Usage
Example6.3()Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Example 6.4 in Li (2019)
Description
This is Example 6.4 in Li (2019),which illustrates a two-country economy.
Usage
Example6.4()Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Example 6.5 in Li (2019)
Description
This is Example 6.5 in Li (2019),which illustrates a two-country economy.
Usage
Example6.5()Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
First Part of Example 6.6 in Li (2019)
Description
This is the first part of Example 6.6 in Li (2019),which illustrates a two-country economy.
Usage
Example6.6.1()Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Second Part of Example 6.6 in Li (2019)
Description
This is the second part of Example 6.6 in Li (2019),which illustrates the first country of a two-country economy.
Usage
Example6.6.2()Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Third Part of Example 6.6 in Li (2019)
Description
This is the third part of Example 6.6 in Li (2019),which illustrates the second country of a two-country economy.
Usage
Example6.6.3()Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Example 6.7 in Li (2019)
Description
This is Example 6.7 in Li (2019),which illustrates a two-country economy.
Usage
Example6.7()Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Example 6.9 in Li (2019)
Description
This is Example 6.9 in Li (2019),which illustrates a two-country economy.
Usage
Example6.9()Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Example 7.1 in Li (2019)
Description
This is Example 7.1 in Li (2019),which illustrates a monetary pure exchange economy.
Usage
Example7.1()Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Example 7.10 in Li (2019)
Description
This is Example 7.10 in Li (2019), which illustrates fiat money and representative money.
Usage
Example7.10()Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Extra Part of Example 7.10 in Li (2019)
Description
This is an extra part of Example 7.10 in Li (2019), which illustrates fiat money and representative money.
Usage
Example7.10.2()Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Example 7.11 in Li (2019)
Description
This is Example 7.11 in Li (2019), which illustrates bond.
Usage
Example7.11()Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Example 7.12 in Li (2019)
Description
This is Example 7.12 in Li (2019), which illustrates the foreign exchange rate and international credit.
Usage
Example7.12()Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Example 7.13 in Li (2019)
Description
This is Example 7.13 in Li (2019), which illustrates indirect financing based on commercial banks.
Usage
Example7.13()Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Example 7.14 in Li (2019)
Description
This is Example 7.14 in Li (2019), which illustrates shadow prices.
Usage
Example7.14()Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Example 7.15 in Li (2019)
Description
This is Example 7.15 in Li (2019), which illustrates shadow prices and international trade.
Usage
Example7.15()Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Example 7.2 in Li (2019)
Description
This is Example 7.2 in Li (2019),which illustrates a monetary Cobb-Douglas zero-growth corn economy.
Usage
Example7.2()Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Examples
## Another way to compute this equilibrium, i.e. treating money as tax receipt.
r <- 0.25
ge <- sdm(
A = function(state) {
alpha <- rbind(1, 1, 1)
Beta <- matrix(c(
0.5, 0.5, 0.5,
0.5, 0.5, 0.5
), 2, 3, TRUE)
tmp.A <- CD_A(alpha, Beta, state$p[1:2])
tmp <- apply(tmp.A, 2, function(x) sum(x * state$p[1:2]))
rbind(tmp.A, r * tmp / state$p[3])
},
B = diag(3),
S0Exg = {
tmp <- matrix(NA, 3, 3)
tmp[2, 2] <- 100
tmp[3, 3] <- 100
tmp
}
)
ge$p / ge$p[3] * r
p <- ge$p
p[3] <- p[3] / r
p / p[3]
Example 7.3 in Li (2019)
Description
This is Example 7.3 in Li (2019),which illustrates a monetary Leontief corn economy.
Usage
Example7.3()Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Example 7.4 in Li (2019)
Description
This is Example 7.4 in Li (2019),which illustrates a monetary Cobb-Douglas positive-growth corn economy.
Usage
Example7.4()Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
First Part of Example 7.5 in Li (2019)
Description
This is the first part of Example 7.5 in Li (2019),which illustrates a monetary Cobb-Douglas corn economy including dividend.
Usage
Example7.5.1()Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Second Part of Example 7.5 in Li (2019)
Description
This is the second part of Example 7.5 in Li (2019), which illustrates a monetary Cobb-Douglas corn economy including dividend.
Usage
Example7.5.2()Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Example 7.6 in Li (2019)
Description
This is Example 7.6 in Li (2019), which illustrates foreign exchange rates.
Usage
Example7.6()Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Example 7.7 in Li (2019)
Description
This is Example 7.7 in Li (2019), which illustrates foreign exchange rates.
Usage
Example7.7()Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Example 7.8 in Li (2019)
Description
This is Example 7.8 in Li (2019), which illustrates commodity money.
Usage
Example7.8()Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Example 7.9 in Li (2019)
Description
This is Example 7.9 in Li (2019), which illustrates commodity money and representative money.
Usage
Example7.9X()Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Example 8.1 in Li (2019)
Description
This is Example 8.1 in Li (2019), which expounds the equilibrium coffee problem.
Usage
Example8.1()Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Example 8.2 in Li (2019)
Description
This is Example 8.2 in Li (2019), which expounds a Cobb-Douglas market-clearing exchange process.
Usage
Example8.2()Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Example 8.7 in Li (2019)
Description
This is Example 8.7 in Li (2019), which discusses price changes in the coffee economy.
Usage
Example8.7()Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Examples
ge <- Example8.7()
matplot(ge$ts.p, type = "l")
matplot(ge$ts.z, type = "l")
Example 8.8 in Li (2019)
Description
This is Example 8.8 in Li (2019), which illustrates a dynamic exchange model with one type of money.
Usage
Example8.8()Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Examples
ge <- Example8.8()
matplot(ge$ts.p, type = "l")
matplot(ge$ts.z, type = "l")
Example 8.9 in Li (2019)
Description
This is Example 8.9 in Li (2019), which illustrates a dynamic exchange model with multiple types of money.
Usage
Example8.9()Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Examples
ge <- Example8.9()
matplot(ge$ts.p, type = "l")
matplot(ge$ts.z, type = "l")
Example 9.10-9.14 in Li (2019)
Description
This is Example 9.10-14 in Li (2019), which illustrates economic cycles in a monetary economy and economic policies ironing economic cycles.
Usage
Example9.10(
policy = NULL,
pExg = rbind(NA, NA, 0.25),
p0 = rbind(0.625, 0.375, 0.25),
priceAdjustmentVelocity = 0.3,
ts = TRUE
)
Arguments
Those arguments will be passed to the function sdm. See sdm.
policy |
a policy function |
pExg |
an n-vector indicating the exogenous prices (if any). |
p0 |
an initial price n-vector. |
priceAdjustmentVelocity |
the price adjustment velocity. |
ts |
if TRUE, the time series of the last iteration are returned. |
Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
See Also
sdm;
Example9.10.policy.interest.rate;
Example9.10.policy.money.supply;
Example9.10.policy.deflation;
Example9.10.policy.quantitative.easing;
Example9.10.policy.tax;
Example9.10.policy.deficit.fiscal
Examples
##### no policy
ge <- Example9.10()
matplot(ge$ts.p, type = "l")
matplot(ge$ts.z, type = "l")
##### interest rate policy (Fig. 9.12)
Example9.10(policy = Example9.10.policy.interest.rate)
##### monetary supply policy (Fig. 9.13)
Example9.10(policy = Example9.10.policy.money.supply)
##### deflation policy (Fig. 9.14)
ge <- Example9.10(
policy = Example9.10.policy.deflation,
pExg = rbind(NA, NA, 0),
p0 = rbind(0.625, 0.375, 0), ts = TRUE
)
plot(ge$ts.S[3, 3, ], type = "l")
plot(ge$ts.q[, 3], type = "l")
##### quantitative easing policy (Fig. 9.15)
ge <- Example9.10(
policy = Example9.10.policy.quantitative.easing,
pExg = rbind(NA, NA, 0),
p0 = rbind(0.625, 0.375, 0),
ts = TRUE
)
plot(log(ge$ts.S[3, 3, ]), type = "l")
plot(ge$ts.q[, 3], type = "l")
plot(log(ge$ts.p[, 1]), type = "l")
lines(log(ge$ts.p[, 2]), col = "blue")
##### deficit fiscal policy (Fig. 9.17; Fig. 9.18)
ge <- Example9.10(
policy = Example9.10.policy.deficit.fiscal,
priceAdjustmentVelocity = 0.5, ts = TRUE
)
plot(ge$ts.S[3, 3, ], type = "l")
plot(ge$ts.q[, 1], type = "l")
deficit.Example9.10 <- ge$policy.data
plot(deficit.Example9.10, type = "l")
plot(deficit.Example9.10[, 1], cumsum(deficit.Example9.10[, 2]), type = "l")
plot(deficit.Example9.10[, 1],
cumsum(deficit.Example9.10[, 2]) /
(tail(ge$ts.z[, 1] * ge$ts.p[, 1], -399)),
type = "l"
)
##### tax policy (Fig. 9.16)
ge <- Example9.10(policy = Example9.10.policy.tax)
plot(ge$policy.data, type = "l")
Deficit Fiscal Policy for Example 9.10 in Li (2019)
Description
This is the deficit fiscal policy for the economy of Example 9.10 in Li (2019), which is discussed in Example 9.14.
Usage
Example9.10.policy.deficit.fiscal(time, state, state.history)
Arguments
time |
the current time. |
state |
a list indicating the current economic state including prices, exchange levels (i.e. activity levels, production levels or utility levels) and supplies. |
state.history |
the history of economic states. |
Value
Example9.10.policy.deficit.fiscal returns a list indicating the modified current economic state including prices, exchange levels (i.e. activity levels, production levels or utility levels), supplies and current policy data.
Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
See Also
Example9.10;
Example9.10.policy.interest.rate;
Example9.10.policy.money.supply;
Example9.10.policy.deflation;
Example9.10.policy.quantitative.easing;
Example9.10.policy.tax
Deflation Policy for Example9.10 in Li (2019)
Description
This is the deflation policy for the economy of Example 9.10 in Li (2019), which is discussed in Example 9.12.
Usage
Example9.10.policy.deflation(time, state, state.history)
Arguments
time |
the current time. |
state |
a list indicating the current economic state including prices, exchange levels (i.e. activity levels, production levels or utility levels) and supplies. |
state.history |
the history of economic states. |
Value
Example9.10.policy.deflation returns a list indicating the modified current economic state including prices, exchange levels (i.e. activity levels, production levels or utility levels) and supplies.
Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
See Also
Example9.10;
Example9.10.policy.interest.rate;
Example9.10.policy.money.supply;
Example9.10.policy.quantitative.easing;
Example9.10.policy.tax;
Example9.10.policy.deficit.fiscal
Interest Rate Policy for Example9.10 in Li (2019)
Description
This is the interest rate policy for the economy of Example 9.10 in Li (2019), which is discussed in Example 9.11.
Usage
Example9.10.policy.interest.rate(time, state, state.history)
Arguments
time |
the current time. |
state |
a list indicating the current economic state including prices, exchange levels (i.e. activity levels, production levels or utility levels) and supplies. |
state.history |
the history of economic states. |
Value
Example9.10.policy.interest.rate returns a list indicating the modified current economic state including prices, exchange levels (i.e. activity levels, production levels or utility levels) and supplies.
Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
See Also
Example9.10;
Example9.10.policy.money.supply;
Example9.10.policy.deflation;
Example9.10.policy.quantitative.easing;
Example9.10.policy.tax;
Example9.10.policy.deficit.fiscal
Money Supply Policy for Example9.10 in Li (2019)
Description
This is the money supply policy for the economy of Example 9.10 in Li (2019), which is discussed in Example 9.12.
Usage
Example9.10.policy.money.supply(time, state, state.history)
Arguments
time |
the current time. |
state |
a list indicating the current economic state including prices, exchange levels (i.e. activity levels, production levels or utility levels) and supplies. |
state.history |
the history of economic states. |
Value
Example9.10.policy.money.supply returns a list indicating the modified current economic state including prices, exchange levels (i.e. activity levels, production levels or utility levels) and supplies.
Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
See Also
Example9.10;
Example9.10.policy.interest.rate;
Example9.10.policy.deflation;
Example9.10.policy.quantitative.easing;
Example9.10.policy.tax;
Example9.10.policy.deficit.fiscal
Quantitative Easing Policy for Example 9.10 in Li (2019)
Description
This is the deflation policy for the economy of Example 9.10 in Li (2019), which is discussed in Example 9.12.
Usage
Example9.10.policy.quantitative.easing(time, state, state.history)
Arguments
time |
the current time. |
state |
a list indicating the current economic state including prices, exchange levels (i.e. activity levels, production levels or utility levels) and supplies. |
state.history |
the history of economic states. |
Value
Example9.10.policy.quantitative.easing returns a list indicating the modified current economic state including prices, exchange levels (i.e. activity levels, production levels or utility levels) and supplies.
Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
See Also
Example9.10;
Example9.10.policy.interest.rate;
Example9.10.policy.money.supply;
Example9.10.policy.deflation;
Example9.10.policy.tax;
Example9.10.policy.deficit.fiscal
Tax Policy for Example9.10 in Li (2019)
Description
This is the tax policy for the economy of Example 9.10 in Li (2019), which is discussed in Example 9.13.
Usage
Example9.10.policy.tax(time, state, state.history)Arguments
time |
the current time. |
state |
a list indicating the current economic state including prices, exchange levels (i.e. activity levels, production levels or utility levels) and supplies. |
state.history |
the history of economic states. |
Value
Example9.10.policy.tax returns a list indicating the modified current economic state including prices, exchange levels (i.e. activity levels, production levels or utility levels), supplies and current policy data.
Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
See Also
Example9.10;
Example9.10.policy.interest.rate;
Example9.10.policy.money.supply;
Example9.10.policy.deflation;
Example9.10.policy.quantitative.easing;
Example9.10.policy.deficit.fiscal
Example 9.3 in Li (2019)
Description
This is Example 9.3 in Li (2019), which illustrates economic cycles in a pure production economy.
Usage
Example9.3()Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Examples
ge<-Example9.3()
matplot(ge$ts.p, type="l")
matplot(ge$ts.z, type="l")
Example 9.4 in Li (2019)
Description
This is Example 9.4 in Li (2019), which illustrates economic cycles in a corn economy.
Usage
Example9.4()Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Examples
ge<-Example9.4()
matplot(ge$ts.p, type="l")
matplot(ge$ts.z, type="l")
Example 9.5 in Li (2019)
Description
This is Example 9.5 in Li (2019), which illustrates the price-control equilibrium.
Usage
Example9.5()Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Examples
ge<-Example9.5()
matplot(ge$ts.p, type="l")
matplot(ge$ts.z, type="l")
Example 9.6 in Li (2019)
Description
This is Example 9.6 in Li (2019), which illustrates the technological progress and capital accumulation in the corn economy.
Usage
Example9.6()Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Examples
ge<-Example9.6()
matplot(ge$ts.p, type="l")
matplot(ge$ts.z, type="l")
Example 9.7 in Li (2019)
Description
This is Example 9.7 in Li (2019), which illustrates fixed assets and economic cycles.
Usage
Example9.7()Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Examples
ge<-Example9.7()
matplot(ge$ts.p, type="l")
matplot(ge$ts.z, type="l")
Exchange Function
Description
Given a price vector, a demand coefficient matrix and a supply matrix, this function computes the (disequilibrium) exchange results of an exchange process. There are n commodities and m agents in the exchange process.
Usage
F_Z(A, p, S)
Arguments
A |
a n-by-m demand coefficient matrix. |
p |
a price n-vector. |
S |
a n-by-m supply matrix. |
Value
F_Z returns a list containing the following components:
z |
an exchange amount m-vector. |
q |
a sales rate n-vector. |
Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Examples
A <- matrix(c(
0.05, 0.05, 0.1,
0.1, 0, 0.1,
0, 0.15, 0.05
), 3, 3, TRUE)
S <- diag(3)
# a market-clearing price vector
p <- c(0.6, 0.9, 1)
result <- F_Z(A, p, S)
# Each sales rate is equal to 1
result$q
# the purchase matrix
A %*% diag(result$z)
# a non-market-clearing price vector
p <- c(1, 1, 1)
result <- F_Z(A, p, S)
# Some sales rates don't equal 1
result$q
# the purchase matrix
A %*% diag(result$z)
Leontief Monetary Demand Coefficient Matrix
Description
This function computes a Leontief monetary demand coefficient matrix in a monetary economy.
Usage
Leontief_mA(A.pre, p)
Arguments
A.pre |
a numeric n-by-m matrix. |
p |
a nonnegative numeric n-vector or n-by-1 matrix. |
Details
Some elements of A corresponding to money equal -1.
Value
A n-by-m matrix is computed which indicates the (monetary) demand structure of agents (firms or consumers) with Leontief production functions or utility functions under the price vector p.
Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
Examples
A.pre <- matrix(c(
0.5, 1, 1,
0.1, 0, 0,
-1, -1, -1
), 3, 3, TRUE)
p <- c(1, 2, 0.1)
Leontief_mA(A.pre, p)
P-F (i.e. Perron-Frobenius) Eigenvalue and Eigenvector
Description
This function computes the P-F (i.e. Perron-Frobenius) eigenvalue and eigenvector of an indecomposable nonnegative square matrix.
Usage
PF_eig(M)Arguments
M |
an indecomposable nonnegative square matrix. |
Value
PF_eig returns a list containing the following components:
val |
the P-F eigenvalue of M. |
vec |
the normalized P-F eigenvector of M. |
Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
Horn, R. A., Johnson, C. R. (2012, ISBN: 0521548233) Matrix Analysis. Cambridge University Press.
Examples
M<-matrix(c(0.5,1,
1, 0),2,2,TRUE)
PF_eig(M)
A Modified diag Function
Description
This function works in the way analogous to the diag function of Matlab.
Usage
dg(x)
Arguments
x |
a number, vector or square matrix. |
Value
If x is a number, dg returns itself. If x is a vector, a one-row matrix or a one-column matrix, dg returns a matrix with x as the main diagnol. Otherwise dg returns diag(x).
Author(s)
LI Wu <liwu@staff.shu.edu.cn>
Examples
diag(matrix(2, 3))
dg(matrix(2, 3))
Compute Instantaneous Equilibrium Path (alias Market Clearing Path)
Description
This function computes the instantaneous equilibrium path (alias market clearing path).
Usage
iep(A.iep = NULL, A = NULL, B.iep = NULL, B = NULL,
SExg.iep, InitialEndowments, nPeriods.iep, ...)
Arguments
A.iep |
A.iep(state.iep) is a function which returns a demand coefficient matrix or a function A(state). state.iep is a list consisting of time (the iep time), p (the price vector at the iep time), z (output and utility vector at the iep time). |
A |
a demand coefficient matrix or a function A(state) which returns a demand coefficient matrix. If A.iep is not NULL, A will be ignored. |
B.iep |
B.iep(state.iep) is a function which returns a supply coefficient matrix or a function B(state) at the iep time. |
B |
a supply coefficient matrix or a function B(state) which returns a supply coefficient matrix. If B.iep is not NULL, B will be ignored. |
SExg.iep |
an exogenous supply matrix or a function SExg.iep(state.iep) which returns an exogenous supply matrix at the iep time. |
InitialEndowments |
a matrix indicating the initial endowments. |
nPeriods.iep |
number of periods of the instantaneous equilibrium path. |
... |
parameters of the function sdm. |
Details
This function computes the instantaneous equilibrium path (alias market clearing path) of a dynamic economy with the structural dynamic model (the sdm function).
Value
a list of general equilibria.
Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
Acemoglu, D. (2009, ISBN: 9780691132921) Introduction to Modern Economic Growth. Princeton University Press.
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
LI Wu (2010) A Structural Growth Model and its Applications to Sraffa's System. http://www.iioa.org/conferences/18th/papers/files/104_20100729011_AStructuralGrowthModelanditsApplicationstoSraffasSstem.pdf
Torres, Jose L. (2016, ISBN: 9781622730452). Introduction to Dynamic Macroeconomic General Equilibrium Models (Second Edition). Vernon Press.
See Also
Examples
## example 6.4 of Acemoglu (2009, page 206)
discount.factor <- 0.97
return.rate <- 1 / discount.factor - 1
A <- function(state) {
a1 <- CD_A(
1, rbind(0.35, 0.65, 0),
c(state$p[1] * (1 + return.rate), state$p[2:3])
)
a2 <- c(1, 0, 0)
a1[3] <- state$p[1] * a1[1] * return.rate / state$p[3]
cbind(a1, a2)
}
B <- matrix(c(
1, 0,
0, 1,
0, 1
), 3, 2, TRUE)
SExg.iep <- {
tmp <- matrix(NA, 3, 2)
tmp[2, 2] <- tmp[3, 2] <- 1
tmp
}
InitialEndowments <- {
tmp <- matrix(0, 3, 2)
tmp[1, 1] <- 0.01
tmp[2, 2] <- tmp[3, 2] <- 1
tmp
}
ge.list <- iep(
A = A, B = B, SExg.iep = SExg.iep,
InitialEndowments = InitialEndowments,
nPeriods.iep = 50
)
z <- t(sapply(ge.list, function(x) x$z))
matplot(z, type = "l")
z[1:49, 1] * (1 - 0.97 * 0.35) # the same as z[-1,2] (i.e. consumption)
# stochastic (instantaneous) equilibrium path (SEP) in the economy above.
nPeriods.iep <- 150
set.seed(1)
alpha.SEP <- rep(1, 50)
for (t in 51:nPeriods.iep) {
alpha.SEP[t] <- exp(0.95 * log(alpha.SEP[t - 1]) +
rnorm(1, sd = 0.01))
}
A.iep <- function(state.iep) {
A <- function(state) {
a1 <- CD_A(
alpha.SEP[state.iep$time],
rbind(0.35, 0.65, 0),
c(state$p[1] * (1 + return.rate), state$p[2:3])
)
a2 <- c(1, 0, 0)
a1[3] <- state$p[1] * a1[1] * return.rate / state$p[3]
cbind(a1, a2)
}
return(A)
}
ge.list <- iep(
A.iep = A.iep, B = B, SExg.iep = SExg.iep,
InitialEndowments = InitialEndowments,
nPeriods.iep = nPeriods.iep
)
z <- t(sapply(ge.list, function(x) x$z))
matplot(z, type = "l")
## an example with two firms
sigma <- 0 # 0 implies Cobb-Douglas production functions
gamma1 <- 0.01
gamma2 <- 0.01
gamma3 <- 0.01
beta1 <- 0.35
beta2 <- 0.4
A.iep <- function(state.iep) {
A <- function(state) {
a1 <- CES_A(sigma, exp(gamma1 * (state.iep$time - 1)), rbind(beta1, 0, 1 - beta1), state$p)
a2 <- CES_A(sigma, exp(gamma2 * (state.iep$time - 1)), rbind(beta2, 0, 1 - beta2), state$p)
a3 <- c(0, 1, 0)
cbind(a1, a2, a3)
}
return(A)
}
B <- diag(3)
SExg.iep <- function(state.iep) {
tmp <- matrix(NA, 3, 3)
tmp[3, 3] <- exp(gamma3 * (state.iep$time - 1))
tmp
}
InitialEndowments <- {
tmp <- matrix(0, 3, 3)
tmp[1, 1] <- 0.01
tmp[2, 2] <- 0.02
tmp[3, 3] <- 1
tmp
}
ge.list <- iep(
A.iep = A.iep, B = B, SExg.iep = SExg.iep,
InitialEndowments = InitialEndowments,
nPeriods.iep = 100, trace = FALSE
)
z <- t(sapply(ge.list, function(x) x$z)) # outputs and utility
matplot(z, type = "l")
diff(log(z)) # logarithmic growth rate
## an example with heterogeneous firms
A <- function(state) {
a1 <- CD_A(1, rbind(0.35, 0.65), state$p)
a2 <- CD_A(1.3, rbind(0.9, 0.1), state$p)
a3 <- c(1, 0)
cbind(a1, a2, a3)
}
B <- matrix(c(
1, 1, 0,
0, 0, 1
), 2, 3, TRUE)
SExg.iep <- {
tmp <- matrix(NA, 2, 3)
tmp[2, 3] <- 1
tmp
}
InitialEndowments <- {
tmp <- matrix(0, 2, 3)
tmp[1, 1] <- tmp[1, 2] <- 0.01
tmp[2, 3] <- 1
tmp
}
ge.list <- iep(
A = A, B = B, SExg.iep = SExg.iep,
InitialEndowments = InitialEndowments,
nPeriods.iep = 200, trace = FALSE
)
z <- t(sapply(ge.list, function(x) x$z))
matplot(z, type = "l")
## an iep of the example (see Table 2.1 and 2.2) of the canonical dynamic
## macroeconomic general equilibrium model in Torres (2016).
discount.factor <- 0.97
return.rate <- 1 / discount.factor - 1
depreciation.rate <- 0.06
A <- function(state) {
a1 <- CD_A(1, rbind(0, 0.65, 0.35, 0), state$p)
a2 <- CD_A(1, rbind(0.4, 1 - 0.4, 0, 0), state$p)
a3 <- c(1, 0, 0, state$p[1] * return.rate / state$p[4])
cbind(a1, a2, a3)
}
B <- matrix(c(
1, 0, 1 - depreciation.rate,
0, 1, 0,
0, 0, 1,
0, 1, 0
), 4, 3, TRUE)
SExg.iep <- {
tmp <- matrix(NA, 4, 3)
tmp[2, 2] <- tmp[4, 2] <- 1
tmp
}
InitialEndowments <- {
tmp <- matrix(0, 4, 3)
tmp[1, 1] <- 0.01
tmp[2, 2] <- tmp[4, 2] <- 1
tmp[3, 3] <- 0.01
tmp
}
ge.list <- iep(
A = A, B = B, SExg.iep = SExg.iep,
InitialEndowments = InitialEndowments,
nPeriods.iep = 200, trace = FALSE
)
z <- t(sapply(ge.list, function(x) x$z))
matplot(z, type = "l")
## another iep of the economy above
discount.factor <- 0.97
return.rate <- 1 / discount.factor - 1
depreciation.rate <- 0.06
A <- function(state) {
a1 <- CD_A(
1, rbind(0.35, 0.65, 0),
c(state$p[1] * (return.rate + depreciation.rate), state$p[2:3])
)
a2 <- CD_A(1, rbind(0.4, 1 - 0.4, 0), state$p)
a1[3] <- state$p[1] * a1[1] * return.rate / state$p[3]
cbind(a1, a2)
}
B <- function(state) {
tmp <- matrix(c(
1, 0,
0, 1,
0, 1
), 3, 2, TRUE)
tmp[1] <- tmp[1] + A(state)[1, 1] * (1 - depreciation.rate)
tmp
}
SExg.iep <- {
tmp <- matrix(NA, 3, 2)
tmp[2, 2] <- tmp[3, 2] <- 1
tmp
}
InitialEndowments <- {
tmp <- matrix(0, 3, 2)
tmp[1, 1] <- 0.01
tmp[2, 2] <- tmp[3, 2] <- 1
tmp
}
ge.list <- iep(
A = A, B = B, SExg.iep = SExg.iep,
InitialEndowments = InitialEndowments,
nPeriods.iep = 100, n = 3, m = 2, trace = FALSE
)
z <- t(sapply(ge.list, function(x) x$z))
matplot(z, type = "l")
## TFP shock in the economy above (see Torres, 2016, section 2.8).
nPeriods.iep <- 200
discount.factor <- 0.97
return.rate <- 1 / discount.factor - 1
depreciation.rate <- 0.06
set.seed(1)
alpha.shock <- rep(1, 100)
alpha.shock[101] <- exp(0.01)
for (t in 102:nPeriods.iep) {
alpha.shock[t] <- exp(0.95 * log(alpha.shock[t - 1]))
}
A.iep <- function(state.iep) {
A <- function(state) {
a1 <- CD_A(
alpha.shock[state.iep$time],
rbind(0.35, 0.65, 0),
c(state$p[1] * (return.rate + depreciation.rate), state$p[2:3])
)
a2 <- CD_A(1, rbind(0.4, 1 - 0.4, 0), state$p)
a1[3] <- state$p[1] * a1[1] * return.rate / state$p[3]
cbind(a1, a2)
}
return(A)
}
B.iep <- function(state.iep) {
B <- function(state) {
tmp <- matrix(c(
1, 0,
0, 1,
0, 1
), 3, 2, TRUE)
a1 <- CD_A(
alpha.shock[state.iep$time],
rbind(0.35, 0.65, 0),
c(state$p[1] * (return.rate + depreciation.rate), state$p[2:3])
)
tmp[1] <- tmp[1] + a1[1] * (1 - depreciation.rate)
tmp
}
return(B)
}
SExg.iep <- {
tmp <- matrix(NA, 3, 2)
tmp[2, 2] <- tmp[3, 2] <- 1
tmp
}
InitialEndowments <- {
tmp <- matrix(0, 3, 2)
tmp[1, 1] <- tmp[2, 2] <- tmp[3, 2] <- 1
tmp
}
ge.list <- iep(
A.iep = A.iep, B.iep = B.iep, SExg.iep = SExg.iep,
InitialEndowments = InitialEndowments,
nPeriods.iep = nPeriods.iep, n = 3, m = 2, trace = FALSE
)
z <- t(sapply(ge.list, function(x) x$z))
c <- sapply(ge.list, function(x) x$A[1,2]*x$z[2]) #consumption
par(mfrow = c(2, 2))
matplot(z, type = "l")
x <- 100:140
plot(x, z[x, 1] / z[x[1], 1], type = "b", pch = 20)
plot(x, z[x, 2] / z[x[1], 2], type = "b", pch = 20)
plot(x, c[x] / c[x[1]], type = "b", pch = 20)
## an iep of example 7.2 (a monetary economy) in Li (2019).
A <- function(state) {
alpha <- rbind(1, 1, 1)
Beta <- matrix(c(
0.5, 0.5, 0.5,
0.5, 0.5, 0.5,
-1, -1, -1
), 3, 3, TRUE)
CD_mA(alpha, Beta, state$p)
}
B <- diag(3)
SExg.iep <- {
tmp <- matrix(NA, 3, 3)
tmp[2, 2] <- 100
tmp[3, 3] <- 100
tmp
}
InitialEndowments <- {
tmp <- matrix(0, 3, 3)
tmp[1, 1] <- 10
tmp[2, 2] <- tmp[3, 3] <- 100
tmp
}
ge.list <- iep(
A = A, B = B, SExg.iep = SExg.iep,
InitialEndowments = InitialEndowments,
nPeriods.iep = 20,
moneyIndex = 3,
moneyOwnerIndex = 3,
pExg = rbind(NA, NA, 0.25)
)
par(mfrow = c(1, 2))
z <- t(sapply(ge.list, function(x) x$z))
matplot(z, type = "b", pch = 20)
p <- t(sapply(ge.list, function(x) x$p))
matplot(p, type = "b", pch = 20)
## an example of structural transition policy
A.iep <- function(state.iep) {
a <- 15
b <- 25
A <- function(state) {
alpha1 <- 5
alpha2 <- 15
if (state.iep$time == 1 || state.iep$z[1] <= a) {
alpha <- alpha1
} else if (state.iep$z[1] > b) {
alpha <- alpha2
} else {
alpha <- (b - state.iep$z[1]) / (b - a) * alpha1 +
(state.iep$z[1] - a) / (b - a) * alpha2
}
return(cbind(
CD_A(alpha, c(0.5, 0.5), state$p),
c(1, 0)
))
}
return(A)
}
B <- matrix(c(
1, 0,
0, 1
), 2, 2, TRUE)
SExg.iep <- function(state.iep) {
if (state.iep$time >= 15 && state.iep$z[1] < 30) {
result <- matrix(c(
NA, NA,
0.6, 0.4
), 2, 2, TRUE)
} else {
result <- matrix(c(
NA, NA,
0, 1
), 2, 2, TRUE)
}
return(result)
}
InitialEndowments <- {
tmp <- matrix(0, 2, 2)
tmp[1, 1] <- 1
tmp[2, 2] <- 1
tmp
}
ge.list <- iep(
A.iep = A.iep, B = B, SExg.iep = SExg.iep,
InitialEndowments = InitialEndowments,
nPeriods.iep = 30, trace = FALSE
)
z <- t(sapply(ge.list, function(x) x$z))
matplot(z, type = "b", pch = 20)
Structural Dynamic Model (alias Structural Growth Model)
Description
This function computes the general equilibrium and simulates the economic dynamics. The key part of this function is an exchange function (see F_Z), which is expounded in Li (2010, 2019).
Usage
sdm(
A,
B = diag(nrow(A)),
n = nrow(B),
m = ncol(B),
S0Exg = matrix(NA, n, m),
p0 = matrix(1, nrow = n, ncol = 1),
z0 = matrix(100, nrow = m, ncol = 1),
GRExg = NA,
moneyOwnerIndex = NULL,
moneyIndex = NULL,
pExg = NULL,
tolCond = 1e-5,
maxIteration = 200,
numberOfPeriods = 300,
depreciationCoef = 0.8,
thresholdForPriceAdjustment = 0.99,
priceAdjustmentMethod = "variable",
priceAdjustmentVelocity = 0.15,
trace = TRUE,
ts = FALSE,
policy = NULL,
exchangeFunction = F_Z
)
Arguments
A |
a demand coefficient n-by-m matrix (alias demand structure matrix) or a function A(state) which returns an n-by-m matrix. |
B |
a supply coefficient n-by-m matrix (alias supply structure matrix) or a function which returns an n-by-m matrix. If (i,j)-th element of S0Exg is not NA, the value of the (i,j)-th element of B will be useless and ignored. |
n |
the number of commodities. |
m |
the number of economic agents (or sectors). |
S0Exg |
an initial exogenous supply n-by-m matrix. This matrix may contain NA, but not zero. |
p0 |
an initial price n-vector. |
z0 |
an m-vector consisting of the initial exchange levels (i.e. activity levels, production levels or utility levels). |
GRExg |
an exogenous growth rate of the exogenous supplies in S0Exg. If GRExg is NA and some commodities have exogenous supply, then GRExg will be set to 0. |
moneyOwnerIndex |
a vector consisting of the indices of agents supplying money. |
moneyIndex |
a vector consisting of the commodity indices of all types of money. |
pExg |
an n-vector indicating the exogenous prices (if any). |
tolCond |
the tolerance condition. |
maxIteration |
the maximum iteration count. If the main purpose of running this function is to do simulation instead of calculating equilibrium, then maxIteration should be set to 1. |
numberOfPeriods |
the period number in each iteration. |
depreciationCoef |
the depreciation coefficient (i.e. 1 minus the depreciation rate) of the unsold products. |
thresholdForPriceAdjustment |
the threshold for the fixed percentage price adjustment method. |
priceAdjustmentMethod |
the price adjustment method. Normally it should be set to "variable". If it is set to "fixed", a fixed percentage price adjustment method will be used. |
priceAdjustmentVelocity |
the price adjustment velocity. |
trace |
if TRUE, information is printed during the running of sdm. |
ts |
if TRUE, the time series of the last iteration are returned. |
policy |
a policy function. |
exchangeFunction |
the exchange function. |
Details
The parameters A may be a function A(state) wherein state is a list consisting of p (the price vector), z (the output and utility vector), w (the wealth vector), t (the time) and e (the foreign exchange rate vector if any). state indicates the states at time t.
The parameters B also may be a function B(state) wherein state is a list consisting of p (the price vector), z (the output and utility vector) and t (the time).
Value
sdm returns a list containing the following components:
tolerance |
the tolerance of the results. |
p |
equilibrium prices. |
z |
equilibrium exchange levels (i.e. activity levels, output levels or utility levels). |
S |
the equilibrium supply matrix at the initial period. |
e |
equilibrium foreign exchange rates in a multi-money economy. |
growthRate |
the endogenous equilibrium growth rate in a pure production economy. |
A |
the equilibrium demand coefficient matrix. |
B |
If B is a function, the equilibrium supply coefficient matrix is returned. |
ts.p |
the time series of prices in the last iteration. |
ts.z |
the time series of exchange levels (i.e. activity levels, production levels or utility levels) in the last iteration. |
ts.S |
the time series of supply matrix in the last iteration. |
ts.q |
the time series of sales rates in the last iteration. |
ts.e |
the time series of foreign exchange rates in the last iteration. |
policy.data |
the policy data. |
Author(s)
LI Wu <liwu@staff.shu.edu.cn>
References
LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)
LI Wu (2010) A Structural Growth Model and its Applications to Sraffa's System. http://www.iioa.org/conferences/18th/papers/files/104_20100729011_AStructuralGrowthModelanditsApplicationstoSraffasSstem.pdf
Torres, Jose L. (2016, ISBN: 9781622730452) Introduction to Dynamic Macroeconomic General Equilibrium Models (Second Edition). Vernon Press.
Varian, Hal R. (1992, ISBN: 0393957357) Microeconomic Analysis. W. W. Norton & Company.
See Also
iep;
Example2.2;
Example2.3;
Example.Section.3.1.2.corn;
Example3.1;
Example3.2;
Example3.4;
Example3.8;
Example3.9;
Example3.10;
Example3.12;
Example3.14;
Example4.2;
Example4.8;
Example4.9;
Example4.10;
Example4.11.1;
Example4.11.2;
Example4.12;
Example4.13;
Example4.15;
Example4.16;
Example5.1;
Example5.2;
Example5.3.2;
Example5.4;
Example5.5;
Example5.6;
Example5.10;
Example5.11.1;
Example5.11.2;
Example6.2.1;
Example6.2.2;
Example6.3;
Example6.4;
Example6.5;
Example6.6.1;
Example6.6.2;
Example6.6.3;
Example6.7;
Example6.9;
Example6.10;
Example6.11;
Example7.1;
Example7.2;
Example7.3;
Example7.4;
Example7.5.1;
Example7.5.2;
Example7.6;
Example7.7;
Example7.8;
Example7.9X;
Example7.10;
Example7.10.2;
Example7.11;
Example7.12;
Example7.13;
Example7.14;
Example7.15;
Example8.1;
Example8.2;
Example8.7;
Example8.8;
Example8.9;
Example9.3;
Example9.4;
Example9.5;
Example9.6;
Example9.7;
Example9.10;
Examples
## the example on page 352 in Varian (1992)
ge <- sdm(
A = function(state) {
a <- 0.5
alpha <- rep(1, 3)
Beta <- matrix(c(0, a, a,
0.5, 0, 0,
0.5, 1 - a, 1 - a), 3, 3, TRUE)
#the demand coefficient matrix.
CD_A(alpha, Beta, state$p)
},
B = diag(3),
S0Exg = matrix(c(NA, NA, NA,
NA, 1, NA,
NA, NA, 1), 3, 3, TRUE),
GRExg = 0,
tolCond = 1e-10
)
ge$p/ge$p[1]
## the example (see Table 2.1 and 2.2) of the canonical dynamic
## macroeconomic general equilibrium model in Torres (2016).
discount.factor <- 0.97
return.rate <- 1 / discount.factor - 1
depreciation.rate <- 0.06
ge <- sdm(
n = 4, m = 3,
A = function(state) {
a1 <- CD_A(1, rbind(0, 0.65, 0.35, 0), state$p)
a2 <- CD_A(1, rbind(0.4, 1 - 0.4, 0, 0), state$p)
a3 <- c(1, 0, 0, state$p[1] * return.rate / state$p[4])
cbind(a1, a2, a3)
},
B = matrix(c(
1, 0, 1 - depreciation.rate,
0, 1, 0,
0, 0, 1,
0, 1, 0
), 4, 3, TRUE),
S0Exg = {
tmp <- matrix(NA, 4, 3)
tmp[2, 2] <- 1
tmp[4, 2] <- 1
tmp
},
priceAdjustmentVelocity = 0.03,
maxIteration = 1,
numberOfPeriods = 5000,
ts = TRUE
)
ge$A %*% diag(ge$z) # the demand matrix
ge$p / ge$p[1]
plot(ge$ts.z[, 1], type = "l")