| gemOLGF_OneFirm {GE} | R Documentation |
Overlapping Generations Financial Sequential Models with One Firm
Description
Some examples of overlapping generations financial sequential models with one firm.
When there is a population growth, we will take the security-split assumption (see gemOLGF_PureExchange).
Usage
gemOLGF_OneFirm(...)
Arguments
... |
arguments to be passed to the function sdm2. |
References
Samuelson, P. A. (1958) An Exact Consumption-Loan Model of Interest with or without the Social Contrivance of Money. Journal of Political Economy, vol. 66(6): 467-482.
de la Croix, David and Philippe Michel (2002, ISBN: 9780521001151) A Theory of Economic Growth: Dynamics and Policy in Overlapping Generations. Cambridge University Press.
See Also
gemOLG_PureExchange
gemOLG_TimeCircle
Examples
#### an OLGF economy with a firm and two-period-lived consumers
beta.firm <- c(1 / 3, 2 / 3)
# the population growth rate
GRExg <- 0.03
saving.rate <- 0.5
ratio.saving.consumption <- saving.rate / (1 - saving.rate)
dst.firm <- node_new(
"prod",
type = "CD", alpha = 5,
beta = beta.firm,
"lab", "prod"
)
dst.age1 <- node_new(
"util",
type = "FIN",
rate = c(1, ratio.saving.consumption),
"prod", "secy" # security, the financial instrument
)
dst.age2 <- node_new(
"util",
type = "Leontief", a = 1,
"prod"
)
ge <- sdm2(
A = list(
dst.firm, dst.age1, dst.age2
),
B = matrix(c(
1, 0, 0,
0, 0, 0,
0, 0, 0
), 3, 3, TRUE),
S0Exg = matrix(c(
NA, NA, NA,
NA, 1, NA,
NA, NA, 1
), 3, 3, TRUE),
names.commodity = c("prod", "lab", "secy"),
names.agent = c("firm", "age1", "age2"),
numeraire = "lab",
GRExg = GRExg,
maxIteration = 1,
ts = TRUE
)
ge$p
matplot(ge$ts.p, type = "l")
matplot(growth_rate(ge$ts.z), type = "l") # GRExg
addmargins(ge$D, 2) # the demand matrix of the current period
addmargins(ge$S, 2) # the supply matrix of the current period
addmargins(ge$S * (1 + GRExg), 2) # the supply matrix of the next period
addmargins(ge$DV)
addmargins(ge$SV)
## Suppose consumers consume product and labor (i.e. service) and
## age1 and age2 may have different instantaneous utility functions.
dst.age1 <- node_new(
"util",
type = "FIN",
rate = c(1, ratio.saving.consumption),
"cc1", "secy" # security, the financial instrument
)
node_set(dst.age1, "cc1",
type = "Leontief",
a = c(0.5, 0.5),
"prod", "lab"
)
node_plot(dst.age1)
dst.age2 <- node_new("util",
type = "Leontief",
a = c(0.2, 0.8),
"prod", "lab"
)
ge <- sdm2(
A = list(
dst.firm, dst.age1, dst.age2
),
B = matrix(c(
1, 0, 0,
0, 0, 0,
0, 0, 0
), 3, 3, TRUE),
S0Exg = matrix(c(
NA, NA, NA,
NA, 1, NA,
NA, NA, 1
), 3, 3, TRUE),
names.commodity = c("prod", "lab", "secy"),
names.agent = c("firm", "age1", "age2"),
numeraire = "lab",
GRExg = GRExg,
priceAdjustmentVelocity = 0.05
)
ge$p
addmargins(ge$D, 2)
addmargins(ge$S, 2)
addmargins(ge$DV)
addmargins(ge$SV)
## Aggregate the above consumers into one infinite-lived consumer,
## who always spends the same amount on cc1 and cc2.
dst.consumer <- node_new("util",
type = "CD", alpha = 1,
beta = c(0.5, 0.5),
"cc1", "cc2"
)
node_set(dst.consumer, "cc1",
type = "Leontief",
a = c(0.5, 0.5),
"prod", "lab"
)
node_set(dst.consumer, "cc2",
type = "Leontief",
a = c(0.2, 0.8),
"prod", "lab"
)
ge <- sdm2(
A = list(
dst.firm, dst.consumer
),
B = matrix(c(
1, 0,
0, 0
), 2, 2, TRUE),
S0Exg = matrix(c(
NA, NA,
NA, 1
), 2, 2, TRUE),
names.commodity = c("prod", "lab"),
names.agent = c("firm", "consumer"),
numeraire = "lab",
GRExg = GRExg,
priceAdjustmentVelocity = 0.05
)
ge$p
addmargins(ge$D, 2)
addmargins(ge$S, 2)
addmargins(ge$DV)
addmargins(ge$SV)
#### an OLGF economy with a firm and two-period-lived consumers
## Suppose each consumer has a Leontief-type utility function min(c1, c2/a).
beta.firm <- c(1 / 3, 2 / 3)
# the population growth rate, the equilibrium interest rate and profit rate
GRExg <- 0.03
rho <- 1 / (1 + GRExg)
a <- 0.9
dst.firm <- node_new(
"prod",
type = "CD", alpha = 5,
beta = beta.firm,
"lab", "prod"
)
dst.age1 <- node_new(
"util",
type = "FIN",
rate = c(1, ratio.saving.consumption = a * rho),
"prod", "secy" # security, the financial instrument
)
dst.age2 <- node_new(
"util",
type = "Leontief", a = 1,
"prod"
)
ge <- sdm2(
A = list(
dst.firm, dst.age1, dst.age2
),
B = matrix(c(
1, 0, 0,
0, 0, 0,
0, 0, 0
), 3, 3, TRUE),
S0Exg = matrix(c(
NA, NA, NA,
NA, 1, NA,
NA, NA, 1
), 3, 3, TRUE),
names.commodity = c("prod", "lab", "secy"),
names.agent = c("firm", "age1", "age2"),
numeraire = "lab",
GRExg = GRExg,
maxIteration = 1,
ts = TRUE
)
ge$p
matplot(ge$ts.p, type = "l")
matplot(growth_rate(ge$ts.z), type = "l") # GRExg
addmargins(ge$D, 2)
addmargins(ge$S, 2)
addmargins(ge$DV)
addmargins(ge$SV)
## the corresponding time-cycle model
n <- 5 # the number of periods, consumers and firms.
S <- matrix(NA, 2 * n, 2 * n)
S.lab.consumer <- diag((1 + GRExg)^(0:(n - 1)), n)
S[(n + 1):(2 * n), (n + 1):(2 * n)] <- S.lab.consumer
B <- matrix(0, 2 * n, 2 * n)
B[1:n, 1:n] <- diag(n)[, c(2:n, 1)]
B[1, n] <- rho^n
dstl.firm <- list()
for (k in 1:n) {
dstl.firm[[k]] <- node_new(
"prod",
type = "CD", alpha = 5,
beta = beta.firm,
paste0("lab", k), paste0("prod", k)
)
}
dstl.consumer <- list()
for (k in 1:(n - 1)) {
dstl.consumer[[k]] <- node_new(
"util",
type = "FIN",
rate = c(1, ratio.saving.consumption = a * rho),
paste0("prod", k), paste0("prod", k + 1)
)
}
dstl.consumer[[n]] <- node_new(
"util",
type = "FIN",
rate = c(1, ratio.saving.consumption = a * rho),
paste0("prod", n), "cc1"
)
node_set(dstl.consumer[[n]], "cc1",
type = "Leontief", a = rho^n, # a discounting factor
"prod1"
)
ge2 <- sdm2(
A = c(dstl.firm, dstl.consumer),
B = B,
S0Exg = S,
names.commodity = c(paste0("prod", 1:n), paste0("lab", 1:n)),
names.agent = c(paste0("firm", 1:n), paste0("consumer", 1:n)),
numeraire = "lab1",
policy = makePolicyMeanValue(30),
maxIteration = 1,
numberOfPeriods = 600,
ts = TRUE
)
ge2$p
growth_rate(ge2$p[1:n]) + 1 # rho
growth_rate(ge2$p[(n + 1):(2 * n)]) + 1 # rho
ge2$D
[Package GE version 0.4.5 Index]