gemOLGF_OneFirm: Overlapping Generations Financial Models with One Firm
In GE: General Equilibrium Modeling

gemOLGF_OneFirm

R Documentation

Overlapping Generations Financial Models with One Firm

Description

Some examples of overlapping generations financial 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.

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

GE documentation built on Nov. 8, 2023, 9:07 a.m.