GE (version 0.3.8)

gemIntertemporal_TimeCircle_2_2: Some Examples of a 2-by-2 Time Circle Equilibrium Model

Description

Some examples of a 2-by-2 (intertemporal) time circle equilibrium model. In a time circle model, the economy borrows some resources from the outside in the beginning, and will repay it after the economy ends.

In these examples, there is an np-period-lived consumer maximizing intertemporal utility, and there is a type of firm which produces from period 1 to np. There are two commodities, i.e. product and labor. Suppose the firm can borrow some product from outside in the first period and return them in the (np+1)-th period. And the supply of product in the first period can be regarded as the output of the firm in the (np+1)-th period. Hence the product supply in the first period is an endogenous variable. Suppose that the amount returned is zeta times the amount borrowed.

Usage

gemIntertemporal_TimeCircle_2_2(...)

Arguments

...

arguments to be passed to the function sdm2.

See Also

gemOLGTimeCircle

Examples

# \donttest{
#### an example with a Cobb-Douglas intertemporal utility function
np <- 5 # the number of internal periods, firms.

zeta <- 1.25 # the ratio of repayments to loans
S <- matrix(NA, 2 * np, np + 1)
S[(np + 1):(2 * np), np + 1] <- 100

B <- matrix(0, 2 * np, np + 1)
B[1:np, 1:np] <- diag(np)[, c(2:np, 1)]
B[1, np] <- 1 / zeta

dstl.firm <- list()
for (k in 1:np) {
  dstl.firm[[k]] <- node_new(
    "prod",
    type = "CD", alpha = 2,
    beta = c(0.5, 0.5),
    paste0("lab", k), paste0("prod", k)
  )
}

dst.consumer <- node_new(
  "util",
  type = "CD", alpha = 1,
  beta = prop.table(rep(1, np)),
  paste0("prod", 1:np)
)

ge <- sdm2(
  A = c(dstl.firm, dst.consumer),
  B = B,
  S0Exg = S,
  names.commodity = c(paste0("prod", 1:np), paste0("lab", 1:np)),
  names.agent = c(paste0("firm", 1:np), "consumer"),
  numeraire = "lab1",
  ts = TRUE
)

ge$p
ge$z
ge$D
ge$S
ge$DV
ge$SV

## an example with a Leontief intertemporal utility function
dst.consumer <- node_new(
  "util",
  type = "Leontief",
  a = rep(1, np),
  paste0("prod", 1:np)
)

ge2 <- sdm2(
  A = c(dstl.firm, dst.consumer),
  B = B,
  S0Exg = S,
  names.commodity = c(paste0("prod", 1:np), paste0("lab", 1:np)),
  names.agent = c(paste0("firm", 1:np), "consumer"),
  numeraire = "lab1",
  ts = TRUE
)

ge2$p
ge2$z
ge2$D
ge2$S
ge2$DV
ge2$SV

## Use a mean-value policy function to accelerate convergence.
ge3 <- sdm2(
  A = c(dstl.firm, dst.consumer),
  B = B,
  S0Exg = S,
  names.commodity = c(paste0("prod", 1:np), paste0("lab", 1:np)),
  names.agent = c(paste0("firm", 1:np), "consumer"),
  numeraire = "lab1",
  ts = TRUE,
  policy = makePolicyMeanValue(30)
)

#### an example with a linear intertemporal utility function (e.g. beta1*x1+beta2*x2)
## The demand structure of the consumer will be adjusted sluggishly to accelerate convergence.
np <- 5 # the number of internal periods, firms.
rho <- 0.9 # subjective discount factor

beta.consumer <- rep(rho ^ (0:(np - 1)))

zeta <-  (1 / rho) ^ np

S <- matrix(NA, 2 * np, np + 1)
S[(np + 1):(2 * np), np + 1] <- 100

B <- matrix(0, 2 * np, np + 1)
B[1:np, 1:np] <- diag(np)[, c(2:np, 1)]
B[1, np] <- 1 / zeta

dstl.firm <- list()
for (k in 1:np) {
  dstl.firm[[k]] <- node_new(
    "prod",
    type = "CD",
    alpha = 2,
    beta = c(0.5, 0.5),
    paste0("lab", k),
    paste0("prod", k)
  )
}

dst.consumer <- node_new(
  "util",
  type = "FUNC",
  last.a = rep(1, np),
  func = function(p) {
    value.marginal.utility <- beta.consumer / p
    ratio <- value.marginal.utility / mean(value.marginal.utility)
    a <- dst.consumer$last.a
    a <- prop.table(a * ratio_adjust(ratio, 0.15))
    dst.consumer$last.a <- a
    a
  },
  paste0("prod", 1:np)
)

ge <- sdm2(
  A = c(dstl.firm, dst.consumer),
  B = B,
  S0Exg = S,
  names.commodity = c(paste0("prod", 1:np), paste0("lab", 1:np)),
  names.agent = c(paste0("firm", 1:np), "consumer"),
  numeraire = "lab1",
  ts = TRUE,
  priceAdjustmentVelocity = 0.1
)

ge$p
ge$z
ge$D
ge$S
growth_rate(ge$p[1:np])
growth_rate(ge$p[(np + 1):(2 * np)])
# }