gemIntertemporal_TimeCircle_3_4 {GE}

A Time Circle Model with Two Consumers and Two Types of Firms

Description

An (intertemporal) time circle model with two consumers and two types of firms. There are three commodities in the model, namely wheat, iron, and labor.

Usage

gemIntertemporal_TimeCircle_3_4(...)

Arguments

...

arguments to be passed to the function sdm2.

Examples

#### an example with a Cobb-Douglas intertemporal utility function
np <- 5 # the number of economic periods, firms.
zeta <- 1.25 # the ratio of repayments to loans

n <- 3 * np # the number of commodity kinds
m <- 2 * np + 2 # the number of agent kinds

names.commodity <- c(
  paste0("wheat", 1:np),
  paste0("iron", 1:np),
  paste0("lab", 1:np)
)
names.agent <- c(
  paste0("firm.wheat", 1:np), paste0("firm.iron", 1:np),
  "consumer1", "consumer2"
)

# the exogenous supply matrix.
S0Exg <- matrix(NA, n, m, dimnames = list(names.commodity, names.agent))
S0Exg[paste0("lab", 1:np), c("consumer1", "consumer2")] <- 100 # the supply of labor

# the output coefficient matrix.
B <- matrix(0, n, m, dimnames = list(names.commodity, names.agent))
for (k in 1:(np - 1)) {
  B[paste0("wheat", k + 1), paste0("firm.wheat", k)] <- 1
  B[paste0("iron", k + 1), paste0("firm.iron", k)] <- 1
}
B["wheat1", paste0("firm.wheat", np)] <- 1 / zeta
B["iron1", paste0("firm.iron", np)] <- 1 / zeta

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

  dstl.firm.iron[[k]] <- node_new(
    "prod",
    type = "CD", alpha = 2, beta = c(0.5, 0.5),
    paste0("iron", k), paste0("lab", k)
  )
}

dst.consumer1 <- node_new(
  "util",
  type = "CD", alpha = 1, beta = prop.table(rep(1, np)),
  paste0("wheat", 1:np)
)

dst.consumer2 <- node_new(
  "util",
  type = "CD", alpha = 1, beta = prop.table(rep(1, np)),
  paste0("cc", 1:np)
)
for (k in 1:np) {
  node_set(
    dst.consumer2, paste0("cc", k),
    type = "CD", alpha = 1, beta = c(0.5, 0.5),
    paste0("wheat", k), paste0("iron", k)
  )
}

ge <- sdm2(
  A = c(dstl.firm.wheat, dstl.firm.iron, dst.consumer1, dst.consumer2),
  B = B,
  S0Exg = S0Exg,
  names.commodity = names.commodity,
  names.agent = names.agent,
  numeraire = "lab1",
  ts = TRUE
)

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