gemIntertemporal_3_3: Some Examples of Intertemporal Models with One Consumer and...

In GE: General Equilibrium Modeling

Some Examples of Intertemporal Models with One Consumer and Two Types of Firms

Description

Some examples of intertemporal models with one consumer and two types of firms. There are three types of commodities (i.e. corn, iron and labor). The consumer may consume corn and iron in each period, and may have a nested intertemporal utility function.

Usage

gemIntertemporal_3_3(...)

Arguments

...	arguments to be passed to the function sdm2.

References

Zen Xiangjin (1995, ISBN: 7030046560). Basics of Economic Cybernetics. Beijing: Science Press. (In Chinese)

Examples

#### an example with a nested intertemporal utility function
np <- 5 # the number of economic periods

n <- 3 * np - 1 # the number of commodity kinds
m <- 2 * (np - 1) + 1 # the number of agent kinds

names.commodity <- c(
  paste0("corn", 1:np),
  paste0("iron", 1:np),
  paste0("lab", 1:(np - 1))
)
names.agent <- c(
  paste0("firm.corn", 1:(np - 1)),
  paste0("firm.iron", 1:(np - 1)),
  "consumer"
)

## the exogenous supply matrix.
S0Exg <- matrix(NA, n, m, dimnames = list(names.commodity, names.agent))
S0Exg[paste0("lab", 1:(np - 1)), "consumer"] <- 100
S0Exg["corn1", "consumer"] <- 25
S0Exg["iron1", "consumer"] <- 100

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

dstl.firm.corn <- dstl.firm.iron <- list()
for (k in 1:(np - 1)) {
  dstl.firm.corn[[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.consumer <- 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.consumer,
    paste0("cc", k),
    type = "CD", alpha = 1, beta = c(0.5, 0.5),
    paste0("corn", k), paste0("iron", k)
  )
}

ge <- sdm2(
  A = c(dstl.firm.corn, dstl.firm.iron, dst.consumer),
  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

#### an example with a non-nested intertemporal utility function
np <- 3 # the number of economic periods

## There are np types of corn, np-1 types of iron and np-1 types of labor.
## There are np-1 corn firms, np-2 iron firms and one consumer.
n <- 3 * np - 2
m <- 2 * np - 2

names.commodity <- c(
  paste0("corn", 1:np),
  paste0("iron", 1:(np - 1)),
  paste0("lab", 1:(np - 1))
)
names.agent <- c(
  paste0("firm.corn", 1:(np - 1)),
  paste0("firm.iron", 1:(np - 2)),
  "consumer"
)

## the exogenous supply matrix.
S0Exg <- matrix(NA, n, m, dimnames = list(names.commodity, names.agent))
S0Exg[paste0("lab", 1:(np - 1)), "consumer"] <- 100
S0Exg["corn1", "consumer"] <- 25
S0Exg["iron1", "consumer"] <- 100

# the output coefficient matrix.
B <- matrix(0, n, m, dimnames = list(names.commodity, names.agent))
for (k in 1:(np - 1)) {
  B[paste0("corn", k + 1), paste0("firm.corn", k)] <- 1
}
for (k in 1:(np - 2)) {
  B[paste0("iron", k + 1), paste0("firm.iron", k)] <- 1
}

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

for (k in seq_along(np:(2 * np - 3))) {
  dstl.firm.iron[[k]] <- node_new(
    "prod",
    type = "CD", alpha = 2, beta = c(0.5, 0.5),
    paste0("iron", k), paste0("lab", k)
  )
}

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

ge <- sdm2(
  A = c(dstl.firm.corn, dstl.firm.iron, dst.consumer),
  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

#### an example of Zeng (1995, page 227)
ic1 <- 1 / 10 # input coefficient
ic2 <- 1 / 7
dc1 <- 2 / 3 # depreciation coefficient
dc2 <- 9 / 10

ge <- sdm2(
  A = {
    # corn, iron1, iron2, iron3, iron4
    a1.1 <- c(0, ic1, 0, 0, 0)
    a1.2 <- c(0, ic2, 0, 0, 0)
    a2.1 <- c(0, 0, ic1, 0, 0)
    a2.2 <- c(0, 0, ic2, 0, 0)
    a3.1 <- c(0, 0, 0, ic1, 0)
    a3.2 <- c(0, 0, 0, ic2, 0)
    a4.1 <- c(0, 0, 0, 0, ic1)
    a4.2 <- c(0, 0, 0, 0, ic2)

    a.consumer <- c(1, 0, 0, 0, 0)

    cbind(a1.1, a1.2, a2.1, a2.2, a3.1, a3.2, a4.1, a4.2, a.consumer)
  },
  B = {
    b1.1 <- c(1, 0, ic1 * dc1, 0, 0)
    b1.2 <- c(1, 0, ic2 * dc2, 0, 0)
    b2.1 <- c(1, 0, 0, ic1 * dc1, 0)
    b2.2 <- c(1, 0, 0, ic2 * dc2, 0)
    b3.1 <- c(1, 0, 0, 0, ic1 * dc1)
    b3.2 <- c(1, 0, 0, 0, ic2 * dc2)
    b4.1 <- c(1, 0, 0, 0, 0)
    b4.2 <- c(1, 0, 0, 0, 0)
    b.consumer <- c(0, 0, 0, 0, 0)

    cbind(b1.1, b1.2, b2.1, b2.2, b3.1, b3.2, b4.1, b4.2, b.consumer)
  },
  S0Exg = {
    tmp <- matrix(NA, 5, 9)
    tmp[2, 9] <- 100
    tmp
  },
  names.commodity = c("corn", paste0("iron", 1:4)),
  names.agent = c(paste0("firm", 1:8), "consumer"),
  numeraire = "corn",
  policy = makePolicyMeanValue(30),
  priceAdjustmentVelocity = 0.05,
  maxIteration = 1,
  numberOfPeriods = 1000,
  ts = TRUE
)

matplot(ge$ts.z, type = "l")

ge$p
ge$z
ge$D
ge$S

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