gemIntertemporal_4_4: An Intertemporal Model with Land, Two Consumers and Two Types...

In GE: General Equilibrium Modeling

An Intertemporal Model with Land, Two Consumers and Two Types of Firms

Description

An (intertemporal) timeline model with two consumers (i.e. a laborer and a landowner) and two types of firms (i.e. wheat producers and iron producers). There are four commodities in the model, namely wheat, iron, labor and land.

Usage

gemIntertemporal_4_4(...)

Arguments

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

Examples

np <- 15 # the number of economic periods

alpha.firm.wheat <- rep(5, np - 1)

alpha.firm.iron <- rep(5, np - 1)

rho.beta <- 0.97 # 1, 1.03 # the subjective discount factor of consumers

y1.wheat <- 100 # 126, 129.96
y1.iron <- 30 # 40.59, 43.47

gr <- 0 # the growth rate in the steady state equilibrium
eis <- 0.5 # the elasticity of intertemporal substitution  of consumers

last.beta.laborer <- 0
last.beta.landowner <- 0

n <- 4 * np - 2 # the number of commodity kinds
m <- 2 * np # the number of agent kinds

names.commodity <- c(
  paste0("wheat", 1:np),
  paste0("iron", 1:np),
  paste0("lab", 1:(np - 1)),
  paste0("land", 1:(np - 1))
)

names.agent <- c(
  paste0("firm.wheat", 1:(np - 1)), paste0("firm.iron", 1:(np - 1)),
  "laborer", "landowner"
)

# the exogenous supply matrix.
S0Exg <- matrix(NA, n, m, dimnames = list(names.commodity, names.agent))
S0Exg["wheat1", "laborer"] <- y1.wheat
S0Exg["iron1", "landowner"] <- y1.iron
S0Exg[paste0("lab", 1:(np - 1)), "laborer"] <- 100 * (1 + gr)^(0:(np - 2)) # the supply of labor
S0Exg[paste0("land", 1:(np - 1)), "landowner"] <- 100 * (1 + gr)^(0:(np - 2)) # the supply of land

# 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
}

dstl.firm.wheat <- dstl.firm.iron <- list()
for (k in 1:(np - 1)) {
  dstl.firm.wheat[[k]] <- node_new(
    "prod",
    type = "CES", es = 0.8,
    alpha = alpha.firm.wheat[k], beta = c(0.2, 0.4, 0.4),
    paste0("iron", k), paste0("lab", k), paste0("land", k)
  )

  dstl.firm.iron[[k]] <- node_new(
    "prod",
    type = "CES", es = 0.8,
    alpha = alpha.firm.iron[k], beta = c(0.4, 0.4, 0.2),
    paste0("iron", k), paste0("lab", k), paste0("land", k)
  )
}

tmp.beta <- rho.beta^(1:(np - 1))
tmp.beta <- tmp.beta / tmp.beta[np - 1]
tmp.beta <- c(tmp.beta, last.beta.laborer)
dst.laborer <- node_new(
  "util",
  type = "CES", es = eis,
  alpha = 1, beta = prop.table(tmp.beta),
  paste0("cc", 1:(np - 1)), paste0("wheat", np)
)
for (k in 1:(np - 1)) {
  node_set(dst.laborer, paste0("cc", k),
    type = "CES", es = 1,
    alpha = 1, beta = c(0.4, 0.4, 0.2),
    paste0("wheat", k), paste0("lab", k), paste0("land", k)
  )
}

tmp.beta <- rho.beta^(1:(np - 1))
tmp.beta <- tmp.beta / tmp.beta[np - 1]
tmp.beta <- c(tmp.beta, last.beta.landowner)
dst.landowner <- node_new(
  "util",
  type = "CES", es = eis,
  alpha = 1, beta = prop.table(tmp.beta),
  paste0("cc", 1:(np - 1)), paste0("iron", np)
)
for (k in 1:(np - 1)) {
  node_set(dst.landowner, paste0("cc", k),
    type = "CES", es = 1,
    alpha = 1, beta = c(0.2, 0.4, 0.4),
    paste0("wheat", k), paste0("lab", k), paste0("land", k)
  )
}

f <- function(policy = NULL) {
  ge <- sdm2(
    A = c(dstl.firm.wheat, dstl.firm.iron, Clone(dst.laborer), Clone(dst.landowner)),
    B = B,
    S0Exg = S0Exg,
    names.commodity = names.commodity,
    names.agent = names.agent,
    numeraire = "lab1",
    policy = policy,
    ts = TRUE,
    maxIteration = 1,
    numberOfPeriods = 1000,
    priceAdjustmentVelocity = 0.05
  )

  plot(ge$z[1:(np - 1)],
    type = "o", pch = 20, ylab = "production level",
    xlab = "time", ylim = range(ge$z[1:(2 * np - 2)])
  )
  lines(ge$z[np:(2 * np - 2)], type = "o", pch = 21)
  legend("bottom", c("wheat", "iron"), pch = 20:21)

  invisible(ge)
}

f()

## Compute the steady state based on head and tail adjustments.
policyHeadAdjustment <- function(time, state) {
  if (time > 100) {
    state$S[1, m - 1] <- state$last.z[round(np / 2)] / (1 + gr)^(round(np / 2))
    state$S[np + 1, m] <- state$last.z[np - 1 + round(np / 2)] / (1 + gr)^(round(np / 2))
  }
  state
}

policyTailAdjustment <- function(A, state) {
  # wheat
  ratio.output.tail <- state$last.z[np - 1] / (state$last.z[np - 2] * (1 + gr))
  tmp.node <- A[[m - 1]]
  tmp.n <- length(tmp.node$beta)
  tail.beta <- tmp.node$beta[tmp.n]
  if (tail.beta == 0) tail.beta <- 1 / tmp.n
  tail.beta <- tail.beta / ratio.output.tail
  tmp.node$beta <- prop.table(c(tmp.node$beta[1:(tmp.n - 1)], tail.beta))

  # iron
  ratio.output.tail <- state$last.z[2 * np - 2] / (state$last.z[2 * np - 3] * (1 + gr))
  tmp.node <- A[[m]]
  tmp.n <- length(tmp.node$beta)
  tail.beta <- tmp.node$beta[tmp.n]
  if (tail.beta == 0) tail.beta <- 1 / tmp.n
  tail.beta <- tail.beta / ratio.output.tail
  tmp.node$beta <- prop.table(c(tmp.node$beta[1:(tmp.n - 1)], tail.beta))
}

f(list(policyHeadAdjustment, policyTailAdjustment))
# f(policyHeadAdjustment)
# f(policyTailAdjustment)

### a structural transformation path
# tax.rate <- 0.1 # the tax rate imposed on income from land and labor income.
# tax.time <- 1
#
# # the exogenous supply matrix.
# S0Exg <- matrix(NA, n, m, dimnames = list(names.commodity, names.agent))
# S0Exg["wheat1", "laborer"] <- y1.wheat
# S0Exg["iron1", "landowner"] <- y1.iron
# S0Exg[paste0("lab", 1:(np - 1)), "laborer"] <- 100 * (1 + gr)^(0:(np - 2)) # the supply of labor
# S0Exg[paste0("land", 1:(np - 1)), "landowner"] <- 100 * (1 + gr)^(0:(np - 2)) # the supply of land
#
# S0Exg[paste0("lab", tax.time), paste0("firm.iron", tax.time)] <-
#   S0Exg[paste0("lab", tax.time), "laborer"] * tax.rate
# S0Exg[paste0("land", tax.time), paste0("firm.iron", tax.time)] <-
#   S0Exg[paste0("land", tax.time), "landowner"] * tax.rate
#
# S0Exg[paste0("lab", tax.time), "laborer"] <-
#   S0Exg[paste0("lab", tax.time), "laborer"] * (1 - tax.rate)
# S0Exg[paste0("land", tax.time), "landowner"] <-
#   S0Exg[paste0("land", tax.time), "landowner"] * (1 - tax.rate)
#
# # Suppose the tax rate is high enough so that the iron
# # producer's efficiency coefficient immediately rises to 10.
# for (k in 1:(np - 1)) {
#   dstl.firm.iron[[k]]$alpha <- ifelse(k <= tax.time, 5, 10)
# }
#
# f(policy=policyTailAdjustment)
# f()

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