gemIntertemporal_5_5: An Intertemporal Model with Land, Two Consumers, and Three...

In GE: General Equilibrium Modeling

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

Description

An (intertemporal) timeline model with two consumers (i.e. a laborer and a landowner) and three types of firms (i.e. wheat producers, iron producers and iron leaser). Here the iron leasing firm is actually a quasi-firm, which does not require primary factors such as labor and land in its production process. There are four commodities in the model, namely wheat, iron, iron leased out as a capital good, labor and land.

Usage

gemIntertemporal_5_5(...)

Arguments

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

Examples

np <- 15 # the number of economic periods
gr <- 0 # the growth rate in the steady state equilibrium
eis <- 1 # the elasticity of intertemporal substitution  of consumers
rho.beta <- 0.97 # the subjective discount factor of consumers
last.beta.laborer <- 0
last.beta.landowner <- 0
depreciation.rate <- 0.06

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

y1.wheat <- 200
y1.iron <- 100

n <- 5 * np - 3 # the number of commodity kinds
m <- 3 * np - 1 # the number of agent kinds

names.commodity <- c(
  paste0("wheat", 1:np),
  paste0("iron", 1:np),
  paste0("cap", 1:(np - 1)),
  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)),
  paste0("quasifirm.cap", 1:(np - 1)), # a quasifirm
  "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
  B[paste0("cap", k), paste0("quasifirm.cap", k)] <- 1
  B[paste0("iron", k + 1), paste0("quasifirm.cap", k)] <- 1 - depreciation.rate
}

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

  dstl.firm.iron[[k]] <- node_new(
    "prod",
    type = "CES", es = 1,
    alpha = alpha.firm.iron[k], beta = c(0.4, 0.4, 0.2),
    paste0("cap", k), paste0("lab", k), paste0("land", k)
  )

  dstl.quasifirm.cap[[k]] <- node_new(
    "output",
    type = "Leontief", a = 1,
    paste0("iron", 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)
  )
}

ge <- sdm2(
  A = c(
    dstl.firm.wheat, dstl.firm.iron, dstl.quasifirm.cap,
    dst.laborer, dst.landowner
  ),
  B = B,
  S0Exg = S0Exg,
  names.commodity = names.commodity,
  names.agent = names.agent,
  numeraire = "lab1",
  policy = makePolicyMeanValue(50),
  ts = TRUE,
  priceAdjustmentVelocity = 0.03
)

ge$p
ge$z
plot(ge$z[2 * (np - 1) + (1:(np - 1))], type = "b", pch = 20)
lines(1:(np - 1), ge$z[1:(np - 1)], type = "b", pch = 21)
lines(1:(np - 1), ge$z[np - 1 + (1:(np - 1))], type = "b", pch = 22)
legend("topleft", c("cap","wheat", "iron"), pch = 20:21)

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