gemCESAK_Timeline_2_2 {GE}

Some Timeline Equilibrium Models with CESAK Production Function

Description

Some timeline general equilibrium models with CESAK production function.

Usage

gemCESAK_Timeline_2_2(...)

Arguments

...

arguments to be passed to the function sdm2.

Examples

np <- 5
gr <- 0
initial.product.supply <- 20
beta.prod.firm <- 0.35
eis <- 1
Gamma.beta <- 0.97
gr <- 0.05
alphaK <- 1.05

S0Exg <- matrix(NA, 2 * np - 1, np)
S0Exg[(np + 1):(2 * np - 1), np] <- 100 * (1 + gr)^(0:(np - 2))
S0Exg[1, np] <- initial.product.supply

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

dstl.firm <- list()
for (k in 1:(np - 1)) {
  dstl.firm[[k]] <- node_new("output",
                             type = "CESAK", es = 1,
                             alpha = 0.1, betaK = beta.prod.firm, alphaK = alphaK,
                             paste0("prod", k), paste0("lab", k)
  )
}

dst.consumer <- node_new(
  "util",
  type = "CES", es = eis,
  alpha = 1, beta = prop.table(Gamma.beta^(1:np)),
  paste0("prod", 1:np)
)

ge <- sdm2(
  A = c(dstl.firm, dst.consumer),
  B = B,
  S0Exg = S0Exg,
  names.commodity = c(paste0("prod", 1:np), paste0("lab", 1:(np - 1))),
  names.agent = c(paste0("firm", 1:(np - 1)), "consumer"),
  numeraire = "lab1",
  priceAdjustmentVelocity = 0.03
)

growth_rate(ge$p[1:np])
growth_rate(ge$z[1:np])
ge$D

#### a AK model
np <- 5
initial.product.supply <- 20
eis <- 1
Gamma.beta <- 1
alphaK <- 1.25

S0Exg <- matrix(NA, np, np)
S0Exg[1, np] <- initial.product.supply

B <- matrix(0, np, np)
B[2:np, 1:(np - 1)] <- diag(np - 1)

dstl.firm <- list()
for (k in 1:(np - 1)) {
  dstl.firm[[k]] <- node_new("output",
                             type = "Leontief", a = 1 / alphaK,
                             paste0("prod", k)
  )
}

dst.consumer <- node_new(
  "util",
  type = "CES", es = eis,
  alpha = 1, beta = prop.table(Gamma.beta^(1:np)),
  paste0("prod", 1:np)
)

ge <- sdm2(
  A = c(dstl.firm, dst.consumer),
  B = B,
  S0Exg = S0Exg,
  names.commodity = paste0("prod", 1:np),
  names.agent = c(paste0("firm", 1:(np - 1)), "consumer"),
  numeraire = "prod1",
  priceAdjustmentVelocity = 0.03,
  policy = makePolicyMeanValue(50),
)

growth_rate(ge$p)
growth_rate(ge$z[1:(np - 1)])
ge$D

## Simplify the production function in the model above.
dstl.firm <- list()
for (k in 1:(np - 1)) {
  dstl.firm[[k]] <- node_new("output",
                             type = "Leontief", a = 1 / alphaK^(k),
                             "prod1"
  )
}

ge2 <- sdm2(
  A = c(dstl.firm, dst.consumer),
  B = B,
  S0Exg = S0Exg,
  names.commodity = paste0("prod", 1:np),
  names.agent = c(paste0("firm", 1:(np - 1)), "consumer"),
  numeraire = "prod1",
  priceAdjustmentVelocity = 0.03,
  policy = makePolicyMeanValue(50),
)

growth_rate(ge2$p)
growth_rate(ge2$z[1:(np - 1)])
ge2$D