gemBalancedGrowthPath {GE}

Some Examples of Balanced Growth Paths

Description

Some examples of spot market clearing paths (alias instantaneous equilibrium paths) which converge to balanced growth paths.

Usage

gemBalancedGrowthPath(...)

Arguments

...

arguments to be passed to the function sdm2.

Examples

#### an example with a firm and a laborer
dst.firm <- node_new(
  "prod",
  type = "CD", alpha = 5, beta = c(0.5, 0.5),
  "prod", "lab"
)

dst.consumer <- node_new(
  "util",
  type = "Leontief", a = 1,
  "prod"
)

dstl <- list(dst.firm, dst.consumer)

ge <- sdm2(
  A = dstl,
  B = matrix(c(
    1, 0,
    0, 0
  ), 2, 2, TRUE),
  S0Exg = matrix(c(
    NA, NA,
    NA, 1
  ), 2, 2, TRUE),
  names.commodity = c("prod", "lab"),
  names.agent = c("firm", "consumer"),
  numeraire = "lab",
  z0 = c(1, 1),
  ts = TRUE,
  policy = policyMarketClearingPrice,
  numberOfPeriods = 40,
  maxIteration = 1,
  GRExg = 0.03
)

matplot(ge$ts.z, type = "o", pch = 20)
matplot(growth_rate(ge$ts.z), type = "o", pch = 20)

#### an example with two firms and a laborer
dst.firm.corn <- node_new(
  "corn",
  type = "CD", alpha = 1, beta = c(0.5, 0.5),
  "iron", "lab"
)

dst.firm.iron <- node_new(
  "iron",
  type = "CD", alpha = 5, beta = c(0.5, 0.5),
  "iron", "lab"
)

dst.consumer <- node_new(
  "util",
  type = "Leontief", a = 1,
  "corn"
)

ge <- sdm2(
  A = list(dst.firm.corn, dst.firm.iron, dst.consumer),
  B = matrix(c(
    1, 0, 0,
    0, 1, 0,
    0, 0, 0
  ), 3, 3, TRUE),
  S0Exg = matrix(c(
    NA, NA, NA,
    NA, NA, NA,
    NA, NA, 100
  ), 3, 3, TRUE),
  names.commodity = c("corn", "iron", "lab"),
  names.agent = c("firm.corn", "firm.iron", "consumer"),
  numeraire = "lab",
  ts = TRUE,
  policy = policyMarketClearingPrice,
  numberOfPeriods = 30,
  maxIteration = 1,
  GRExg = 0.03
)

matplot(ge$ts.z, type = "o", pch = 20)
matplot(growth_rate(ge$ts.z), type = "o", pch = 20)

#### another example with two firms and a laborer
dst.manu <- node_new("manu",
                     type = "SCES", es = 1, alpha = 1,
                     beta = c(0.6, 0.4),
                     "manu", "lab"
)

dst.serv <- node_new("serv",
                     type = "SCES", es = 1, alpha = 1,
                     beta = c(0.4, 0.6),
                     "manu", "lab"
)

dst.consumer <- node_new("util",
                         type = "SCES", es = 1, alpha = 1,
                         beta = c(0.4, 0.6),
                         "manu", "serv"
)

dstl <- list(dst.manu, dst.serv, dst.consumer)

S0Exg <- matrix(NA, 3, 3)
S0Exg[3, 3] <- 100

ge <- sdm2(
  A = dstl,
  B = matrix(c(
    1, 0, 0,
    0, 1, 0,
    0, 0, 0
  ), 3, 3, TRUE),
  S0Exg = S0Exg,
  names.commodity = c("manu", "serv", "lab"),
  names.agent = c("manu", "serv", "consumer"),
  numeraire = c("manu"),
  ts = TRUE,
  policy = list(
    function(time, state) {
      if (time >= 5) {
        state$S[3, 3] <- 100 * 1.03^(time - 4)
      }
      state
    },
    policyMarketClearingPrice
  ),
  numberOfPeriods = 20,
  maxIteration = 1,
  z0 = c(160, 60, 100),
  p0 = c(1, 1, 1)
)

ge$p
ge$D
ge$S

matplot(ge$ts.z, type = "o", pch = 20)
matplot(growth_rate(ge$ts.z), type = "o", pch = 20)