gemPersistentTechnologicalProgress {GE}

Some Examples of Spot Market Clearing Paths with Persistent Technological Progress

Description

Some examples of spot market clearing paths (alias instantaneous equilibrium paths) with persistent technological progress. From the fifth period, technological progress occurs.

Usage

gemPersistentTechnologicalProgress(...)

Arguments

...

arguments to be passed to the function sdm2.

See Also

gemCapitalAccumulation

Examples

#### a 2-by-2 example with labor-saving technological progress
tpr <- 0.03 # technological progress rate

dst.firm <- node_new(
  "prod",
  type = "SCES",
  es = 0.5, alpha = 1,
  beta = c(0.5, 0.5),
  "prod", "cc1"
)
node_set(dst.firm, "cc1",
         type = "Leontief", a = 1,
         "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, 100
  ), 2, 2, TRUE),
  names.commodity = c("prod", "lab"),
  names.agent = c("firm", "consumer"),
  numeraire = "prod",
  ts = TRUE,
  policy = list(
    function(time, A) {
      if (time >= 5) {
        node_set(A[[1]], "cc1",
                 a = (1 + tpr)^-(time - 4)
        )
      }
    },
    policyMarketClearingPrice
  ),
  numberOfPeriods = 40,
  maxIteration = 1,
  z0 = c(200, 100),
  p0 = c(1, 1)
)

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

#### a 3-by-3 example with labor-saving technological progress
tpr <- 0.03 # technological progress rate

dst.manu <- node_new("manu",
                     type = "SCES", es = 0.5, alpha = 1,
                     beta = c(0.6, 0.4),
                     "manu", "cc1"
)
node_set(dst.manu, "cc1",
         type = "Leontief", a = 1,
         "lab"
)

dst.serv <- node_new("serv",
                     type = "SCES", es = 0.5, alpha = 1,
                     beta = c(0.4, 0.6),
                     "manu", "lab"
)

dst.consumer <- node_new("util",
                         type = "SCES", es = 0.5, alpha = 1,
                         beta = c(0.4, 0.6),
                         "manu", "serv"
)

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

ge <- sdm2(
  A = dstl,
  B = matrix(c(
    1, 0, 0,
    0, 1, 0,
    0, 0, 0
  ), 3, 3, TRUE),
  S0Exg = {
    S0Exg <- matrix(NA, 3, 3)
    S0Exg[3, 3] <- 100
    S0Exg
  },
  names.commodity = c("manu", "serv", "lab"),
  names.agent = c("manu", "serv", "consumer"),
  numeraire = c("manu"),
  ts = TRUE,
  policy = list(
    function(time, A) {
      if (time >= 5) {
        node_set(A[[1]], "cc1",
                 a = (1 + tpr)^-(time - 4)
        )
      }
    },
    policyMarketClearingPrice
  ),
  numberOfPeriods = 40,
  maxIteration = 1,
  z0 = c(160, 60, 100),
  p0 = c(1, 1, 1)
)

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

#### a 3-by-3 example with labor-saving technological
#### progress and capital accumulation
dst.firm1 <- node_new(
  "prod",
  type = "CD",
  alpha = 2, beta = c(0.5, 0.5),
  "cap", "cc1"
)
node_set(dst.firm1, "cc1",
         type="Leontief", a=1,
         "lab")

dst.consumer <- dst.firm2 <- node_new(
  "util",
  type = "Leontief",
  a= 1,
  "prod"
)

ge <- sdm2(
  A = list(dst.firm1, dst.consumer, dst.firm2),
  B = matrix(c(
    1, 0, 0.5,
    0, 0, 1,
    0, 0, 0
  ), 3, 3, TRUE),
  S0Exg = matrix(c(
    NA, NA, NA,
    NA, NA, NA,
    NA, 100,NA
  ), 3, 3, TRUE),
  names.commodity = c("prod", "cap", "lab"),
  names.agent = c("firm1", "laborer","firm2"),
  numeraire = "prod",
  z0=c(400,200,400),
  policy = list(
    function(time, A) {
      if (time >= 5) {
        node_set(A[[1]],"cc1", a = (1 + 0.03)^-(time - 4))
      }
    },
    policyMarketClearingPrice
  ),
  maxIteration = 1,
  numberOfPeriods = 30,
  ts=TRUE
)

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