gemLand_Labor_Capital_4_3 {GE}

Some Examples of Spot Market Clearing Paths Involving Land, Labor and Capital

Description

Some examples of spot market clearing paths (alias instantaneous equilibrium paths) involving land, labor and capital.

Usage

gemLand_Labor_Capital_4_3(...)

Arguments

...

arguments to be passed to the function sdm2.

Examples

depreciation.rate <- 0.05

dst.firm.production <- node_new("prod",
  type = "CD",
  alpha = 1, beta = c(0.4, 0.4, 0.2),
  "lab", "cap", "land"
)

dst.firm.capital.leasing <- node_new("cap",
  type = "Leontief", a = 1,
  "prod"
)

dst.consumer <- node_new("util",
  type = "CD",
  alpha = 1, beta = c(0.5, 0.5),
  "prod", "lab"
)

dstl <- list(dst.firm.production, dst.consumer, dst.firm.capital.leasing)
f <- function(policy = policyMarketClearingPrice,
              p0 = c(1, 1, 1, 1),
              z0 = c(10, 10, 10),
              numberOfPeriods = 100) {
  sdm2(
    A = dstl,
    B = matrix(c(
      1, 0, 1 - depreciation.rate,
      0, 0, 0,
      0, 0, 1,
      0, 0, 0
    ), 4, 3, TRUE),
    S0Exg = {
      S0Exg <- matrix(NA, 4, 3)
      S0Exg[2, 2] <- S0Exg[4, 2] <- 1
      S0Exg
    },
    names.commodity = c("prod", "lab", "cap", "land"),
    names.agent = c("firm.production", "consumer", "firm.capital.leasing"),
    numeraire = "prod",
    maxIteration = 1,
    numberOfPeriods = numberOfPeriods,
    p0 = p0,
    z0 = z0,
    policy = policy,
    ts = TRUE
  )
}

ge1 <- f()
ge1$p
ge1$DV
ge1$SV
matplot(ge1$ts.z, type = "l")

## a spot market clearing path with population growth
policy.population.growth <- function(time, state) {
  if (time >= 5) {
    state$S[2, 2] <- 1.01^(time - 4)
  }
  state
}

ge2 <- f(
  policy = list(
    policy.population.growth,
    policyMarketClearingPrice
  ),
  p0 = ge1$p, z0 = ge1$z,
  numberOfPeriods = 30
)
matplot(ge2$ts.z, type = "o", pch = 40)
matplot(growth_rate(ge2$ts.z), type = "o", pch = 20)

## a spot market clearing path with technology progress
policy.technology.progress <- function(time, A) {
  if (time >= 5) {
    A[[1]]$alpha <- 1.02^(time - 4)
  }
}

ge3 <- f(
  policy = list(
    policy.technology.progress,
    policyMarketClearingPrice
  ),
  p0 = ge1$p, z0 = ge1$z,
  numberOfPeriods = 30
)

matplot(ge3$ts.z, type = "o", pch = 20)
matplot(growth_rate(ge3$ts.z), type = "o", pch = 20)

## a spot market clearing path with population growth and technology progress
ge4 <- f(
  policy = list(
    policy.population.growth,
    policy.technology.progress,
    policyMarketClearingPrice
  ),
  p0 = ge1$p, z0 = ge1$z,
  numberOfPeriods = 30
)

matplot(ge4$ts.z, type = "o", pch = 20)
matplot(growth_rate(ge4$ts.z), type = "o", pch = 20)