gemCapitalAccumulation {GE}

Some Examples of Spot Market Clearing Paths with Capital Accumulation

Description

Some examples of spot market clearing paths (alias instantaneous equilibrium paths) with capital accumulation. The economy contains a production firm, a capital-leasing firm and a consumer.

Usage

gemCapitalAccumulation(...)

Arguments

...

arguments to be passed to the function sdm2.

See Also

gemPersistentTechnologicalProgress

Examples

#### a 3-by-3 example
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"
)

dstl <- 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)

ge <- sdm2(
  A = dstl,
  B = B,
  S0Exg = S0Exg,
  names.commodity = c("prod", "cap", "lab"),
  names.agent = c("firm1", "laborer", "firm2"),
  numeraire = "prod",
  z0 = c(100, 0, 50),
  policy = policyMarketClearingPrice,
  maxIteration = 1,
  numberOfPeriods = 30,
  ts = TRUE
)

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

## a MCP with labor supply change
ge <- sdm2(
  A = dstl,
  B = B,
  S0Exg = S0Exg,
  names.commodity = c("prod", "cap", "lab"),
  names.agent = c("firm1", "laborer", "firm2"),
  numeraire = "prod",
  z0 = c(400, 200, 400),
  policy = list(
    function(time, state) {
      if (time >= 5) state$S[3, 2] <- 150
      state
    },
    policyMarketClearingPrice
  ),
  maxIteration = 1,
  numberOfPeriods = 30,
  ts = TRUE
)

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

## a MCP with transitory technological progress
ge <- sdm2(
  A = dstl,
  B = B,
  S0Exg = S0Exg,
  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) {
        A[[1]]$alpha <- 3
      } else {
        A[[1]]$alpha <- 2
      }
    },
    policyMarketClearingPrice
  ),
  maxIteration = 1,
  numberOfPeriods = 30,
  ts = TRUE
)

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

## a MCP with permanent technological progress
ge <- sdm2(
  A = dstl,
  B = B,
  S0Exg = S0Exg,
  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) {
        A[[1]]$alpha <- 3
      } else {
        A[[1]]$alpha <- 2
      }
    },
    policyMarketClearingPrice
  ),
  maxIteration = 1,
  numberOfPeriods = 30,
  ts = TRUE
)

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

#### A 4-by-4 example wherein the capital goods
#### have a useful life of two periods.
ge <- sdm2(
  A = function(state) {
    a.firm1 <- CD_A(alpha = 2, Beta = c(0, 0.5, 0.5, 0), state$p)
    a.consumer <- c(1, 0, 0, 0)
    a.firm2 <- c(1, 0, 0, 0)
    a.firm3 <- c(0, 0, 0, 1)
    cbind(a.firm1, a.consumer, a.firm2, a.firm3)
  },
  B = matrix(c(
    1, 0, 0, 0,
    0, 0, 1, 1,
    0, 0, 0, 0,
    0, 0, 1, 0
  ), 4, 4, TRUE),
  S0Exg = matrix(c(
    NA, NA, NA, NA,
    NA, NA, NA, NA,
    NA, 100, NA, NA,
    NA, NA, NA, NA
  ), 4, 4, TRUE),
  names.commodity = c("prod", "cap", "lab", "prod.used"),
  names.agent = c("firm1", "consumer", "firm2", "firm3"),
  numeraire = "prod",
  policy = policyMarketClearingPrice,
  z0 = c(100, 100, 100, 100),
  ts = TRUE,
  numberOfPeriods = 30,
  maxIteration = 1
)

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