gemMarketClearingPath_2_2 {GE}

Some Examples of Spot Market Clearing Paths

Description

Some examples of zero-dividend spot market clearing paths (alias instantaneous equilibrium paths) containing a firm and a laborer (consumer).

Usage

gemMarketClearingPath_2_2(...)

Arguments

...

arguments to be passed to the function sdm2.

Examples

## the benchmark equilibrium
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)

f <- function(policy = NULL) {
  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 = policy,
    numberOfPeriods = 40,
    maxIteration = 1
  )
}

ge <- f(policy = policyMarketClearingPrice)
matplot(ge$ts.S[1, 1, ], type = "o", pch = 20)
matplot(ge$ts.z, type = "o", pch = 20)

## labor supply change
ge.LSC <- f(policy = list(
  function(time, state) {
    if (time >= 21) state$S[2, 2] <- state$S[2, 2] * 2
    state
  },
  policyMarketClearingPrice
))

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

## technology progress
ge.TP <- f(policy = list(
  makePolicyTechnologyChange(
    adjumentment.ratio = 2,
    agent = "firm",
    time.win = c(21, 21)
  ),
  policyMarketClearingPrice
))

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

## the same as above
ge.TP2 <- f(policy = list(
  function(time, A) {
    if (time >= 21) {
      A[[1]]$alpha <- 10
    } else {
      A[[1]]$alpha <- 5
    }
  },
  policyMarketClearingPrice
))

matplot(ge.TP2$ts.z, type = "o", pch = 20)

#### A timeline model, the equilibrium of which is the same as the benchmark equilibrium.
# In this model, in terms of form, firms are treated as consumer-type agents rather than
# producer-type agents. Firms hold products. The utility level of each firm determines
# the quantity of the product that the firm owns in the subsequent economic period.
np <- 5 # the number of economic periods
y1 <- 1 # the initial product supply
eis <- 1 # elasticity of intertemporal substitution
Gamma.beta <- 1 # the subjective discount factor

n <- 2 * np # the number of commodity kinds
m <- np + 1 # the number of agent kinds

names.commodity <- c(paste0("prod", 1:np), paste0("lab", 1:np))
names.agent <- c(paste0("firm", 1:np), "consumer")

# the exogenous supply matrix.
S0Exg <- matrix(0, n, m, dimnames = list(names.commodity, names.agent))
S0Exg[paste0("lab", 1:np), "consumer"] <- 1
for (k in 1:np) {
  S0Exg[paste0("prod", k), paste0("firm", k)] <- y1
}

dstl.firm <- list()
for (k in 1:np) {
  dstl.firm[[k]] <- node_new(
    "prod",
    type = "CD",
    alpha = 5, beta = c(0.5, 0.5),
    paste0("prod", k), paste0("lab", k)
  )
}

dst.consumer.CD <- node_new(
  "util",
  type = "CD",
  alpha = 1, beta = prop.table(rep(1, np)),
  paste0("prod", 1:np)
)

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

ge.timeline <- sdm2(
  A = c(dstl.firm, dst.consumer),
  B = matrix(0, n, m),
  S0Exg = S0Exg,
  names.commodity = names.commodity,
  names.agent = names.agent,
  numeraire = "prod1",
  ts = TRUE,
  policy = function(time, state) {
    names(state$last.z) <- state$names.agent
    dimnames(state$S) <- list(names.commodity, names.agent)

    for (k in 2:np) {
      state$S[paste0("prod", k), paste0("firm", k)] <- state$last.z[paste0("firm", k - 1)]
    }

    return(state)
  }
)

head(ge.timeline$p, np) / tail(ge.timeline$p, np)
ge$ts.p[1:5, 1] # the same as above

ge.timeline$z[1:np]
ge$ts.z[1:np, 1] # the same as above

ge.timeline$D
ge.timeline$S