gemExogenousPrice {GE}

Some Examples with Exogenous Price (Price Control)

Description

Some examples with exogenous price (i.e. price control, price regulation). When a price control policy is imposed in a structural dynamic model, the economy may converge to a steady state where the market does not clear.

Usage

gemExogenousPrice(...)

Arguments

...

arguments to be passed to the function sdm2.

References

LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)

See Also

gemExogenousPrice_EndogenousLaborSupply_3_3

Examples

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

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

f <- function(pExg = NULL, policy = NULL) {
  pcss <- sdm2(
    A = list(dst.firm, dst.consumer),
    B = diag(c(1, 0)),
    S0Exg = {
      S0Exg <- matrix(NA, 2, 2)
      S0Exg[2, 2] <- 100
      S0Exg
    },
    names.commodity = c("prod", "lab"),
    names.agent = c("firm", "consumer"),
    numeraire = "lab",
    maxIteration = 1,
    numberOfPeriods = 100,
    p0 = c(0.16, 1),
    ts = TRUE,
    pExg = pExg,
    policy = policy
  )

  print(pcss$p)
  print(pcss$z)
  par(mfrow = c(1, 2))
  matplot(pcss$ts.p, type = "l")
  matplot(pcss$ts.z, type = "l")
  invisible(pcss)
}

## No price control policy.
f()

## Set the market prices to the steady-state equilibrium prices from the beginning.
## The labor market keeps oversupplied.
result <- f(pExg = c(0.16, 1))
matplot(result$ts.q, type = "l") # sale rates

## the same as above
f(policy = function(state) {
  state$p <- c(0.16, 1)
  state
})

## The price control policy is implemented from the 10th period.
f(policy = function(time, state) {
  if (time >= 10) state$p <- c(0.16, 1)
  state
})

## The price control policy is implemented from the 30th period.
f(policy = function(time, state) {
  if (time >= 30) state$p <- c(0.16, 1)
  state
})

## price ceil
f(policy = function(time, state) {
  if (time >= 30) {
    state$p <- state$p / state$p[2]
    if (state$p[1] > 0.15) state$p[1] <- 0.15
  }
  state
})

##
pcss <- f(policy = function(time, state) {
  if (time >= 30) state$p <- c(0.17, 1)
  state
})

tail(pcss$ts.q)

#### another 2-by-2 example.
f <- function(GRExg = 0, pExg = c(2, 1)) {
  pcss <- sdm(
    A = matrix(c(
      0, 1,
      1, 0
    ), 2, 2, TRUE),
    B = matrix(c(
      1, 0,
      0, 0
    ), 2, 2, TRUE),
    S0Exg = matrix(c(
      NA, NA,
      NA, 100
    ), 2, 2, TRUE),
    GRExg = GRExg,
    pExg = pExg,
    maxIteration = 1,
    numberOfPeriods = 300,
    depreciationCoef = 0,
    z0 = c(100, 0),
    ts = TRUE
  )
  matplot(pcss$ts.z, type = "l")
  print("pcss$z:")
  pcss$z
  print("tail(pcss$ts.q, 3)")
  print(tail(pcss$ts.q, 3))
  invisible(pcss)
}

f()
f(GRExg = 0.01)
f(pExg = c(1, 2))

#### Example 9.5 in Li (2019).
f <- function(GRExg = 0, pExg = c(1, NA, 0.625)) {
  pcss <- sdm(
    A = function(state) {
      alpha <- rbind(1, 1, 1)
      Beta <- matrix(c(
        0, 1, 1,
        0.5, 0, 0,
        0.5, 0, 0
      ), 3, 3, TRUE)
      CD_A(alpha, Beta, state$p)
    },
    B = diag(c(1, 0, 0)),
    S0Exg = matrix(c(
      NA, NA, NA,
      NA, 100, NA,
      NA, NA, 100
    ), 3, 3, TRUE),
    GRExg = GRExg,
    pExg = pExg,
    maxIteration = 1,
    numberOfPeriods = 300,
    depreciationCoef = 0,
    z0 = c(100, 0, 0),
    ts = TRUE
  )
  matplot(pcss$ts.z, type = "l")
  print("pcss$z:")
  pcss$z
  print("tail(pcss$ts.q, 3)")
  print(tail(pcss$ts.q, 3))
  invisible(pcss)
}

f()
f(GRExg = 0.01)
f(pExg = c(1, 0.25, 0.25))
f(pExg = c(1, 0.2, 0.25))