gemTemporaryEquilibriumPath {GE}

Some Examples of Temporary Equilibrium Paths

Description

Some examples of temporary equilibrium paths. The temporary equilibrium path consists of a series of temporary equilibria. Each temporary equilibrium achieves market clearing, and these markets may include futures markets in addition to spot markets. An instantaneous equilibrium path is a temporary equilibrium path that only includes spot markets.

Usage

gemTemporaryEquilibriumPath(...)

Arguments

...

arguments to be passed to the function sdm2.

References

Grandmont, J.M. (1977). Temporary General Equilibrium Theory. Econometrica 45, 535-572.

See Also

policyMarketClearingPrice

Examples

#### A pure exchange economy.
## Consumers 1 and 2 each supply 50 units of payoff each period.
## Consumers have limited foresight into the future and always expect
## that the supply of consumer 1 will be 50 and the supply of
## consumer 2 will be 40 in the next period.
dst.consumer1 <- node_new("util",
  type = "SCES", es = 2,
  alpha = 1, beta = c(0.5, 0.5),
  "payoff1", "payoff2"
)

dst.consumer2 <- node_new("util",
  type = "SCES", es = 1,
  alpha = 1, beta = c(0.5, 0.5),
  "payoff1", "payoff2"
)

result <- list()
for (time in 1:20) {
  if (time == 1) {
    S0Exg <- matrix(c(
      50, 50,
      50, 40
    ), 2, 2, TRUE)
  } else {
    S0Exg <- rbind(ge$D[2, ] + c(0, 10), c(50, 40))
  }

  ge <- sdm2(
    A = list(dst.consumer1, dst.consumer2),
    B = matrix(0, 2, 2),
    S0Exg = S0Exg,
    names.commodity = c("payoff1", "payoff2"),
    names.agent = c("consumer1", "consumer2"),
    numeraire = "payoff1"
  )

  result[[time]] <- ge
}

sapply(result, \(x) x$p)
sapply(result, \(x) x$z)
# lapply(result, \(x) x$D)
# lapply(result, \(x) x$S)

#### An economy with production.
dst.consumer <- node_new("util",
  type = "CD",
  alpha = 1,
  beta = c(1 / 3, 2 / 3), # beta = c(1/2, 1/2)
  "prod1", "prod2"
)

dst.firm <- node_new("prod2",
  type = "CD", alpha = 2, beta = c(0.5, 0.5),
  "prod1", "lab"
)

result <- list()
for (time in 1:20) {
  if (time == 1) {
    S0Exg <- matrix(c(
      10, 0,
      0, NA,
      100, 0
    ), 3, 2, TRUE)
  } else {
    S0Exg <- matrix(c(
      ge$D[2, 1], 0,
      0, NA,
      100, 0
    ), 3, 2, TRUE)
  }

  ge <- sdm2(
    A = list(dst.consumer, dst.firm),
    B = matrix(c(
      0, 0,
      0, 1,
      0, 0
    ), 3, 2, TRUE),
    S0Exg = S0Exg,
    names.commodity = c("prod1", "prod2", "lab"),
    names.agent = c("consumer", "firm"),
    numeraire = "prod1"
  )

  result[[time]] <- ge
}


sapply(result, \(x) x$p)
sapply(result, \(x) x$z)
# lapply(result, \(x) x$D)
# lapply(result, \(x) x$S)

##
result <- list()
last.output <- 10
for (time in 1:30) {
  if (time == 1) {
    S0Exg <- matrix(c(
      10, 0,
      0, last.output,
      100, 0
    ), 3, 2, TRUE)
  } else {
    S0Exg <- rbind(
      c(ge$D[2, 1], max(ge$z[2] - last.output, 0)),
      c(0, last.output),
      c(100, 0)
    )

    last.output <- ge$z[2]
  }

  ge <- sdm2(
    A = list(dst.consumer, dst.firm),
    B = matrix(c(
      0, 0,
      0, 1,
      0, 0
    ), 3, 2, TRUE),
    # B = matrix(0, 3, 2),
    S0Exg = S0Exg,
    names.commodity = c("prod1", "prod2", "lab"),
    names.agent = c("consumer", "firm"),
    numeraire = "prod1"
  )

  result[[time]] <- ge
}
sapply(result, \(x) x$p)
sapply(result, \(x) x$z)
# lapply(result, \(x) x$D)
# lapply(result, \(x) x$S)