gemstEndogenousUtilityFunction {GE}

Some General Equilibrium Models with Endogenous Utility Function

Description

Some examples of the spot market clearing path (alias instantaneous equilibrium path) with an endogenous utility function. The parameters of the utility function will change with the utility level.

To deal with non-homothetic preferences, we can simply use an endogenous CES-type utility function instead of a utility function with a more complex form.

Usage

gemstEndogenousUtilityFunction(...)

Arguments

...

arguments to be passed to the function sdm2.

Examples

#### a 2-by-2 example
dst.firm <- node_new(
  "output",
  type = "CD", alpha = 5, beta = c(0.5, 0.5),
  "prod", "lab"
)

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

ge <- sdm2(
  A = list(dst.firm, dst.consumer),
  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(0.01, 1),
  p0 = c(1, 1),
  ts = TRUE,
  policy = list(
    function(A, state) {
      util <- state$last.z[2]
      beta2 <- 0.95 * plogis(util, location = 2, scale = 2)
      A[[2]]$beta <- c(1 - beta2, beta2)
    },
    policyMarketClearingPrice
  ),
  numberOfPeriods = 20,
  maxIteration = 1
)

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

#### a 3-by-3 example with 100 laborers
#### Assume that each laborer desires to consume one unit of
#### corn per period, regardless of her level of utility.
dst.firm.corn <- node_new(
  "corn",
  type = "CD", alpha = 1, beta = c(0.5, 0.5),
  "iron", "lab"
)

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

dst.consumer <- node_new(
  "util",
  type = "Leontief",
  a = c(0.5, 0.5),
  "corn", "iron"
)

ge <- sdm2(
  A = list(dst.firm.corn, dst.firm.iron, dst.consumer),
  B = matrix(c(
    1, 0, 0,
    0, 1, 0,
    0, 0, 0
  ), 3, 3, TRUE),
  S0Exg = matrix(c(
    NA, NA, NA,
    NA, NA, NA,
    NA, NA, 100
  ), 3, 3, TRUE),
  names.commodity = c("corn", "iron", "lab"),
  names.agent = c("firm.corn", "firm.iron", "consumer"),
  numeraire = "lab",
  ts = TRUE,
  policy = list(
    function(A, state) {
      last.util <- state$last.z[3] / 100 # the previous utility level of each laborer
      a1 <- min(1 / last.util, 1)
      A[[3]]$a <- c(a1, 1 - a1)
    },
    policyMarketClearingPrice
  ),
  numberOfPeriods = 40,
  maxIteration = 1
)

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

#### a 4-by-4 example with 100 homogeneous laborers
dst.agri <- node_new(
  "output",
  type = "SCES",
  es = 0.5, alpha = 2, beta = c(0.2, 0.8),
  "manu", "lab"
)

dst.manu <- node_new(
  "output",
  type = "SCES",
  es = 0.5, alpha = 3, beta = c(0.6, 0.4),
  "manu", "lab"
)

dst.serv <- node_new(
  "output",
  type = "SCES",
  es = 0.5, alpha = 2, beta = c(0.4, 0.6),
  "manu", "lab"
)

dst.consumer <- node_new(
  "util",
  type = "CD", alpha = 1, beta = c(0.6, 0.3, 0.1),
  "agri", "manu", "serv"
)

ge <- sdm2(
  A = list(dst.agri, dst.manu, dst.serv, dst.consumer),
  B = diag(c(1, 1, 1, 0)),
  S0Exg = {
    tmp <- matrix(NA, 4, 4)
    tmp[4, 4] <- 100
    tmp
  },
  names.commodity = c("agri", "manu", "serv", "lab"),
  names.agent = c("agri", "manu", "serv", "consumer"),
  numeraire = "lab",
  z0 = c(1, 1, 1, 0),
  ts = TRUE,
  policy = list(
    function(A, state) {
      util <- state$last.z[4] / 100
      beta1 <- structural_function(util, c(1, 6), 0.6, 0.1)
      beta3 <- structural_function(util, c(1, 6), 0.1, 0.5)
      beta2 <- 1 - beta1 - beta3
      A[[4]]$beta <- c(beta1, beta2, beta3)
    },
    policyMarketClearingPrice
  ),
  numberOfPeriods = 20,
  maxIteration = 1
)

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