gemstEndogenousUtilityFunction: Some General Equilibrium Models with Endogenous Utility...

In GE: General Equilibrium Modeling

Some General Equilibrium Models with Endogenous Utility Function

Description

Some examples of the market-clearing 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

GE documentation built on Nov. 8, 2023, 9:07 a.m.