gem_2_2 {GE}

Some Simple 2-by-2 General Equilibrium Models

Description

Some simple 2-by-2 general equilibrium models with a firm and a laborer.

Usage

gem_2_2(...)

Arguments

...

arguments to be passed to the function sdm2.

References

http://www.econ.ucla.edu/riley/MAE/Course/SolvingForTheWE.pdf

Examples

#### a 2-by-2 general equilibrium model with a Leontief production function.
ge.Leontief <- sdm2(
  A = matrix(c(
    0.5, 1,
    0.5, 0
  ), 2, 2, TRUE),
  B = matrix(c(
    1, 0,
    0, 0
  ), 2, 2, TRUE),
  S0Exg = matrix(c(
    NA, NA,
    NA, 100
  ), 2, 2, TRUE),
  names.commodity = c("prod", "lab"),
  names.agent = c("firm", "laborer"),
  numeraire = "prod"
)

ge.Leontief$p
ge.Leontief$z
addmargins(ge.Leontief$D, 2)
addmargins(ge.Leontief$S, 2)

## the same as above.
ge2.Leontief <- sdm2(
  A = list(
    dst.firm = node_new(
      "output",
      type = "Leontief",
      a = c(0.5, 0.5),
      "prod", "lab"
    ),
    dst.consumer = node_new(
      "util",
      type = "Leontief", a = 1,
      "prod"
    )
  ),
  B = matrix(c(
    1, 0,
    0, 0
  ), 2, 2, TRUE),
  S0Exg = matrix(c(
    NA, NA,
    NA, 100
  ), 2, 2, TRUE),
  names.commodity = c("prod", "lab"),
  names.agent = c("firm", "laborer"),
  numeraire = "prod"
)

ge2.Leontief$p
ge2.Leontief$z
addmargins(ge2.Leontief$D, 2)
addmargins(ge2.Leontief$S, 2)

#### a 2-by-2 general equilibrium model with a CD production function.
ge.CD <- sdm2(
  A = function(state) {
    ## the vector of demand coefficients of the firm
    a1 <- CD_A(alpha = 2, Beta = c(0.5, 0.5), state$p)
    ## the vector of demand coefficients of the laborer
    a2 <- c(1, 0)
    cbind(a1, a2)
  },
  B = matrix(c(
    1, 0,
    0, 0
  ), 2, 2, TRUE),
  S0Exg = matrix(c(
    NA, NA,
    NA, 100
  ), 2, 2, TRUE),
  names.commodity = c("prod", "lab"),
  names.agent = c("firm", "laborer"),
  numeraire = "prod"
)

ge.CD$p
ge.CD$z
addmargins(ge.CD$D, 2)
addmargins(ge.CD$S, 2)

## the same as above.
ge2.CD <- sdm2(
  A = list(
    dst.firm = node_new(
      "output",
      type = "CD", alpha = 2, beta = c(0.5, 0.5),
      "prod", "lab"
    ),
    dst.consumer = node_new(
      "util",
      type = "Leontief", a = 1,
      "prod"
    )
  ),
  B = matrix(c(
    1, 0,
    0, 0
  ), 2, 2, TRUE),
  S0Exg = matrix(c(
    NA, NA,
    NA, 100
  ), 2, 2, TRUE),
  names.commodity = c("prod", "lab"),
  names.agent = c("firm", "laborer"),
  numeraire = "prod"
)

ge2.CD$p
ge2.CD$z
addmargins(ge2.CD$D, 2)
addmargins(ge2.CD$S, 2)

#### a 2-by-2 general equilibrium model with a SCES production function.
ge.SCES <- sdm2(
  A = function(state) {
    a1 <- SCES_A(es = 0.5, alpha = 1, Beta = c(0.5, 0.5), p = state$p)
    a2 <- c(1, 0)
    cbind(a1, a2)
  },
  B = matrix(c(
    1, 0,
    0, 0
  ), 2, 2, TRUE),
  S0Exg = matrix(c(
    NA, NA,
    NA, 100
  ), 2, 2, TRUE),
  names.commodity = c("prod", "lab"),
  names.agent = c("firm", "laborer"),
  numeraire = "prod"
)

ge.SCES$p
ge.SCES$z
addmargins(ge.SCES$D, 2)
addmargins(ge.SCES$S, 2)

## the same as above.
ge2.SCES <- sdm2(
  A = list(
    dst.firm = node_new(
      "output",
      type = "SCES",
      es = 0.5, alpha = 1, beta = c(0.5, 0.5),
      "prod", "lab"
    ),
    dst.consumer = node_new(
      "util",
      type = "Leontief", a = 1,
      "prod"
    )
  ),
  B = matrix(c(
    1, 0,
    0, 0
  ), 2, 2, TRUE),
  S0Exg = matrix(c(
    NA, NA,
    NA, 100
  ), 2, 2, TRUE),
  names.commodity = c("prod", "lab"),
  names.agent = c("firm", "laborer"),
  numeraire = "prod"
)

ge2.SCES$p
ge2.SCES$z
addmargins(ge2.SCES$D, 2)
addmargins(ge2.SCES$S, 2)

#### a 2-by-2 general equilibrium model with a CESAK production function.
ge.CESAK <- sdm2(
  A = function(state) {
    a.firm <- CESAK_dc(alpha = 2, betaK = 0.5, alphaK = 0.5, p = state$p, es = 1)
    a.consumer <- c(1, 0)
    cbind(a.firm, a.consumer)
  },
  B = matrix(c(
    1, 0,
    0, 0
  ), 2, 2, TRUE),
  S0Exg = matrix(c(
    NA, NA,
    NA, 100
  ), 2, 2, TRUE),
  names.commodity = c("prod", "lab"),
  names.agent = c("firm", "consumer"),
  numeraire = "prod"
)

ge.CESAK$p
ge.CESAK$z
addmargins(ge.CESAK$D, 2)
addmargins(ge.CESAK$S, 2)

## the same as above.
ge2.CESAK <- sdm2(
  A = list(
    dst.firm = node_new(
      "output",
      type = "CESAK", es = 1,
      alpha = 2, betaK = 0.5, alphaK = 0.5,
      "prod", "lab"
    ),
    dst.consumer = node_new(
      "util",
      type = "Leontief", a = 1,
      "prod"
    )
  ),
  B = matrix(c(
    1, 0,
    0, 0
  ), 2, 2, TRUE),
  S0Exg = matrix(c(
    NA, NA,
    NA, 100
  ), 2, 2, TRUE),
  names.commodity = c("prod", "lab"),
  names.agent = c("firm", "consumer"),
  numeraire = "prod"
)

ge2.CESAK$p
ge2.CESAK$z
addmargins(ge2.CESAK$D, 2)
addmargins(ge2.CESAK$S, 2)

#### Example 1 in the ucla reference.
ge3.SCES <- sdm2(
  A = function(state) {
    a.firm <- c(0, 0.25)
    a.consumer <- SCES_A(es = 0.5, alpha = 1, Beta = c(0.5, 0.5), p = state$p)
    cbind(a.firm, a.consumer)
  },
  B = matrix(c(
    1, 0,
    0, 0
  ), 2, 2, TRUE),
  S0Exg = matrix(c(
    NA, NA,
    NA, 30
  ), 2, 2, TRUE),
  names.commodity = c("prod", "lab"),
  names.agent = c("firm", "laborer"),
  numeraire = "prod"
)

ge3.SCES$p
ge3.SCES$z
ge3.SCES$D
ge3.SCES$S

#### The laborer has some product.
ge <- sdm2(
  A = function(state) {
    a.firm <- c(0, 1) # c(0, 2)
    a.consumer <- SCES_A(es = 0.5, alpha = 1, Beta = c(0.5, 0.5), p = state$p)
    cbind(a.firm, a.consumer)
  },
  B = matrix(c(
    1, 0,
    0, 0
  ), 2, 2, TRUE),
  S0Exg = matrix(c(
    NA, 50, # 500
    NA, 100
  ), 2, 2, TRUE),
  names.commodity = c("prod", "lab"),
  names.agent = c("firm", "laborer"),
  numeraire = "prod"
)

ge$p
ge$z
ge$D
ge$S