gemTax_QuasilinearPreference_4_4: A General Equilibrium Model with Tax and Quasilinear Utility...

In GE: General Equilibrium Modeling

A General Equilibrium Model with Tax and Quasilinear Utility Functions.

Description

This model is essentially a pure exchange economy. The model contains 4 types of commodities (i.e. corn, iron, taxed iron and tax payment receipts) and 4 agents (i.e. consumer 1, consumer 2, a firm and the government). Consumer 1 has corn and the utility function is x1 + beta1 * (alpha1 * x3 - 0.5 * x3^2) wherein x1 is corn and x3 is taxed iron. Consumer 2 has iron and the utility function is x1 + beta2 * (alpha2 * x2 - 0.5 * x2^2) wherein x1 is corn and x2 is iron. Consumer 1 (i.e. the iron demander) wants to buy iron from consumer 2 (i.e. the iron supplier) and the government will tax the transaction. The firm (i.e. a tax agency) inputs iron and tax payment receipts (similar to tax stamp) to output taxed iron, and due to government taxation requirements consumer 1 have to buy taxed iron from the firm and consumer 2 have to sell iron through the firm. Government has tax payment receipts and the utility function is x1.

Usage

gemTax_QuasilinearPreference_4_4(...)

Arguments

...	arguments to be passed to the function sdm2.

Examples

tax.rate <- 1

beta1 <- 0.05
alpha1 <- 3 / beta1 + 60

iron.endowment <- 100
beta2 <- 0.05
alpha2 <- iron.endowment - 60 + (3 / beta2)

ge <- sdm2(
  A = function(state) {
    a1 <- QL_demand(
      w = state$w[1],
      p = c(state$p[1], state$p[3]),
      alpha = alpha1, beta = beta1,
      type = "quadratic2"
    )
    a1 <- c(a1[1], 0, a1[2], 0)

    a2 <- QL_demand(
      w = state$w[2],
      p = state$p[1:2],
      alpha = alpha2, beta = beta2,
      type = "quadratic2"
    )
    a2 <- c(a2, 0, 0)

    a.firm <- c(0, 1, 0, tax.rate * state$p[2] / state$p[4])

    a.gov <- c(1, 0, 0, 0)

    cbind(a1, a2, a.firm, a.gov)
  },
  B = matrix(c(
    0, 0, 0, 0,
    0, 0, 0, 0,
    0, 0, 1, 0,
    0, 0, 0, 0
  ), 4, 4, TRUE),
  S0Exg = matrix(c(
    1000, NA, NA, NA,
    NA, iron.endowment, NA, NA,
    NA, NA, NA, NA,
    NA, NA, NA, 1
  ), 4, 4, TRUE),
  names.commodity = c("corn", "iron", "taxed.iron", "tax"),
  names.agent = c("consumer1", "consumer2", "firm", "gov"),
  numeraire = "corn",
  priceAdjustmentVelocity = 0.05
)

ge$p
ge$D
ge$S
addmargins(ge$DV)
addmargins(ge$SV)

ge.x <- ge$D[3, 1]
ge.pl <- ge$p[2]
ge.ph <- ge$p[3]
plot(function(x) (alpha1 - x) * beta1, 0, alpha1,
  xlim = c(0, 100), ylim = c(0, 6), xlab = "iron", ylab = "price"
)
curve((alpha2 - iron.endowment + x) * beta2, 0,
  alpha1,
  add = TRUE
)
grid()
points(ge.x, ge.ph, col = "red", pch = 20) # pch=8
points(ge.x, ge.pl, col = "red", pch = 20)

polygon(c(0, ge.x, ge.x, 0), c(ge.ph, ge.ph, ge.pl, ge.pl))
segments(0, 3, x1 = 60, y1 = 3, col = "red")
text(c(0, ge.x, ge.x, 0) + 3, c(
  ge.ph + 0.3, ge.ph + 0.3,
  ge.pl - 0.3, ge.pl - 0.3
), c("A", "B", "C", "D"))
text(c(3, ge.x + 3, 60), 3.3, c("E", "F", "G"))

u.consumer1 <- function(x) x[1] + beta1 * (alpha1 * x[2] - 0.5 * x[2]^2)
u.consumer2 <- function(x) x[1] + beta2 * (alpha2 * x[2] - 0.5 * x[2]^2)

u.consumer1(ge$D[c(1, 3), 1]) + u.consumer2(ge$D[c(1:2), 2]) + ge$z[4]
# The value above is 1430 when the tax rate is 0.

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