gemTax_5_4: A General Equilibrium Model with Tax (see Cardenete et al., 2012).

Description

A general equilibrium model with tax (see chapter 4, Cardenete et al., 2012), wherein there are 5 commodities (i.e. product 1, product 2, labor, capital goods, and tax receipt) and 4 agents (i.e. 2 firms and 2 consumers).

Usage

gemTax_5_4(
  dstl,
  names.commodity = c("prod1", "prod2", "lab", "cap", "tax"),
  names.agent = c("taxed.firm1", "taxed.firm2", "consumer1", "consumer2"),
  delta = 1,
  supply.lab.consumer1 = 30,
  supply.cap.consumer1 = 20,
  supply.lab.consumer2 = 20,
  supply.cap.consumer2 = 5,
  policy.tax = NULL
)

Value

A general equilibrium (see sdm2), wherein labor is the numeraire.

Arguments

dstl: the demand structure tree list.
names.commodity: names of commodities.
names.agent: names of agents.
delta: the proportion of tax revenue allocated to consumer 1. 1-delta is the proportion of tax revenue allocated to consumer 2.
supply.lab.consumer1: the labor supply of consumer 1.
supply.cap.consumer1: the capital supply of consumer 1.
supply.lab.consumer2: the labor supply of consumer 2.
supply.cap.consumer2: the capital supply of consumer 2.
policy.tax: a tax policy function (see sdm2).

References

Manuel Alejandro Cardenete, Ana-Isabel Guerra, Ferran Sancho (2012, ISBN: 9783642247453) Applied General Equilibrium: An Introduction. Springer-Verlag Berlin Heidelberg.

Examples

Run this code

# \donttest{
dst.consumer1 <- node_new("utility",
  type = "CD",
  alpha = 1,
  beta = c(0.3, 0.7),
  "prod1", "prod2"
)

dst.consumer2 <- Clone(dst.consumer1)
dst.consumer2$beta <- c(0.6, 0.4)

dst.firm1 <- node_new("output",
  type = "Leontief",
  a = c(0.5, 0.2, 0.3),
  "VA", "prod1", "prod2"
)
node_set(dst.firm1, "VA",
  type = "CD",
  alpha = 0.8^-0.8 * 0.2^-0.2,
  beta = c(0.8, 0.2),
  "lab", "cap"
)

dst.firm2 <- Clone(dst.firm1)
node_set(dst.firm2, "output",
  a = c(0.25, 0.5, 0.25)
)
node_set(dst.firm2, "VA",
  alpha = 0.4^-0.4 * 0.6^-0.6,
  beta = c(0.4, 0.6)
)

## no taxation
dstl <- list(dst.firm1, dst.firm2, dst.consumer1, dst.consumer2)
ge <- gemTax_5_4(dstl, delta = 1)

## ad valorem output tax (see Table 4.1)
output.tax.rate <- 0.1
dst.taxed.firm1 <- node_new("taxed.output",
  type = "FIN", rate = c(1, output.tax.rate),
  dst.firm1, "tax"
)
node_plot(dst.taxed.firm1)

dst.taxed.firm2 <- node_new("taxed.output",
  type = "FIN", rate = c(1, output.tax.rate),
  dst.firm2, "tax"
)
node_plot(dst.taxed.firm2)

dstl <- list(dst.taxed.firm1, dst.taxed.firm2, dst.consumer1, dst.consumer2)

ge.output.tax1 <- gemTax_5_4(dstl, delta = 1)
ge.output.tax2 <- gemTax_5_4(dstl, delta = 0.5)
ge.output.tax3 <- gemTax_5_4(dstl, delta = 0)

## labor tax (see Table 4.3)
lab.tax.rate <- 0.1

dst.taxed.lab <- node_new("taxed.lab",
  type = "FIN",
  rate = c(1, lab.tax.rate),
  "lab",
  "tax"
)

dst.labor.taxed.firm1 <- Clone(dst.firm1)
node_prune(dst.labor.taxed.firm1, "lab", "cap")
node_set(
  dst.labor.taxed.firm1, "VA",
  dst.taxed.lab,
  "cap"
)

dst.labor.taxed.firm2 <- Clone(dst.labor.taxed.firm1)
node_set(dst.labor.taxed.firm2, "output",
  a = c(0.25, 0.5, 0.25)
)
node_set(dst.labor.taxed.firm2, "VA",
  alpha = 0.4^-0.4 * 0.6^-0.6,
  beta = c(0.4, 0.6)
)

dstl.labor.tax <- list(dst.labor.taxed.firm1, dst.labor.taxed.firm2, dst.consumer1, dst.consumer2)

ge.lab.tax <- gemTax_5_4(dstl.labor.tax, delta = 0.5)

ge.lab.tax$p
ge.lab.tax$z / ge$z - 1

## income tax (see Table 4.3)
income.tax.rate <- 0.2
consumption.tax.rate <- income.tax.rate / (1 - income.tax.rate)
dst.taxed.consumer1 <- node_new("taxed.utility",
  type = "FIN",
  rate = c(1, consumption.tax.rate),
  dst.consumer1,
  "tax"
)

dst.taxed.consumer2 <- node_new("taxed.utility",
  type = "FIN",
  rate = c(1, consumption.tax.rate),
  dst.consumer2,
  "tax"
)

dstl <- list(dst.firm1, dst.firm2, dst.taxed.consumer1, dst.taxed.consumer2)

ge.income.tax <- gemTax_5_4(dstl, delta = 0.5)
ge.income.tax$z / ge$z - 1

## labor tax (see Table 4.3)
lab.tax.rate <- 0.3742
node_set(dst.labor.taxed.firm1, "taxed.lab",
  rate = c(1, lab.tax.rate)
)
node_set(dst.labor.taxed.firm2, "taxed.lab",
  rate = c(1, lab.tax.rate)
)

ge.lab.tax <- gemTax_5_4(list(
  dst.labor.taxed.firm1,
  dst.labor.taxed.firm2,
  dst.consumer1,
  dst.consumer2
), delta = 0.5)
ge.lab.tax$z / ge$z - 1

## variable labor tax rate
policy.var.tax.rate <- function(time, A, state) {
  current.tax.rate <- NA
  if (time >= 200) {
    tax.amount <- (state$p / state$p[3])[5]
    adjustment.ratio <- ratio_adjust(tax.amount / 18.7132504, coef = 0.1)
    last.tax.rate <- node_set(A[[1]], "taxed.lab")$rate[2]
    current.tax.rate <- last.tax.rate / adjustment.ratio
  } else {
    current.tax.rate <- 0.1
  }
  node_set(A[[1]], "taxed.lab", rate = c(1, current.tax.rate))
  node_set(A[[2]], "taxed.lab", rate = c(1, current.tax.rate))

  state$current.policy.data <- c(time, current.tax.rate)
  state
}

ge.var.lab.tax <- gemTax_5_4(dstl.labor.tax, policy = policy.var.tax.rate)
matplot(ge.var.lab.tax$ts.z, type = "l")
matplot(ge.var.lab.tax$ts.p / ge.var.lab.tax$p[3], type = "l")
plot(ge.var.lab.tax$policy.data[, 1], ge.var.lab.tax$policy.data[, 2],
  ylab = "labor tax rate"
)
ge.var.lab.tax$p / ge.var.lab.tax$p[3]
# }