GE (version 0.1.1)

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

Description

This is a general equilibrium model with tax (see chapter 4, Cardenete et al., 2012).

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
)

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).

Value

A general equilibrium, which is a list with the following elements:

• p - the price vector with labor as numeraire.

• D - the demand matrix.

• DV - the demand value matrix.

• SV - the supply value matrix.

• ... - some elements returned by the CGE::sdm function

Details

A general equilibrium model with 5 commodities (i.e. product 1, product 2, labor, capital goods, and tax) and 4 agents (i.e. 2 firms and 2 consumers). Both firms pay ad valorem output tax to consumers.

References

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

Examples

# NOT RUN {
dst.consumer1 <- node_set("utility", NA,
  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_set("output", NA,
  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_set("taxed.output", NA,
  type = "FIN",
  rate = c(1, output.tax.rate),
  dst.firm1, "tax"
)
node_plot(dst.taxed.firm1)

dst.taxed.firm2 <- node_set("taxed.output", NA,
  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_set("taxed.lab", NA,
  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_set("taxed.utility", NA,
  type = "FIN",
  rate = c(1, consumption.tax.rate),
  dst.consumer1,
  "tax"
)

dst.taxed.consumer2 <- node_set("taxed.utility", NA,
  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, dstl, 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(dstl[[1]], "taxed.lab")$rate[2]
    current.tax.rate <- last.tax.rate / adjustment.ratio
  } else {
    current.tax.rate <- 0.1
  }
  node_set(dstl[[1]], "taxed.lab", rate = c(1, current.tax.rate))
  node_set(dstl[[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]
# }
# NOT RUN {
# }