gemIntertemporal_AdValoremClaim {GE}

Some Intertemporal Models with Ad Valorem Claim

Description

Some intertemporal models with ad valorem claim. Ad valorem claims may be equities, bonds, ad valorem taxation rights (ad valorem tax receipt), fiat money etc, which can be treated in the same way in models.

Usage

gemIntertemporal_AdValoremClaim(...)

Arguments

...

arguments to be passed to the function sdm2.

Examples

#### a model with tax.
np <- 5 # the number of economic periods
gr.lab <- 0.03 # the growth rate of the labor supply
tax.rate <- 0.25

n <- 2 * np + 1 # the number of commodity kinds
m <- np + 1 # the number of agent kinds

names.commodity <- c(paste0("prod", 1:np), paste0("lab", 1:np), "tax receipt")
names.agent <- c(paste0("firm", 1:(np - 1)), "laborer", "government")

# the exogenous supply matrix.
S0Exg <- matrix(NA, n, m, dimnames = list(names.commodity, names.agent))
S0Exg[paste0("lab", 1:np), "laborer"] <- 100 * (1 + gr.lab)^(0:(np - 1)) # the labor supply
S0Exg["prod1", "laborer"] <- 10 # the product supply in the first period
S0Exg["tax receipt", "government"] <- np * 100 # the supply of tax receipt (i.e. ad valorem claim)

# the output coefficient matrix.
B <- matrix(0, n, m, dimnames = list(names.commodity, names.agent))
for (k in 1:(np - 1)) {
  B[paste0("prod", k + 1), paste0("firm", k)] <- 1
}

dstl.firm <- list()
for (k in 1:(np - 1)) {
  dstl.firm[[k]] <- node_new(
    "prod",
    type = "FIN", rate = c(1, tax.rate),
    "cc1", "tax receipt"
  )
  node_set(dstl.firm[[k]], "cc1",
           type = "CD",
           alpha = 1, beta = c(0.5, 0.5),
           paste0("prod", k), paste0("lab", k)
  )
}

dst.laborer <- node_new(
  "util",
  type = "FIN", rate = c(1, tax.rate),
  "cc1", "tax receipt"
)
node_set(dst.laborer, "cc1",
         type = "CES", es = 0.5,
         alpha = 1, beta = rep(1 / np, np),
         paste0("cc1.", 1:np)
)
for (k in 1:np) {
  node_set(dst.laborer, paste0("cc1.", k),
           type = "CD", alpha = 1, beta = c(0.5, 0.5),
           paste0("prod", k), paste0("lab", k)
  )
}

dst.government <- node_new(
  "util",
  type = "CD",
  alpha = 1, beta = rep(1 / np, np),
  paste0("cc1.", 1:np)
)
for (k in 1:np) {
  node_set(dst.government, paste0("cc1.", k),
           type = "CD", alpha = 1, beta = c(0.5, 0.5),
           paste0("prod", k), paste0("lab", k)
  )
}
node_plot(dst.government, TRUE)

ge <- sdm2(
  A = c(dstl.firm, dst.laborer, dst.government),
  B = B,
  S0Exg = S0Exg,
  names.commodity = names.commodity,
  names.agent = names.agent,
  numeraire = "prod1",
  # policy = makePolicyHeadTailAdjustment(gr = gr.lab, np = np)
)

ge$D
ge$z
ge$DV

#### a pure exchange model with money.
np <- 3 # the number of economic periods
gr.lab <- 0.03 # the growth rate of the labor supply
eis <- 0.8 # the elasticity of intertemporal substitution
Gamma.beta <- 0.8 # the subjective discount factor
interest.rate <- sserr(eis, Gamma.beta, gr.lab, prepaid = TRUE) # 0.2593

dst.laborer <- node_new(
  "util",
  type = "CES", es = eis,
  alpha = 1, beta = Gamma.beta^(0:(np - 1)),
  paste0("cc", 1:np)
)

for (k in 1:np) {
  node_set(dst.laborer, paste0("cc", k),
    type = "FIN",
    rate = c(1, interest.rate),
    paste0("lab", k), paste0("money", k)
  )
}

node_plot(dst.laborer, TRUE)

dst.moneyOwner <- Clone(dst.laborer)

ge <- sdm2(
  A = list(dst.laborer, dst.moneyOwner),
  B = matrix(0, 2 * np, 2),
  S0Exg = {
    tmp <- matrix(0, 2 * np, 2)
    tmp[1:np, 1] <- 100 * (1 + gr.lab)^(0:(np - 1))
    tmp[(np + 1):(2 * np), 2] <- 200
    tmp
  },
  names.commodity = c(paste0("lab", 1:np), paste0("money", 1:np)),
  names.agent = c("laborer", "moneyOwner"),
  numeraire = c(money1 = interest.rate)
)

ge$p
growth_rate(ge$p[1:3]) + 1
ge$z
addmargins(ge$D, 2)
addmargins(ge$S, 2)

## In the following program, the periods to which
## the money belongs are not distinguished.
dst.laborer <- node_new(
  "util",
  type = "FIN",
  rate = c(1, interest.rate),
  "cc1", "money"
)
node_set(dst.laborer, "cc1",
  type = "CES", es = eis,
  alpha = 1, beta = Gamma.beta^(0:(np - 1)),
  paste0("lab", 1:np)
)

dst.moneyOwner <- Clone(dst.laborer)

ge <- sdm2(
  A = list(dst.laborer, dst.moneyOwner),
  B = matrix(0, np + 1, 2),
  S0Exg = {
    tmp <- matrix(0, np + 1, 2)
    tmp[1:np, 1] <- 100 * (1 + gr.lab)^(0:(np - 1))
    tmp[np + 1, 2] <- 100
    tmp
  },
  names.commodity = c(paste0("lab", 1:np), "money"),
  names.agent = c("laborer", "moneyOwner"),
  numeraire = c(money = interest.rate)
)

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

#### a two-period model with production and money.
interest.rate1 <- 0.25
interest.rate2 <- 0.1

dst.firm <- node_new(
  "prod",
  type = "FIN",
  rate = c(1, interest.rate1),
  "cc1", "money1"
)
node_set(dst.firm, "cc1",
  type = "CES",
  es = 1, alpha = 2, beta = c(0.5, 0.5),
  "prod1", "lab1"
)

dst.laborer <- node_new(
  "util",
  type = "CES",
  es = 0.5, alpha = 1, beta = c(2 / 3, 1 / 3),
  "cc1", "cc2"
)
node_set(dst.laborer, "cc1",
  type = "FIN",
  rate = c(1, interest.rate1),
  "prod1", "money1"
)

node_set(dst.laborer, "cc2",
  type = "FIN",
  rate = c(1, interest.rate2),
  "prod2", "money2"
)

dst.moneyOwner <- Clone(dst.laborer)

ge <- sdm2(
  A = list(dst.firm, dst.laborer, dst.moneyOwner),
  B = matrix(c(
    0, 0, 0,
    0, 0, 0,
    0, 0, 0,
    1, 0, 0,
    0, 0, 0
  ), 5, 3, TRUE),
  S0Exg = matrix(c(
    NA, 200, NA,
    NA, 100, NA,
    NA, NA, 100,
    NA, NA, NA,
    NA, NA, 100
  ), 5, 3, TRUE),
  names.commodity = c("prod1", "lab1", "money1", "prod2", "money2"),
  names.agent = c("firm", "laborer", "moneyOwner"),
  numeraire = c(money1 = interest.rate1)
)

ge$p
ge$DV