GE (version 0.3.5)

gemIntertemporal_TimeCircle_Bank_1_2: Some Examples of a Time Circle Model with a Consumer and a Type of Bank

Description

Some examples of a time circle model with a consumer and a type of bank. These models can be used to solve some intertemporal savings problems.

In these example, an np-period-lived consumer gets some payoff (or cash, exhaustible resource etc.) in each period. In each period the consumer can use payoff for consumption, save payoff into bank or get a loan from the bank. The interest rate is given. The consumer has a CES intertemporal utility function and attempts to maximize intertemporal utility by saving and borrowing.

Usage

gemIntertemporal_TimeCircle_Bank_1_2(...)

Arguments

...

arguments to be passed to the function sdm2.

Examples

# \donttest{
#### an example with a 5-period-lived consumer (see Zhang, 2008, section 1.3)
np <- 5 # the number of periods

interest.rate <- 0.1
zeta <- (1+interest.rate)^np
S <- matrix(NA, np, np + 1)
S[1:np, np + 1] <- 100/(1:np)

B <- matrix(0, np, np + 1)
B[1:np, 1:np] <- diag(np)[, c(2:np, 1)]
B[1, np] <- 1 / zeta

dstl.bank <- list()
for (k in 1:np) {
  dstl.bank[[k]] <- node_new(
    "output",
    type = "Leontief",
    a = 1/(1+interest.rate),
    paste0("payoff", k)
  )
}

dst.consumer <- node_new(
  "util",
  type = "CES",
  es = 0.5, alpha = 1,
  beta = prop.table(1:np),
  paste0("payoff", 1:np)
)

ge <- sdm2(
  A = c(dstl.bank, dst.consumer),
  B = B,
  S0Exg = S,
  names.commodity = paste0("payoff", 1:np),
  names.agent = c(paste0("bank", 1:np), "consumer"),
  numeraire = "payoff1",
  ts = TRUE,
  policy = makePolicyMeanValue(30)
)

ge$p
ge$z
ge$D
ge$S
ge$DV
ge$SV
growth_rate(ge$p)

####
dst.consumer$es <- 0

ge <- sdm2(
  A = c(dstl.bank, dst.consumer),
  B = B,
  S0Exg = S,
  names.commodity = paste0("payoff", 1:np),
  names.agent = c(paste0("bank", 1:np), "consumer"),
  numeraire = "payoff1",
  ts = TRUE,
  policy = makePolicyMeanValue(30)
)

ge$p
ge$z
ge$D
ge$S
ge$DV
ge$SV
growth_rate(ge$p)
# }