gemIntertemporal_TimeCircle_Bank_1_2 {GE}

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

#### an example with a 5-period-lived consumer (see Zhang, 2008, section 1.3)
np <- 5 # the number of economic periods
interest.rate <- 0.1
zeta <- (1 + interest.rate)^np # the ratio of repayments to loans

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

names.commodity <- paste0("payoff", 1:np)
names.agent <- c(paste0("bank", 1:np), "consumer")

# the exogenous supply matrix.
S0Exg <- matrix(NA, n, m, dimnames = list(names.commodity, names.agent))
S0Exg[paste0("payoff", 1:np), "consumer"] <- 100 / (1:np)

# the output coefficient matrix.
B <- matrix(0, n, m, dimnames = list(names.commodity, names.agent))
for (k in 1:(np - 1)) {
  B[paste0("payoff", k + 1), paste0("bank", k)] <- 1
}
B["payoff1", paste0("bank", 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 = S0Exg,
  names.commodity = names.commodity,
  names.agent = names.agent,
  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 = S0Exg,
  names.commodity = names.commodity,
  names.agent = names.agent,
  numeraire = "payoff1",
  ts = TRUE,
  policy = makePolicyMeanValue(30)
)

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