gemIntertemporal_TimeCircle_Stochastic_2_2 {GE}

Some 2-by-2 Time Circle Models with Uncertainty

Description

Some time circle models with uncertainty. In these models, there is a consumer who will live for two periods and has a von Neumann-Morgenstern expected utility function. There is one natural state in the first period, and two natural states in the second period. In the economy, there are two types of commodities: product and labor. In the first period, the economy can borrow a certain amount of product from an external source, such as a bank, and repay it after the economic operation is complete. The amount of product to be repaid is zeta times the amount borrowed. zeta is an exogenous variable.

Usage

gemIntertemporal_TimeCircle_Stochastic_2_2(...)

Arguments

...

arguments to be passed to the function sdm2.

Examples

#### Assume that the consumer supplies labor only in the first period,
## and the firm produces only in the first period.
zeta <- 1.25 # the ratio of repayments to loans
dst.firm <- node_new(
  "prod2",
  type = "CD", alpha = 1,
  beta = c(0.5, 0.5),
  "prod1", "lab1"
)

dst.bank <- node_new(
  "prod1",
  type = "Leontief",
  a = c(1, 1) * zeta,
  "prod2.1", "prod2.2"
)

dst.consumer <- node_new(
  "util",
  type = "CD", alpha = 1,
  beta = c(0.5, 0.25, 0.25),
  "prod1", "prod2.1", "prod2.2"
)

ge <- sdm2(
  A = c(dst.firm, dst.bank, dst.consumer),
  B = matrix(c(
    0, 1, 0,
    2, 0, 0,
    1, 0, 0,
    0, 0, 0
  ), 4, 3, TRUE),
  S0Exg = matrix(c(
    NA, NA, NA,
    NA, NA, NA,
    NA, NA, NA,
    NA, NA, 100
  ), 4, 3, TRUE),
  names.commodity = c("prod1", "prod2.1", "prod2.2", "lab1"),
  names.agent = c("firm", "bank", "consumer"),
  numeraire = "lab1",
  policy = makePolicyMeanValue(30),
  ts = TRUE
)

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

#### Assume that the consumer supplies labor in both periods and
## firms produce in both periods.
zeta <- 1.25 # the ratio of repayments to loans
dst.firm1 <- node_new(
  "prod2",
  type = "CD", alpha = 2,
  beta = c(0.5, 0.5),
  "lab1", "prod1"
)

dst.firm2.1 <- node_new(
  "prod3.1",
  type = "CD", alpha = 2,
  beta = c(0.5, 0.5),
  "lab2.1", "prod2.1"
)

dst.firm2.2 <- node_new(
  "prod3.2",
  type = "CD", alpha = 1,
  beta = c(0.5, 0.5),
  "lab2.2", "prod2.2"
)

dst.bank <- node_new(
  "prod1",
  type = "Leontief",
  a = c(1, 1) * zeta,
  "prod3.1", "prod3.2"
)

dst.consumer <- node_new(
  "util",
  type = "CD", alpha = 1,
  beta = c(1 / 3, 1 / 3, 1 / 3),
  "prod1", "prod2.1", "prod2.2"
)

ge <- sdm2(
  A = c(
    dst.firm1, dst.firm2.1, dst.firm2.2,
    dst.bank, dst.consumer
  ),
  B = matrix(c(
    0, 0, 0, 1, 0,
    1, 0, 0, 0, 0,
    1, 0, 0, 0, 0,
    0, 1, 0, 0, 0,
    0, 0, 1, 0, 0,
    0, 0, 0, 0, 0,
    0, 0, 0, 0, 0,
    0, 0, 0, 0, 0
  ), 8, 5, TRUE),
  S0Exg = matrix(c(
    NA, NA, NA, NA, NA,
    NA, NA, NA, NA, NA,
    NA, NA, NA, NA, NA,
    NA, NA, NA, NA, NA,
    NA, NA, NA, NA, NA,
    NA, NA, NA, NA, 100,
    NA, NA, NA, NA, 100,
    NA, NA, NA, NA, 100
  ), 8, 5, TRUE),
  names.commodity = c(
    "prod1", "prod2.1", "prod2.2",
    "prod3.1", "prod3.2",
    "lab1", "lab2.1", "lab2.2"
  ),
  names.agent = c(
    "firm1", "firm2.1", "firm2.2",
    "bank", "consumer"
  ),
  numeraire = "lab1",
  policy = makePolicyMeanValue(30),
  ts = TRUE
)

ge$p
ge$z
ge$D
ge$S
ge$DV
ge$SV