gemOLG_PrivateFirm: Overlapping Generations Models with Private Firm

In GE: General Equilibrium Modeling

Overlapping Generations Models with Private Firm

Description

Some examples of overlapping generations models with private firm. A public (i.e. publicly held) firm exists permanently and operates independently. If a public firm ownership transfers between generations, this transfer will be done through the exchange of shares. In contrast, here a private firm is established by a consumer and only runs before she retires.

In the first example, there are some two-period-lived consumers and a private firm. Suppose age1 has a unit of labor and age2 has not. In each period age1 establishes a private firm and the firm gets some labor as investment from age1 and will sell it in the market to buy some inputs for production. In the next period, age2 (i.e. age1 in the previous period) gets the output of the firm. Age2 consumes product and labor (i.e. service). Hence age1 and the firm can sell labor to age2 and buy product from age2.

In the second example with three-period-lived consumers, there are two private firms (i.e. firm1 and firm2). In each period age1 establishes a new firm1 and age2 establishes a new firm2. Firm1 gets some labor as investment from age1 and firm2 gets some product and labor as investment from age2. The output of firm1 belongs to age2 in the next period and the output of firm2 belongs to age3 in the next period. In each period age2 (i.e. age1 in the previous period) takes away the output of firm1 and age3 (i.e. age2 in the previous period) takes away the output of firm2.

Usage

gemOLG_PrivateFirm(...)

Arguments

...	arguments to be passed to the function sdm2.

References

Acemoglu, D. (2009, ISBN: 9780691132921) Introduction to Modern Economic Growth. Princeton University Press.

See Also

gemOLGF_PureExchange

Examples

#### an example with a private firm and two-period-lived consumers
saving.rate <- 0.5
beta.consumer <-  c(1 / 2, 1 / 2) # c(9 / 10, 1 / 10)

dst.firm <- node_new(
  "prod",
  type = "CD", alpha = 5,
  beta = c(2 / 3, 1 / 3),
  "prod", "lab"
)

dst.age1 <- node_new(
  "util",
  type = "CD", alpha = 1,
  beta = beta.consumer,
  "prod", "lab"
)

dst.age2 <- Clone(dst.age1)

ge <- sdm2(
  A = list(
    dst.firm, dst.age1, dst.age2
  ),
  B = matrix(c(
    1, 0, 0,
    0, 0, 0
  ), 2, 3, TRUE),
  S0Exg = matrix(c(
    NA, NA, NA,
    NA, 1, NA
  ), 2, 3, TRUE),
  names.commodity = c("prod", "lab"),
  names.agent = c("firm", "age1", "age2"),
  numeraire = "lab",
  policy = function(time, state) {
    if (time > 1) {
      supply.prod <- state$S[1, 1]
      supply.lab <- state$S[2, 2]
      state$S <- 0 * state$S
      state$S[1, 3] <- supply.prod # age2 supplies prod.
      state$S[2, 1] <- saving.rate * supply.lab # The firm gets investment from age1.
      state$S[2, 2] <- (1 - saving.rate) * supply.lab
    }
    state
  }
)

ge$p
addmargins(ge$D, 2)
addmargins(ge$S, 2)
addmargins(ge$DV)
addmargins(ge$SV)

#### an example with two private firm and three-period-lived consumers
saving.rate.age1 <- 1 / 3
saving.rate.age2 <- 0.95

dst.firm1 <- dst.firm2 <- node_new(
  "prod",
  type = "CD", alpha = 5,
  beta = c(2 / 3, 1 / 3),
  "prod", "lab"
)

dst.age1 <- dst.age2 <- dst.age3 <- node_new(
  "util",
  type = "Leontief", a = 1,
  "prod"
)

ge <- sdm2(
  A = list(
    dst.firm1, dst.firm2, dst.age1, dst.age2, dst.age3
  ),
  B = matrix(c(
    1, 1, 0, 0, 0,
    0, 0, 0, 0, 0
  ), 2, 5, TRUE),
  S0Exg = matrix(c(
    NA, NA, NA, NA, NA,
    NA, NA, 1, 1, NA
  ), 2, 5, TRUE),
  names.commodity = c("prod", "lab"),
  names.agent = c("firm1", "firm2", "age1", "age2", "age3"),
  numeraire = "lab",
  policy = function(time, state) {
    if (time > 1) {
      state$S[1, 5] <- state$S[1, 2] # Age3 takes away the output of firm2.
      state$S[1, 2] <- 0

      # Age2 takes away the output of firm1.
      prod.age2 <- state$S[1, 1]
      state$S[1, 1] <- 0
      # Age2 establishes a new firm2.
      lab.age2 <- state$S[2, 4]
      state$S[2, 2] <- lab.age2 * saving.rate.age2 # Firm2 sells labor.
      state$S[1, 2] <- prod.age2 * saving.rate.age2 # Firm2 sells product.

      state$S[2, 4] <- lab.age2 * (1 - saving.rate.age2) # Age2 sells labor.
      state$S[1, 4] <- prod.age2 * (1 - saving.rate.age2) # Age2 sells product.

      # Age1 establishes a new firm1.
      state$S[2, 1] <- state$S[2, 3] * saving.rate.age1 # Firm1 sells labor.
      state$S[2, 3] <- state$S[2, 3] * (1 - saving.rate.age1) # Age1 sells labor.
    }
    state
  }
)

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

GE documentation built on May 29, 2024, 2:52 a.m.