gemOLG_PublicFirm: Some Examples of (Timeline) OLG Models with Production and...

In GE: General Equilibrium Modeling

Some Examples of (Timeline) OLG Models with Production and Public Firms

Description

Some examples of (timeline) OLG models with production and public firms. A public producer is akin to a consumer with an infinite lifespan. The public producer owns the products it manufactures. In each period, it exchanges the products it has produced for the inputs required for production. In the model, a public producer can be treated as multiple public firms that each only produces for a single period. Each public firm hands over its products to the public firm of the next period, which in turn uses these products for trading.

Usage

gemOLG_PublicFirm(...)

Arguments

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

Examples

ng <- 8 # the number of generations
alpha.firm <- 2 # the efficient parameter of firms
beta.prod.firm <- 0.5 # the product (i.e. capital) share parameter of firms
beta.consumer <- c(1 / 3, 1 / 3, 1 / 3) # the share parameter of consumers
gr.laborer <- 0 # the population growth rate
labor.first <- c(100, 100, 0) # the labor supply of the first generation
labor.last <- 100 * (1 + gr.laborer)^((ng - 1):(ng + 1)) # the labor supply of the last generation
y1 <- 350 # the initial product supply

policy.PublicFirm <- function(state) {
  for (k in 1:(ng + 1)) {
    state$S[k + 1, k + 1] <- state$S[k + 1, k]
    state$S[k + 1, k] <- 0
  }
  state
}

f <- function(policy = policy.PublicFirm) {
  names.commodity <- c(paste0("prod", 1:(ng + 2)), paste0("lab", 1:(ng + 2)))
  names.agent <- c(paste0("firm", 1:(ng + 2)), paste0("consumer", 1:ng))

  n <- length(names.commodity) # the number of commodity kinds
  m <- length(names.agent) # the number of agent kinds

  # the exogenous supply matrix.
  S0Exg <- matrix(NA, n, m, dimnames = list(names.commodity, names.agent))
  for (k in 1:(ng - 1)) {
    S0Exg[paste0("lab", k:(k + 2)), paste0("consumer", k)] <- labor.first * (1 + gr.laborer)^(k - 1)
  }
  S0Exg[paste0("lab", ng:(ng + 2)), paste0("consumer", ng)] <- labor.last
  S0Exg["prod1", "firm1"] <- y1

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

  dstl.consumer <- list()
  for (k in 1:ng) {
    dstl.consumer[[k]] <- node_new(
      "util",
      type = "CD", alpha = 1,
      beta = beta.consumer,
      paste0("prod", k:(k + 2))
    )
  }

  dstl.firm <- list()
  for (k in 1:(ng + 2)) {
    dstl.firm[[k]] <- node_new(
      "prod",
      type = "CD", alpha = alpha.firm,
      beta = c(beta.prod.firm, 1 - beta.prod.firm),
      paste0("prod", k), paste0("lab", k)
    )
  }

  ge <- sdm2(
    A = c(dstl.firm, dstl.consumer),
    B = B,
    S0Exg = S0Exg,
    names.commodity = names.commodity,
    names.agent = names.agent,
    numeraire = "lab1",
    priceAdjustmentVelocity = 0.05,
    policy = policy
  )

  cat("ge$p:\n")
  print(ge$p)
  cat("ge$z:\n")
  print(ge$z)
  invisible(ge)
}

ge <- f()

# the growth rates of prices
growth_rate(ge$p[paste0("prod", 1:ng)]) + 1
growth_rate(ge$p[paste0("lab", 1:ng)]) + 1

##
labor.first <- c(200 / 3, 200 / 3, 200 / 3) # the labor supply of the first generation
ge <- f()

##
tax.rate <- 0.1
policy.PublicFirm.Tax <- function(state) {
  for (k in 1:(ng + 1)) {
    state$S[k + 1, k + 1] <- state$S[k + 1, k] * (1 - tax.rate)
    state$S[k + 1, k + ng] <- state$S[k + 1, k] * tax.rate
    state$S[k + 1, k] <- 0
  }
  state
}

ge <- f(policy.PublicFirm.Tax)

##
beta.consumer <- c(1 / 2, 1 / 2, 0) # the share parameter of consumers
labor.first <- c(100, 10, 0) # the labor supply of the first generation
ge <- f()

GE documentation built on Nov. 8, 2023, 9:07 a.m.