R/gemIntertemporal_4_4.R

In GE: General Equilibrium Modeling

#' @export
#' @title An Intertemporal Model with Land, Two Consumers and Two Types of Firms
#' @aliases gemIntertemporal_4_4
#' @description An (intertemporal) timeline model with two consumers (i.e. a laborer and a landowner) and two types of firms
#' (i.e. wheat producers and iron producers).
#' There are four commodities in the model, namely wheat, iron, labor and land.
#' @param ... arguments to be passed to the function sdm2.
#' @examples
#' \donttest{
#' np <- 15 # the number of economic periods
#'
#' alpha.firm.wheat <- rep(5, np - 1)
#'
#' alpha.firm.iron <- rep(5, np - 1)
#'
#' rho.beta <- 0.97 # 1, 1.03 # the subjective discount factor of consumers
#'
#' y1.wheat <- 100 # 126, 129.96
#' y1.iron <- 30 # 40.59, 43.47
#'
#' gr <- 0 # the growth rate in the steady state equilibrium
#' eis <- 0.5 # the elasticity of intertemporal substitution  of consumers
#'
#' last.beta.laborer <- 0
#' last.beta.landowner <- 0
#'
#' n <- 4 * np - 2 # the number of commodity kinds
#' m <- 2 * np # the number of agent kinds
#'
#' names.commodity <- c(
#'   paste0("wheat", 1:np),
#'   paste0("iron", 1:np),
#'   paste0("lab", 1:(np - 1)),
#'   paste0("land", 1:(np - 1))
#' )
#'
#' names.agent <- c(
#'   paste0("firm.wheat", 1:(np - 1)), paste0("firm.iron", 1:(np - 1)),
#'   "laborer", "landowner"
#' )
#'
#' # the exogenous supply matrix.
#' S0Exg <- matrix(NA, n, m, dimnames = list(names.commodity, names.agent))
#' S0Exg["wheat1", "laborer"] <- y1.wheat
#' S0Exg["iron1", "landowner"] <- y1.iron
#' S0Exg[paste0("lab", 1:(np - 1)), "laborer"] <- 100 * (1 + gr)^(0:(np - 2)) # the supply of labor
#' S0Exg[paste0("land", 1:(np - 1)), "landowner"] <- 100 * (1 + gr)^(0:(np - 2)) # the supply of land
#'
#' # the output coefficient matrix.
#' B <- matrix(0, n, m, dimnames = list(names.commodity, names.agent))
#' for (k in 1:(np - 1)) {
#'   B[paste0("wheat", k + 1), paste0("firm.wheat", k)] <- 1
#'   B[paste0("iron", k + 1), paste0("firm.iron", k)] <- 1
#' }
#'
#' dstl.firm.wheat <- dstl.firm.iron <- list()
#' for (k in 1:(np - 1)) {
#'   dstl.firm.wheat[[k]] <- node_new(
#'     "prod",
#'     type = "CES", es = 0.8,
#'     alpha = alpha.firm.wheat[k], beta = c(0.2, 0.4, 0.4),
#'     paste0("iron", k), paste0("lab", k), paste0("land", k)
#'   )
#'
#'   dstl.firm.iron[[k]] <- node_new(
#'     "prod",
#'     type = "CES", es = 0.8,
#'     alpha = alpha.firm.iron[k], beta = c(0.4, 0.4, 0.2),
#'     paste0("iron", k), paste0("lab", k), paste0("land", k)
#'   )
#' }
#'
#' tmp.beta <- rho.beta^(1:(np - 1))
#' tmp.beta <- tmp.beta / tmp.beta[np - 1]
#' tmp.beta <- c(tmp.beta, last.beta.laborer)
#' dst.laborer <- node_new(
#'   "util",
#'   type = "CES", es = eis,
#'   alpha = 1, beta = prop.table(tmp.beta),
#'   paste0("cc", 1:(np - 1)), paste0("wheat", np)
#' )
#' for (k in 1:(np - 1)) {
#'   node_set(dst.laborer, paste0("cc", k),
#'     type = "CES", es = 1,
#'     alpha = 1, beta = c(0.4, 0.4, 0.2),
#'     paste0("wheat", k), paste0("lab", k), paste0("land", k)
#'   )
#' }
#'
#' tmp.beta <- rho.beta^(1:(np - 1))
#' tmp.beta <- tmp.beta / tmp.beta[np - 1]
#' tmp.beta <- c(tmp.beta, last.beta.landowner)
#' dst.landowner <- node_new(
#'   "util",
#'   type = "CES", es = eis,
#'   alpha = 1, beta = prop.table(tmp.beta),
#'   paste0("cc", 1:(np - 1)), paste0("iron", np)
#' )
#' for (k in 1:(np - 1)) {
#'   node_set(dst.landowner, paste0("cc", k),
#'     type = "CES", es = 1,
#'     alpha = 1, beta = c(0.2, 0.4, 0.4),
#'     paste0("wheat", k), paste0("lab", k), paste0("land", k)
#'   )
#' }
#'
#' f <- function(policy = NULL) {
#'   ge <- sdm2(
#'     A = c(dstl.firm.wheat, dstl.firm.iron, Clone(dst.laborer), Clone(dst.landowner)),
#'     B = B,
#'     S0Exg = S0Exg,
#'     names.commodity = names.commodity,
#'     names.agent = names.agent,
#'     numeraire = "lab1",
#'     policy = policy,
#'     ts = TRUE,
#'     maxIteration = 1,
#'     numberOfPeriods = 1000,
#'     priceAdjustmentVelocity = 0.05
#'   )
#'
#'   plot(ge$z[1:(np - 1)],
#'     type = "o", pch = 20, ylab = "production level",
#'     xlab = "time", ylim = range(ge$z[1:(2 * np - 2)])
#'   )
#'   lines(ge$z[np:(2 * np - 2)], type = "o", pch = 21)
#'   legend("bottom", c("wheat", "iron"), pch = 20:21)
#'
#'   invisible(ge)
#' }
#'
#' f()
#'
#' ## Compute the steady state based on head and tail adjustments.
#' policyHeadAdjustment <- function(time, state) {
#'   if (time > 100) {
#'     state$S[1, m - 1] <- state$last.z[round(np / 2)] / (1 + gr)^(round(np / 2))
#'     state$S[np + 1, m] <- state$last.z[np - 1 + round(np / 2)] / (1 + gr)^(round(np / 2))
#'   }
#'   state
#' }
#'
#' policyTailAdjustment <- function(A, state) {
#'   # wheat
#'   ratio.output.tail <- state$last.z[np - 1] / (state$last.z[np - 2] * (1 + gr))
#'   tmp.node <- A[[m - 1]]
#'   tmp.n <- length(tmp.node$beta)
#'   tail.beta <- tmp.node$beta[tmp.n]
#'   if (tail.beta == 0) tail.beta <- 1 / tmp.n
#'   tail.beta <- tail.beta / ratio.output.tail
#'   tmp.node$beta <- prop.table(c(tmp.node$beta[1:(tmp.n - 1)], tail.beta))
#'
#'   # iron
#'   ratio.output.tail <- state$last.z[2 * np - 2] / (state$last.z[2 * np - 3] * (1 + gr))
#'   tmp.node <- A[[m]]
#'   tmp.n <- length(tmp.node$beta)
#'   tail.beta <- tmp.node$beta[tmp.n]
#'   if (tail.beta == 0) tail.beta <- 1 / tmp.n
#'   tail.beta <- tail.beta / ratio.output.tail
#'   tmp.node$beta <- prop.table(c(tmp.node$beta[1:(tmp.n - 1)], tail.beta))
#' }
#'
#' f(list(policyHeadAdjustment, policyTailAdjustment))
#' # f(policyHeadAdjustment)
#' # f(policyTailAdjustment)
#'
#' ### a structural transformation path
#' # tax.rate <- 0.1 # the tax rate imposed on income from land and labor income.
#' # tax.time <- 1
#' #
#' # # the exogenous supply matrix.
#' # S0Exg <- matrix(NA, n, m, dimnames = list(names.commodity, names.agent))
#' # S0Exg["wheat1", "laborer"] <- y1.wheat
#' # S0Exg["iron1", "landowner"] <- y1.iron
#' # S0Exg[paste0("lab", 1:(np - 1)), "laborer"] <- 100 * (1 + gr)^(0:(np - 2)) # the supply of labor
#' # S0Exg[paste0("land", 1:(np - 1)), "landowner"] <- 100 * (1 + gr)^(0:(np - 2)) # the supply of land
#' #
#' # S0Exg[paste0("lab", tax.time), paste0("firm.iron", tax.time)] <-
#' #   S0Exg[paste0("lab", tax.time), "laborer"] * tax.rate
#' # S0Exg[paste0("land", tax.time), paste0("firm.iron", tax.time)] <-
#' #   S0Exg[paste0("land", tax.time), "landowner"] * tax.rate
#' #
#' # S0Exg[paste0("lab", tax.time), "laborer"] <-
#' #   S0Exg[paste0("lab", tax.time), "laborer"] * (1 - tax.rate)
#' # S0Exg[paste0("land", tax.time), "landowner"] <-
#' #   S0Exg[paste0("land", tax.time), "landowner"] * (1 - tax.rate)
#' #
#' # # Suppose the tax rate is high enough so that the iron
#' # # producer's efficiency coefficient immediately rises to 10.
#' # for (k in 1:(np - 1)) {
#' #   dstl.firm.iron[[k]]$alpha <- ifelse(k <= tax.time, 5, 10)
#' # }
#' #
#' # f(policy=policyTailAdjustment)
#' # f()
#' }

gemIntertemporal_4_4 <- function(...) sdm2(...)