R/gem_4_4.R

In GE: General Equilibrium Modeling

#' @export
#' @title Some Simple 4-by-4 General Equilibrium Models
#' @aliases gem_4_4
#' @description Some simple 4-by-4 general equilibrium models.
#' @param ... arguments to be passed to the function sdm2.
#' @examples
#' \donttest{
#' #### A general equilibrium model containing a capital good with service-life
#' # wear-and-tear. The new product can be used as a capital good with a service
#' # life of two periods, and the used old capital good is the old product.
#' ge <- sdm2(
#'   A = function(state) {
#'     a.firm1 <- CD_A(alpha = 2, Beta = c(0, 0.5, 0.5, 0), state$p)
#'     a.consumer <- c(1, 0, 0, 0)
#'     a.firm2 <- c(1, 0, 0, 0)
#'     a.firm3 <- c(0, 0, 0, 1)
#'     cbind(a.firm1, a.consumer, a.firm2, a.firm3)
#'   },
#'   B = matrix(c(
#'     1, 0, 0, 0,
#'     0, 0, 1, 1,
#'     0, 0, 0, 0,
#'     0, 0, 1, 0
#'   ), 4, 4, TRUE),
#'   S0Exg = matrix(c(
#'     NA, NA, NA, NA,
#'     NA, NA, NA, NA,
#'     NA, 100, NA, NA,
#'     NA, NA, NA, NA
#'   ), 4, 4, TRUE),
#'   names.commodity = c("prod.new", "cap", "lab", "prod.old"),
#'   names.agent = c("firm1", "consumer", "firm2", "firm3"),
#'   numeraire = "prod.new",
#'   priceAdjustmentVelocity = 0.05
#' )
#'
#' ge$p
#' ge$z
#' addmargins(ge$D, 2)
#' addmargins(ge$S, 2)
#'
#' #### the Shoven-Whalley model at
#' ## https://lexjansen.com/nesug/nesug03/st/st002.pdf
#' ge <- sdm2(
#'   A = function(state) {
#'     a.firm.corn <- CES_A(sigma = 1 - 1 / 2, alpha = 1.5, Beta = c(0, 0, 0.4, 0.6), state$p)
#'     a.firm.iron <- CES_A(sigma = 1 - 1 / 0.5, alpha = 2, Beta = c(0, 0, 0.3, 0.7), state$p)
#'     a.consumer1 <- SCES_A(alpha = 1, Beta = c(0.5, 0.5, 0, 0), es = 1.5, p = state$p)
#'     a.consumer2 <- SCES_A(alpha = 1, Beta = c(0.3, 0.7, 0, 0), es = 0.75, p = state$p)
#'
#'     cbind(a.firm.corn, a.firm.iron, a.consumer1, a.consumer2)
#'   },
#'   B = diag(c(1, 1, 0, 0), 4, 4),
#'   S0Exg = {
#'     tmp <- matrix(NA, 4, 4)
#'     tmp[3, 3] <- 25
#'     tmp[4, 4] <- 60
#'     tmp
#'   },
#'   names.commodity = c("corn", "iron", "cap", "lab"),
#'   names.agent = c("firm.corn", "firm.iron", "consumer1", "consumer2"),
#'   numeraire = "lab"
#' )
#'
#' ge$p
#' ge$z
#' ge$D
#' ge$S
#'
#' #### an n-by-n general equilibrium model with Cobb-Douglas functions.
#' f <- function(n, policy = NULL, z0 = rep(100 * n, n), numberOfPeriods = 30,
#'               Beta = matrix(1 / n, n, n), n.firm = n - 1) {
#'   ge <- sdm2(
#'     A = function(state) {
#'       CD_A(alpha = rep(n, n), Beta = Beta, p = state$p)
#'     },
#'     B = {
#'       tmp <- diag(n)
#'       tmp[, (n.firm + 1):n] <- 0
#'       tmp
#'     },
#'     S0Exg = {
#'       tmp <- matrix(NA, n, n)
#'       for (k in (n.firm + 1):n) tmp[k, k] <- 100 * n
#'       tmp
#'     },
#'     numeraire = n,
#'     policy = policy,
#'     z0 = z0,
#'     maxIteration = 1,
#'     numberOfPeriods = numberOfPeriods,
#'     names.agent = c(paste0("firm", 1:n.firm), paste0("consumer", 1:(n - n.firm))),
#'     ts = TRUE
#'   )
#'   print(ge$z)
#'   print(ge$p)
#'   invisible(ge)
#' }
#'
#' n <- 4
#' f(n, n.firm = n - 2)
#' ## a spot equilibrium path
#' ge <- f(n, policy = policyMarketClearingPrice, z0 = runif(n, 10 * n, 100 * n), n.firm = n - 2)
#' matplot(ge$ts.z, type = "b", pch = 20)
#' matplot(ge$ts.p, type = "b", pch = 20)
#' }

gem_4_4 <- function(...) sdm2(...)