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#' @export
#' @title Some Examples of Spot Market Clearing Paths Involving Land and Labor
#' @aliases gemLand_Labor
#' @description Some examples of spot market clearing paths (alias instantaneous equilibrium paths) involving land and labor.
#' The labor supply may increase from the fifth period.
#' @param ... arguments to be passed to the function sdm2.
#' @examples
#' \donttest{
#' #### a 3-by-3 economy
#' f <- function(GRLabor = 0,
#' es.land.labor = 1) {
#' dst.firm <- node_new("output",
#' type = "SCES",
#' es = es.land.labor, alpha = 1,
#' beta = c(0.5, 0.5),
#' "land", "lab"
#' )
#'
#' dst.landowner <- node_new(
#' "util",
#' type = "Leontief", a = 1,
#' "prod"
#' )
#'
#' dst.laborer <- Clone(dst.landowner)
#'
#' dstl <- list(dst.firm, dst.landowner, dst.laborer)
#'
#' ge <- sdm2(
#' A = dstl,
#' B = diag(c(1, 0, 0)),
#' S0Exg = matrix(c(
#' NA, NA, NA,
#' NA, 100, NA,
#' NA, NA, 100
#' ), 3, 3, TRUE),
#' names.commodity = c("prod", "land", "lab"),
#' names.agent = c("firm", "landowner", "laborer"),
#' maxIteration = 1,
#' numberOfPeriods = 30,
#' numeraire = "lab",
#' ts = TRUE,
#' policy = list(
#' function(time, state) {
#' if (time >= 5) {
#' state$S[3, 3] <- 100 * (1 + GRLabor)^(time - 4)
#' }
#' state
#' },
#' policyMarketClearingPrice
#' ),
#' z0 = c(200, 100, 100),
#' p0 = c(1, 1, 1)
#' )
#'
#' par(mfrow = c(1, 2))
#' matplot(growth_rate(ge$ts.p), type = "o", pch = 20)
#' matplot(growth_rate(ge$ts.z), type = "o", pch = 20)
#'
#' ge
#' }
#'
#' ge <- f()
#' ge$p
#' ge$z
#'
#'
#' f(GRLabor = 0.03)
#' f(GRLabor = -0.03)
#' f(GRLabor = 0.03, es.land.labor = 0.5)
#' f(GRLabor = 0.03, es.land.labor = 1.5)
#'
#' #### a 4-by-3 economy
#' GRLabor <- 0.03
#'
#' dst.agri <- node_new("agri",
#' type = "SCES", es = 0.5, alpha = 1,
#' beta = c(0.75, 0.25),
#' "land", "lab"
#' )
#'
#' dst.manu <- node_new("manu",
#' type = "SCES", es = 0.5, alpha = 1,
#' beta = c(0.25, 0.75),
#' "land", "lab"
#' )
#'
#' dst.consumer <- node_new("util",
#' type = "SCES", es = 0.5, alpha = 1,
#' beta = c(0.5, 0.5),
#' "agri", "manu"
#' )
#'
#' dstl <- list(dst.agri, dst.manu, dst.consumer)
#'
#' ge <- sdm2(
#' A = dstl,
#' B = matrix(c(
#' 1, 0, 0,
#' 0, 1, 0,
#' 0, 0, 0,
#' 0, 0, 0
#' ), 4, 3, TRUE),
#' S0Exg = {
#' S0Exg <- matrix(NA, 4, 3)
#' S0Exg[3:4, 3] <- 100
#' S0Exg
#' },
#' names.commodity = c("agri", "manu", "land", "lab"),
#' names.agent = c("agri", "manu", "consumer"),
#' numeraire = c("manu"),
#' ts = TRUE,
#' policy = list(
#' function(time, state) {
#' if (time >= 5) {
#' state$S[4, 3] <- 100 * (1 + GRLabor)^(time - 4)
#' }
#' state
#' },
#' policyMarketClearingPrice
#' ),
#' numberOfPeriods = 40,
#' maxIteration = 1,
#' z0 = c(100, 100, 200),
#' p0 = c(1, 1, 1, 1)
#' )
#'
#' matplot(ge$ts.z, type = "o", pch = 20)
#' matplot(growth_rate(ge$ts.z), type = "o", pch = 20)
#' matplot(growth_rate(ge$ts.p), type = "o", pch = 20)
#' }
gemLand_Labor <- function(...) sdm2(...)
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