# Some Examples of Intertemporal (Timeline) Models with Production and Public Firms Some examples of intertemporal (timeline) 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 intertemporal models, 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. ```r gemIntertemporal_PublicFirm(...) ``` ## Arguments - `...`: arguments to be passed to the function sdm2. ## Examples ```r np <- 15 # the number of economic periods, firms. gr <- 0 # the growth rate of the labor supply eis <- 0.5 # the elasticity of intertemporal substitution Gamma.beta <- 0.9 # the subjective discount factor y1 <- 100 # the initial product supply n <- 2 * np # the number of commodity kinds m <- np + 1 # the number of agent kinds names.commodity <- c(paste0("prod", 1:np), paste0("lab", 1:np)) names.agent <- c(paste0("firm", 1:np), "consumer") # the exogenous supply matrix. S0Exg <- matrix(NA, n, m, dimnames = list(names.commodity, names.agent)) # the supply of labor. S0Exg[paste0("lab", 1:np), "consumer"] <- 100 * (1 + gr)^(0:(np - 1)) S0Exg["prod1", "firm1"] <- y1 # the output coefficient matrix. B <- matrix(0, n, m, dimnames = list(names.commodity, names.agent)) for (k in 1:(np - 1)) { B[paste0("prod", k + 1), paste0("firm", k)] <- 1 } dstl.firm <- list() for (k in 1:np) { dstl.firm[[k]] <- node_new( "prod", type = "CD", alpha = 2, beta = c(0.5, 0.5), paste0("lab", k), paste0("prod", k) ) } dst.consumer <- node_new( "util", type = "CES", es = eis, alpha = 1, beta = prop.table(Gamma.beta^(1:np)), paste0("prod", 1:np) ) policy.PublicFirm <- function(state) { for (k in 1:(np - 1)) { state$S[k + 1, k + 1] <- state$S[k + 1, k] state$S[k + 1, k] <- 0 } state } ge <- sdm2( A = c(dstl.firm, dst.consumer), B = B, S0Exg = S0Exg, names.commodity = names.commodity, names.agent = names.agent, numeraire = "prod1", policy=policy.PublicFirm ) ge$p ge$z[1:15] #### the sequential form of the above model. dst.firm <- node_new( "prod", type = "CD", alpha = 2, beta = c(0.5, 0.5), "prod", "lab" ) dst.consumer <- node_new( "util", type = "Leontief", a = 1, "prod" ) dstl <- list(dst.firm, dst.consumer) ge.seq <- sdm2( A = dstl, B = matrix(c( 1, 0, 0, 0 ), 2, 2, TRUE), S0Exg = matrix(c( NA, NA, NA, 100 ), 2, 2, TRUE), names.commodity = c("prod", "lab"), names.agent = c("firm", "consumer"), numeraire = "lab", z0 = c(100, 1), ts = TRUE, policy = policyMarketClearingPrice, numberOfPeriods = 20, maxIteration = 1 ) growth_rate(ge$p[paste0("prod", 1:np)]) + 1 growth_rate(ge$p[paste0("lab", 1:np)]) + 1 1 / (1 + sserr(eis, Gamma.beta, gr)) ge.seq$ts.z[, 1] ```

gemIntertemporal_PublicFirm function