# Some Examples of Intertemporal Models with One Consumer and Two Types of Firms Some examples of intertemporal models with one consumer and two types of firms. There are three types of commodities (i.e. corn, iron and labor). The consumer may consume corn and iron in each period, and may have a nested intertemporal utility function. ```r gemIntertemporal_3_3(...) ``` ## Arguments - `...`: arguments to be passed to the function sdm2. ## Examples ```r #### an example with a nested intertemporal utility function np <- 5 # the number of economic periods n <- 3 * np - 1 # the number of commodity kinds m <- 2 * (np - 1) + 1 # the number of agent kinds names.commodity <- c( paste0("corn", 1:np), paste0("iron", 1:np), paste0("lab", 1:(np - 1)) ) names.agent <- c( paste0("firm.corn", 1:(np - 1)), paste0("firm.iron", 1:(np - 1)), "consumer" ) ## the exogenous supply matrix. S0Exg <- matrix(NA, n, m, dimnames = list(names.commodity, names.agent)) S0Exg[paste0("lab", 1:(np - 1)), "consumer"] <- 100 S0Exg["corn1", "consumer"] <- 25 S0Exg["iron1", "consumer"] <- 100 # the output coefficient matrix. B <- matrix(0, n, m, dimnames = list(names.commodity, names.agent)) for (k in 1:(np - 1)) { B[paste0("corn", k + 1), paste0("firm.corn", k)] <- B[paste0("iron", k + 1), paste0("firm.iron", k)] <- 1 } dstl.firm.corn <- dstl.firm.iron <- list() for (k in 1:(np - 1)) { dstl.firm.corn[[k]] <- node_new( "prod", type = "CD", alpha = 1, beta = c(0.5, 0.5), paste0("iron", k), paste0("lab", k) ) dstl.firm.iron[[k]] <- node_new( "prod", type = "CD", alpha = 2, beta = c(0.5, 0.5), paste0("iron", k), paste0("lab", k) ) } dst.consumer <- node_new( "util", type = "CD", alpha = 1, beta = prop.table(rep(1, np)), paste0("cc", 1:np) ) for (k in 1:np) { node_set( dst.consumer, paste0("cc", k), type = "CD", alpha = 1, beta = c(0.5, 0.5), paste0("corn", k), paste0("iron", k) ) } ge <- sdm2( A = c(dstl.firm.corn, dstl.firm.iron, dst.consumer), B = B, S0Exg = S0Exg, names.commodity = names.commodity, names.agent = names.agent, numeraire = "lab1", ts = TRUE ) ge$p ge$z ge$D ge$S ge$DV ge$SV #### an example with a non-nested intertemporal utility function np <- 3 # the number of economic periods ## There are np types of corn, np-1 types of iron and np-1 types of labor. ## There are np-1 corn firms, np-2 iron firms and one consumer. n <- 3 * np - 2 m <- 2 * np - 2 names.commodity <- c( paste0("corn", 1:np), paste0("iron", 1:(np - 1)), paste0("lab", 1:(np - 1)) ) names.agent <- c( paste0("firm.corn", 1:(np - 1)), paste0("firm.iron", 1:(np - 2)), "consumer" ) ## the exogenous supply matrix. S0Exg <- matrix(NA, n, m, dimnames = list(names.commodity, names.agent)) S0Exg[paste0("lab", 1:(np - 1)), "consumer"] <- 100 S0Exg["corn1", "consumer"] <- 25 S0Exg["iron1", "consumer"] <- 100 # the output coefficient matrix. B <- matrix(0, n, m, dimnames = list(names.commodity, names.agent)) for (k in 1:(np - 1)) { B[paste0("corn", k + 1), paste0("firm.corn", k)] <- 1 } for (k in 1:(np - 2)) { B[paste0("iron", k + 1), paste0("firm.iron", k)] <- 1 } dstl.firm.corn <- dstl.firm.iron <- list() for (k in 1:(np - 1)) { dstl.firm.corn[[k]] <- node_new( "prod", type = "CD", alpha = 1, beta = c(0.5, 0.5), paste0("iron", k), paste0("lab", k) ) } for (k in seq_along(np:(2 * np - 3))) { dstl.firm.iron[[k]] <- node_new( "prod", type = "CD", alpha = 2, beta = c(0.5, 0.5), paste0("iron", k), paste0("lab", k) ) } dst.consumer <- node_new( "util", type = "CD", alpha = 1, beta = prop.table(rep(1, np)), paste0("corn", 1:np) ) ge <- sdm2( A = c(dstl.firm.corn, dstl.firm.iron, dst.consumer), B = B, S0Exg = S0Exg, names.commodity = names.commodity, names.agent = names.agent, numeraire = "lab1", ts = TRUE ) ge$p ge$z ge$D ge$S ge$DV ge$SV #### an example of Zeng (1995, page 227) ic1 <- 1 / 10 # input coefficient ic2 <- 1 / 7 dc1 <- 2 / 3 # depreciation coefficient dc2 <- 9 / 10 ge <- sdm2( A = { # corn, iron1, iron2, iron3, iron4 a1.1 <- c(0, ic1, 0, 0, 0) a1.2 <- c(0, ic2, 0, 0, 0) a2.1 <- c(0, 0, ic1, 0, 0) a2.2 <- c(0, 0, ic2, 0, 0) a3.1 <- c(0, 0, 0, ic1, 0) a3.2 <- c(0, 0, 0, ic2, 0) a4.1 <- c(0, 0, 0, 0, ic1) a4.2 <- c(0, 0, 0, 0, ic2) a.consumer <- c(1, 0, 0, 0, 0) cbind(a1.1, a1.2, a2.1, a2.2, a3.1, a3.2, a4.1, a4.2, a.consumer) }, B = { b1.1 <- c(1, 0, ic1 * dc1, 0, 0) b1.2 <- c(1, 0, ic2 * dc2, 0, 0) b2.1 <- c(1, 0, 0, ic1 * dc1, 0) b2.2 <- c(1, 0, 0, ic2 * dc2, 0) b3.1 <- c(1, 0, 0, 0, ic1 * dc1) b3.2 <- c(1, 0, 0, 0, ic2 * dc2) b4.1 <- c(1, 0, 0, 0, 0) b4.2 <- c(1, 0, 0, 0, 0) b.consumer <- c(0, 0, 0, 0, 0) cbind(b1.1, b1.2, b2.1, b2.2, b3.1, b3.2, b4.1, b4.2, b.consumer) }, S0Exg = { tmp <- matrix(NA, 5, 9) tmp[2, 9] <- 100 tmp }, names.commodity = c("corn", paste0("iron", 1:4)), names.agent = c(paste0("firm", 1:8), "consumer"), numeraire = "corn", policy = makePolicyMeanValue(30), priceAdjustmentVelocity = 0.05, maxIteration = 1, numberOfPeriods = 1000, ts = TRUE ) matplot(ge$ts.z, type = "l") ge$p ge$z ge$D ge$S ``` ## References Zen Xiangjin (1995, ISBN: 7030046560). Basics of Economic Cybernetics. Beijing: Science Press. (In Chinese)

gemIntertemporal_3_3 function