# Some Simple 4-by-4 General Equilibrium Models Some simple 4-by-4 general equilibrium models. ```r gem_4_4(...) ``` ## Arguments - `...`: arguments to be passed to the function sdm2. ## Examples ```r #### 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