# Some Examples of an Intertemporal Model with a Consumer and a Type of Bank Some examples of an intertemporal model with a consumer and a type of bank. These models can be used to solve some intertemporal savings problems. Below is an example. A np-period-lived consumer has some payoff (or cash, exhaustible resource etc.) in each period. In each period the consumer can use payoff for consumption or save payoff into bank. The interest rate is given. The consumer has a SCES intertemporal utility function and attempts to maximize intertemporal utility by saving. ```r gemIntertemporal_Bank_1_2(...) ``` ## Arguments - `...`: arguments to be passed to the function sdm2. ## Examples ```r #### an example with a 5-period-lived consumer np <- 5 # the number of economic periods interest.rate <- 0.1 n <- np # the number of commodity kinds m <- np # the number of agent kinds names.commodity <- paste0("payoff", 1:np) names.agent <- c(paste0("bank", 1:(np - 1)), "consumer") # the exogenous supply matrix. S0Exg <- matrix(NA, n, m, dimnames = list(names.commodity, names.agent)) S0Exg[paste0("payoff", 1:np), "consumer"] <- 100 / (np:1) # the output coefficient matrix. B <- matrix(0, n, m, dimnames = list(names.commodity, names.agent)) for (k in 1:(np - 1)) { B[paste0("payoff", k + 1), paste0("bank", k)] <- 1 } dstl.bank <- list() for (k in 1:(np - 1)) { dstl.bank[[k]] <- node_new("output", type = "Leontief", a = 1 / (1 + interest.rate), paste0("payoff", k) ) } dst.consumer <- node_new( "util", type = "SCES", es = 1, alpha = 1, beta = prop.table(1:np), paste0("payoff", 1:np) ) ge <- sdm2( A = c(dstl.bank, dst.consumer), B = B, S0Exg = S0Exg, names.commodity = names.commodity, names.agent = names.agent, numeraire = "payoff1", policy = makePolicyMeanValue(30), ts = TRUE ) ge$p ge$z ge$D ge$S ge$DV ge$SV growth_rate(ge$p) ## dst.consumer$es <- 0 dst.consumer$beta <- rep(1 / np, np) S0Exg[paste0("payoff", 1:np), "consumer"] <- 100 / (1:np) ge <- sdm2( A = c(dstl.bank, dst.consumer), B = B, S0Exg = S0Exg, names.commodity = names.commodity, names.agent = names.agent, numeraire = "payoff1", policy = makePolicyMeanValue(30), ts = TRUE ) ge$p ge$z ge$D ge$S ge$DV ge$SV ```

gemIntertemporal_Bank_1_2 function