R/gem_3_2.R

In GE: General Equilibrium Modeling

#' @export
#' @title Some Simple 3-by-2 General Equilibrium Models
#' @aliases gem_3_2
#' @description Some simple 3-by-2 general equilibrium models with a firm and a consumer.
#' @param ... arguments to be passed to the function sdm2.
#' @references http://www.econ.ucla.edu/riley/MAE/Course/SolvingForTheWE.pdf
#' @references He Zhangyong, Song Zheng (2010, ISBN: 9787040297270) Advanced Macroeconomics. Beijing: Higher Education Press.
#' @examples
#' \donttest{
#' ge.CD <- sdm2(
#'   A = function(state) {
#'     ## the vector of demand coefficients of the firm
#'     a1 <- CD_A(alpha = 2, Beta = c(0, 0.5, 0.5), state$p)
#'     ## the vector of demand coefficients of the consumer
#'     a2 <- c(1, 0, 0)
#'     cbind(a1, a2)
#'   },
#'   B = matrix(c(
#'     1, 0,
#'     0, 0,
#'     0, 0
#'   ), 3, 2, TRUE),
#'   S0Exg = matrix(c(
#'     NA, NA,
#'     NA, 100,
#'     NA, 100
#'   ), 3, 2, TRUE),
#'   names.commodity = c("prod", "cap", "lab"),
#'   names.agent = c("firm", "consumer"),
#'   numeraire = "prod"
#' )
#'
#' ge.CD$p
#' ge.CD$z
#' ge.CD$D
#' ge.CD$S
#'
#' #### Example 2 in the ucla reference
#' ## By introducing a new factor of production (called land here)
#' ## a firm with diminishing returns to scale can be converted into
#' ## a firm with constant returns to scale.
#' ge2.CD <- sdm2(
#'   A = function(state) {
#'     a.firm <- CD_A(alpha = 6, Beta = c(0, 0.5, 0.5), state$p)
#'     a.consumer <- CD_A(alpha = 1, Beta = c(0.2, 0.8, 0), state$p)
#'     cbind(a.firm, a.consumer)
#'   },
#'   B = matrix(c(
#'     1, 0,
#'     0, 0,
#'     0, 0
#'   ), 3, 2, TRUE),
#'   S0Exg = matrix(c(
#'     NA, NA,
#'     NA, 81,
#'     NA, 1
#'   ), 3, 2, TRUE),
#'   names.commodity = c("prod", "lab", "land"),
#'   names.agent = c("firm", "consumer"),
#'   numeraire = "prod"
#' )
#'
#' ge2.CD$p
#' ge2.CD$z
#' ge2.CD$D
#' ge2.CD$S
#'
#' ####
#' ge.SCES <- sdm2(
#'   A = function(state) {
#'     a1 <- SCES_A(es = 0.5, alpha = 1, Beta = c(0, 0.5, 0.5), p = state$p)
#'     a2 <- c(1, 0, 0)
#'     cbind(a1, a2)
#'   },
#'   B = matrix(c(
#'     1, 0,
#'     0, 0,
#'     0, 0
#'   ), 3, 2, TRUE),
#'   S0Exg = matrix(c(
#'     NA, NA,
#'     NA, 100,
#'     NA, 100
#'   ), 3, 2, TRUE),
#'   names.commodity = c("prod", "cap", "lab"),
#'   names.agent = c("firm", "consumer"),
#'   numeraire = "prod"
#' )
#'
#' ge.SCES$p
#' ge.SCES$z
#' ge.SCES$D
#' ge.SCES$S
#'
#' ####
#' ge2.SCES <- sdm2(
#'   A = function(state) {
#'     a1 <- SCES_A(es = 0.5, alpha = 1, Beta = c(0.2, 0.4, 0.4), p = state$p)
#'     a2 <- c(1, 0, 0)
#'     cbind(a1, a2)
#'   },
#'   B = matrix(c(
#'     1, 0,
#'     0, 0,
#'     0, 0
#'   ), 3, 2, TRUE),
#'   S0Exg = matrix(c(
#'     NA, NA,
#'     NA, 100,
#'     NA, 100
#'   ), 3, 2, TRUE),
#'   names.commodity = c("prod", "cap", "lab"),
#'   names.agent = c("firm", "consumer"),
#'   numeraire = "prod"
#' )
#'
#' ge2.SCES$p
#' ge2.SCES$z
#' ge2.SCES$D
#' ge2.SCES$S
#'
#' #### nested production function
#' dst.firm <- node_new(
#'   "prod",
#'   type = "Leontief",
#'   a = c(0.2, 0.8),
#'   "prod", "cc1"
#' )
#' node_set(dst.firm, "cc1",
#'          type = "SCES",
#'          es = 0.5, alpha = 1, beta = c(0.5, 0.5),
#'          "cap", "lab"
#' )
#'
#' dst.consumer <- node_new(
#'   "util",
#'   type = "Leontief", a = 1,
#'   "prod"
#' )
#'
#' ge3.SCES <- sdm2(
#'   A = list(dst.firm, dst.consumer),
#'   B = matrix(c(
#'     1, 0,
#'     0, 0,
#'     0, 0
#'   ), 3, 2, TRUE),
#'   S0Exg = matrix(c(
#'     NA, NA,
#'     NA, 100,
#'     NA, 100
#'   ), 3, 2, TRUE),
#'   names.commodity = c("prod", "cap", "lab"),
#'   names.agent = c("firm", "consumer"),
#'   numeraire = "prod"
#' )
#'
#' ge3.SCES$p
#' ge3.SCES$z
#' ge3.SCES$D
#' ge3.SCES$S
#'
#' #### a model with a quasilinear utility function (see He and Song, 2010, page 19).
#' alpha.firm <- 2
#' beta.cap.firm <- 0.6
#' beta.lab.firm <- 1 - beta.cap.firm
#' theta.consumer <- 0.8
#' lab.supply <- 2
#' cap.supply <- 1
#'
#' ge <- sdm2(
#'   A = function(state) {
#'     a1 <- CD_A(alpha.firm, rbind(0, beta.lab.firm, beta.cap.firm), state$p)
#'
#'     demand.lab.prod <- QL_demand(
#'       w = state$w[2], p = state$p[2:1], # the prices of lab and prod
#'       alpha = 1, beta = theta.consumer, type = "CRRA"
#'     )
#'     a2 <- c(demand.lab.prod[2:1], 0)
#'     cbind(a1, a2)
#'   },
#'   B = matrix(c(
#'     1, 0,
#'     0, 0,
#'     0, 0
#'   ), 3, 2, TRUE),
#'   S0Exg = matrix(c(
#'     NA, NA,
#'     NA, lab.supply,
#'     NA, cap.supply
#'   ), 3, 2, TRUE),
#'   names.commodity = c("prod", "lab", "cap"),
#'   names.agent = c("firm", "consumer"),
#'   numeraire = "prod"
#' )
#'
#' ge$p
#' ge$z
#' ge$D
#' ge$S
#'
#' # the equilibrium leisure
#' lab.supply - (beta.lab.firm * (alpha.firm * cap.supply^beta.cap.firm)^(1 - theta.consumer))^
#'   (1 / (beta.cap.firm + beta.lab.firm * theta.consumer))
#'
#' # the equilibrium price of labor
#' w <- ((1 - beta.cap.firm)^(1 - beta.cap.firm) * (alpha.firm * cap.supply^beta.cap.firm))^
#'   (theta.consumer / (beta.cap.firm + (1 - beta.cap.firm) * theta.consumer))
#'
#' # the equilibrium price of capital goods
#' beta.cap.firm * w^(1 / theta.consumer) / cap.supply
#' }

gem_3_2 <- function(...) sdm2(...)