# A General Equilibrium Model based on a 5×4 Input-Output Table (see Zhang Xin, 2017, Table 8.6.1) This is a general equilibrium model based on a 5×4 input-output table (see Zhang Xin, 2017, Table 8.6.1). ```r gemInputOutputTable_5_4( dstl, supply.labor = 850, supply.capital = 770, names.commodity = c("agri", "manu", "serv", "lab", "cap"), names.agent = c("agri", "manu", "serv", "hh") ) ``` ## Arguments - `dstl`: a demand structure tree list. - `supply.labor`: the supply of labor. - `supply.capital`: the supply of capital. - `names.commodity`: names of commodities. - `names.agent`: names of agents. ## Returns A general equilibrium which is a list with the following elements: * D - the demand matrix, also called the input table. Wherein the benchmark prices are used. * DV - the demand value matrix, also called the value input table. Wherein the current price is used. * SV - the supply value matrix, also called the value output table. Wherein the current price is used. * ... - some elements returned by the CGE::sdm function ## Details Given a 5×4 input-output table (e.g., see Zhang Xin, 2017, Table 8.6.1), this model calculates the corresponding general equilibrium. This input-output table contains 3 production sectors and one household. The household consumes products and supplies labor and capital. ## Examples ```r es.agri <- 0.2 # the elasticity of substitution es.manu <- 0.3 es.serv <- 0.1 es.VA.agri <- 0.25 es.VA.manu <- 0.5 es.VA.serv <- 0.8 d.agri <- c(260, 345, 400, 200, 160) d.manu <- c(320, 390, 365, 250, 400) d.serv <- c(150, 390, 320, 400, 210) d.hh <- c(635, 600, 385, 0, 0) # d.hh <- c(635, 600, 100, 0, 0) IT <- cbind(d.agri, d.manu, d.serv, d.hh) OT <- matrix(c( 1365, 0, 0, 0, 0, 1725, 0, 0, 0, 0, 1470, 0, 0, 0, 0, 850, 0, 0, 0, 770 ), 5, 4, TRUE) dimnames(IT) <- dimnames(OT) <- list( c("agri", "manu", "serv", "lab", "cap"), c("agri", "manu", "serv", "hh") ) addmargins(IT) addmargins(OT) dst.agri <- node_new("sector.agri", type = "SCES", es = es.agri, alpha = 1, beta = prop.table( c(sum(d.agri[1:3]), sum(d.agri[4:5])) ), "cc1.agri", "cc2.agri" ) node_set(dst.agri, "cc1.agri", type = "Leontief", a = prop.table(d.agri[1:3]), "agri", "manu", "serv" ) node_set(dst.agri, "cc2.agri", type = "SCES", es = es.VA.agri, alpha = 1, beta = prop.table(d.agri[4:5]), "lab", "cap" ) dst.manu <- node_new("sector.manu", type = "SCES", es = es.manu, alpha = 1, beta = prop.table( c(sum(d.manu[1:3]), sum(d.manu[4:5])) ), "cc1.manu", "cc2.manu" ) node_set(dst.manu, "cc1.manu", type = "Leontief", a = prop.table(d.manu[1:3]), "agri", "manu", "serv" ) node_set(dst.manu, "cc2.manu", type = "SCES", es = es.VA.manu, alpha = 1, beta = prop.table(d.manu[4:5]), "lab", "cap" ) dst.serv <- node_new("sector.serv", type = "SCES", es = es.serv, alpha = 1, beta = prop.table( c(sum(d.serv[1:3]), sum(d.serv[4:5])) ), "cc1.serv", "cc2.serv" ) node_set(dst.serv, "cc1.serv", type = "Leontief", a = prop.table(d.serv[1:3]), "agri", "manu", "serv" ) node_set(dst.serv, "cc2.serv", type = "SCES", es = es.VA.serv, alpha = 1, beta = prop.table(d.serv[4:5]), "lab", "cap" ) ## dst.hh <- node_new("sector.hh", type = "SCES", es = 0.5, alpha = 1, beta = prop.table(d.hh[1:3]), "agri", "manu", "serv" ) dstl <- list(dst.agri, dst.manu, dst.serv, dst.hh) ge <- gemInputOutputTable_5_4(dstl) #### labor supply increase geLSI <- gemInputOutputTable_5_4(dstl, supply.labor = 850 * 1.08) geLSI$p geLSI$z / ge$z ## capital supply change ge.CSC <- sdm2( A = dstl, B = matrix(c( 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1 ), 5, 4, TRUE), S0Exg = { tmp <- matrix(NA, 5, 4) tmp[4, 4] <- 850 tmp[5, 4] <- 770 tmp }, names.commodity = c("agri", "manu", "serv", "lab", "cap"), names.agent = c("agri", "manu", "serv", "hh"), numeraire = "lab", ts = TRUE, numberOfPeriods = 100, maxIteration = 1, z0 = c(1365, 1725, 1470, 1620), p0 = rep(1, 5), policy = function(time, state) { if (time >= 5) { state$S[5, 4] <- 880 } state } ) matplot(ge.CSC$ts.p, type = "l") matplot(ge.CSC$ts.z, type = "l") ## economic fluctuation: a sticky-price path de <- sdm2( A = dstl, B = matrix(c( 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1 ), 5, 4, TRUE), S0Exg = { tmp <- matrix(NA, 5, 4) tmp[4, 4] <- 850 tmp[5, 4] <- 770 tmp }, names.commodity = c("agri", "manu", "serv", "lab", "cap"), names.agent = c("agri", "manu", "serv", "hh"), numeraire = "lab", ts = TRUE, numberOfPeriods = 50, maxIteration = 1, z0 = c(1365, 1725, 1470, 1620), p0 = rep(1, 5), policy = list( function(time, state) { if (time >= 5) { state$S[5, 4] <- 880 } state }, makePolicyStickyPrice(0.5) ), priceAdjustmentVelocity = 0 ) matplot(de$ts.p, type = "o", pch = 20) matplot(de$ts.z, type = "o", pch = 20) ``` ## References Zhang Xin (2017, ISBN: 9787543227637) Principles of Computable General Equilibrium Modeling and Programming (Second Edition). Shanghai: Gezhi Press. (In Chinese)

gemInputOutputTable_5_4 function