# Some General Equilibrium Models with Tax Some general equilibrium models with tax. ```r gemTax_3_3(...) ``` ## Arguments - `...`: arguments to be passed to the function sdm2. ## Examples ```r #### turnover tax. dst.firm <- node_new("prod", type = "FIN", rate = c(1, tax.rate = 0.25), "cc1", "tax" ) node_set(dst.firm, "cc1", type = "CD", alpha = 2, beta = c(0.5, 0.5), "prod", "lab" ) dst.laborer <- dst.government <- node_new("util", type = "Leontief", a = 1, "prod" ) ge.TT <- sdm2( A = list(dst.firm, dst.laborer, dst.government), B = diag(c(1, 0, 0)), S0Exg = matrix(c( NA, NA, NA, NA, 100, NA, NA, NA, 100 ), 3, 3, TRUE), names.commodity = c("prod", "lab", "tax"), names.agent = c("firm", "laborer", "government"), numeraire = "prod" ) ge.TT$p ge.TT$z ge.TT$D ge.TT$S #### product tax. dst.taxed.prod <- node_new("taxed.prod", type = "FIN", rate = c(1, tax.rate = 0.25), "prod", "tax" ) dst.firm <- node_new("prod", type = "CD", alpha = 2, beta = c(0.5, 0.5), dst.taxed.prod, "lab" ) dst.laborer <- dst.government <- node_new("util", type = "Leontief", a = 1, dst.taxed.prod ) ge.PT <- sdm2( A = list(dst.firm, dst.laborer, dst.government), B = diag(c(1, 0, 0)), S0Exg = matrix(c( NA, NA, NA, NA, 100, NA, NA, NA, 100 ), 3, 3, TRUE), names.commodity = c("prod", "lab", "tax"), names.agent = c("firm", "laborer", "government"), numeraire = "prod" ) ge.PT$p ge.PT$z ge.PT$D ge.PT$S #### consumption tax. dst.firm <- node_new("output", type = "CD", alpha = 2, beta = c(0.5, 0.5), "prod", "lab" ) dst.laborer <- node_new("util", type = "FIN", rate = c(1, consumption.tax.rate = 1/3), "prod", "tax" ) dst.government <- node_new("utility", type = "Leontief", a = 1, "prod" ) ge.CT <- sdm2( A = list(dst.firm, dst.laborer, dst.government), B = diag(c(1, 0, 0)), S0Exg = matrix(c( NA, NA, NA, NA, 100, NA, NA, NA, 100 ), 3, 3, TRUE), names.commodity = c("prod", "lab", "tax"), names.agent = c("firm", "laborer", "government"), numeraire = "prod" ) ge.CT$p ge.CT$z ge.CT$D ge.CT$S #### value added tax. dst.firm <- node_new("output", type = "CD", alpha = 2, beta = c(0.5, 0.5), "prod", "taxed.lab" ) node_set(dst.firm, "taxed.lab", type = "FIN", rate = c(1, vat.rate = 1/3), "lab", "tax" ) dst.laborer <- dst.government <- node_new("util", type = "Leontief", a = 1, "prod" ) ge.VAT <- sdm2( A = list(dst.firm, dst.laborer, dst.government), B = diag(c(1, 0, 0)), S0Exg = matrix(c( NA, NA, NA, NA, 100, NA, NA, NA, 100 ), 3, 3, TRUE), names.commodity = c("prod", "lab", "tax"), names.agent = c("firm", "laborer", "government"), numeraire = "prod" ) ge.VAT$p ge.VAT$z ge.VAT$D ge.VAT$S #### income tax. income.tax.rate <- 1 / 4 dst.firm <- node_new("output", type = "CD", alpha = 2, beta = c(0.5, 0.5), "prod", "lab" ) dst.laborer <- dst.government <- node_new("util", type = "Leontief", a = 1, "prod" ) ge.IT <- sdm2( A = list(dst.firm, dst.laborer, dst.government), B <- diag(c(1, 0), 2, 3), S0Exg = matrix(c( NA, NA, NA, NA, 100 * (1 - income.tax.rate), 100 * income.tax.rate ), 2, 3, TRUE), names.commodity = c("prod", "lab"), names.agent = c("firm", "laborer", "government"), numeraire = "prod" ) ge.IT$p ge.IT$z ge.IT$D ge.IT$S #### turnover tax (Li, 2019, example 4.11). dst.firm <- node_new("output", type = "FIN", rate = c(1, turnover.tax.rate = 1), "cc1", "tax" ) node_set(dst.firm, "cc1", type = "CD", alpha = 1, beta = c(0.5, 0.5), "prod", "lab" ) dst.laborer1 <- node_new("util", type = "CD", alpha = 1, beta = c(0.5, 0.5), "prod", "lab" ) dst.laborer2 <- node_new("utility", type = "Leontief", a = 1, "prod" ) ge.TT2 <- sdm2( A = list(dst.firm, dst.laborer1, dst.laborer2), B = diag(c(1, 0, 0)), S0Exg = matrix(c( NA, NA, NA, NA, 100, NA, NA, NA, 100 ), 3, 3, TRUE), names.commodity = c("prod", "lab", "tax"), names.agent = c("firm", "laborer1", "laborer2"), numeraire = "lab" ) ge.TT2$p ge.TT2$z #### commodity tax in a pure exchange economy. tax.rate <- 0.25 es.consumer1 <- 0.5 es.consumer2 <- 2 dst.consumer1 <- node_new("util", type = "SCES", es = es.consumer1, alpha = 1, beta = c(0.5, 0.5), "comm1", "comm2" ) dst.consumer2 <- node_new("util", type = "SCES", es = es.consumer2, alpha = 1, beta = c(0.5, 0.5), "taxed.comm1", "comm2" ) node_set(dst.consumer2, "taxed.comm1", type = "FIN", rate = c(1, tax.rate = tax.rate), "comm1", "tax" ) dst.gov <- node_new("util", type = "SCES", es = 0, alpha = 1, beta = c(0.5, 0.5), "comm1", "comm2" ) ge.CT <- sdm2( A = list(dst.consumer1, dst.consumer2, dst.gov), B = matrix(0, 3, 3), S0Exg = matrix(c( 100, NA, NA, NA, 100, NA, NA, NA, 100 ), 3, 3, TRUE), names.commodity = c("comm1", "comm2", "tax"), names.agent = c("consumer1", "consumer2", "gov"), numeraire = "comm1" ) ge.CT$p ge.CT$z ge.CT$D ``` ## References LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)

gemTax_3_3 function