test/script1.R
In jholderieath/rEDM: Builds and Evaluates Linear Equilibrium Displacement Models
find_q_chg <- function(A,B,X,...) {
ainv <- solve(A)
ainv %*% B %*% X
}
number_of_commodities <- 5
imports <- TRUE
exports <- TRUE
ed <- matrix(data = c(
-0.696, -0.289, -0.094, -0.024, -0.172,
-0.382, -0.536, 0.031, -0.021, -0.046,
-1.665, 0.498, -0.202, 0.056, 0.591,
-0.18, -0.027, 0.114, -0.065, 0.477,
-0.191, 0.108, 0.127, -0.008, -0.235
),nrow = number_of_commodities,ncol = number_of_commodities)
esa <- matrix(data = c(
0.201, -0.108, -0.004, 0, 0,
-0.167, 0.153, -0.005, -0.001, 0,
-0.155, -0.110, 0.201, -0.001, 0,
-0.164, -0.117, -0.006, 0.238, 0,
0, 0, 0, 0, 0.350
),nrow = number_of_commodities,ncol = number_of_commodities)
esw <- matrix(data = c(
0.326, -0.036, -0.003, -0.034, 0,
-0.031, 0.191, -0.008, -0.095, 0,
-0.016, -0.047, 0.331, -0.045, 0,
-0.015, -0.050, -0.004, 0.473, 0,
0, 0, 0, 0, 0.35
),nrow = number_of_commodities,ncol = number_of_commodities)
e0 <- matrix(data = 0,nrow = number_of_commodities,ncol = number_of_commodities)
ed0 <- cbind(ed,e0,e0)
esa0 <- cbind(e0,esa,e0)
esw0 <- cbind(e0,e0,esw)
A <- rbind(ed0,esa0,esw0)
rm(e0,ed0,esa0,esw0)
X <- matrix(data = c(0,0,0,0,0,
0,0,0,0,0,
0.0147,
0.005,
0.0166,
0.0046,
0.018),nrow=15,ncol = 1)
library(rSymPy)
EP_corn <- Var('EP_corn')
EP_soy <- Var('EP_soy')
EP_wheat <- Var('EP_wheat')
EP_rice <- Var('EP_rice')
EP_peanut <- Var('EP_peanut')
e_d_corn <- Var('e_d_corn')
e_d_soy <- Var('e_d_soy')
e_d_wheat <- Var('e_d_wheat')
e_d_rice <- Var('e_d_rice')
e_d_peanut <- Var('e_d_peanut')
ss <- c('ss_AOS_corn', 'ss_FRS_corn',
'ss_AOS_soy', 'ss_FRS_soy',
'ss_AOS_wheat', 'ss_FRS_wheat',
'ss_AOS_rice', 'ss_FRS_rice',
'ss_AOS_peanuts', 'ss_FRS_peanuts',
'ss_imports_corn', 'ss_imports_soy', 'ss_imports_wheat', 'ss_imports_rice', 'ss_imports_peanut',
'ss_exports_corn', 'ss_exports_soy', 'ss_exports_wheat', 'ss_exports_rice', 'ss_exports_peanut'
)
for (i in ss) {
assign(noquote(i),Var(i))
}
B <- c('B_AOS_c','B_AOS_s','B_AOS_w','B_AOS_r','B_AOS_p',
'B_FRS_c', 'B_FRS_s', 'B_FRS_w', 'B_FRS_r', 'B_FRS_p')
for (i in B) {
assign(noquote(i),Var(i))
}
elast <- c(
'e_e_Corn', 'e_e_Soy', 'e_e_Wheat', 'e_e_Rice', 'e_e_Peanuts',
'e_i_Corn', 'e_i_Soy', 'e_i_Wheat', 'e_i_Rice', 'e_i_Peanuts',
'e_s_AOS_cc', 'e_s_AOS_cs', 'e_s_AOS_cw', 'e_s_AOS_cr', 'e_s_AOS_cp',
'e_s_AOS_sc', 'e_s_AOS_ss', 'e_s_AOS_sw', 'e_s_AOS_sr', 'e_s_AOS_sp',
'e_s_AOS_wc', 'e_s_AOS_ws', 'e_s_AOS_ww', 'e_s_AOS_wr', 'e_s_AOS_wp',
'e_s_AOS_rc', 'e_s_AOS_rs', 'e_s_AOS_rw', 'e_s_AOS_rr', 'e_s_AOS_rp',
'e_s_AOS_pc', 'e_s_AOS_ps', 'e_s_AOS_pw', 'e_s_AOS_pr', 'e_s_AOS_pp',
'e_s_FRS_cc', 'e_s_FRS_cs', 'e_s_FRS_cw', 'e_s_FRS_cr', 'e_s_FRS_cp',
'e_s_FRS_sc', 'e_s_FRS_ss', 'e_s_FRS_sw', 'e_s_FRS_sr', 'e_s_FRS_sp',
'e_s_FRS_wc', 'e_s_FRS_ws', 'e_s_FRS_ww', 'e_s_FRS_wr', 'e_s_FRS_wp',
'e_s_FRS_rc', 'e_s_FRS_rs', 'e_s_FRS_rw', 'e_s_FRS_rr', 'e_s_FRS_rp',
'e_s_FRS_pc', 'e_s_FRS_ps', 'e_s_FRS_pw', 'e_s_FRS_pr', 'e_s_FRS_pp'
)
for (i in elast) {
assign(noquote(i),Var(i))
}
##--------------------
e_d_corn = -0.696
e_d_soy = -0.065
e_d_wheat =-0.202
e_d_rice = -0.065
e_d_peanut = -0.235
ss_AOS_corn <- 0.94
ss_FRS_corn <- 0.06
ss_AOS_soy <- 0.88
ss_FRS_soy <- 0.12
ss_AOS_wheat <- 0.90
ss_FRS_wheat <- 0.10
ss_AOS_rice <- 0.24
ss_FRS_rice <- 0.76
ss_AOS_peanuts <- 0.03
ss_FRS_peanuts <- 0.97
ss_imports_corn <- 0.01
ss_imports_soy <- 0.02
ss_imports_wheat <- 0.12
ss_imports_rice <- 0.17
ss_imports_peanut <- 0.03
ss_exports_corn <- 0.14
ss_exports_soy <- 0.83
ss_exports_wheat <- 0.80
ss_exports_rice <- 0.84
ss_exports_peanut <- 0.23
B_AOS_c <- 0
B_AOS_s <- 0
B_AOS_w <- 0
B_AOS_r <- 0
B_AOS_p <- 0
B_FRS_c <- 0.0147
B_FRS_s <- 0.005
B_FRS_w <- 0.0166
B_FRS_r <- 0.0046
B_FRS_p <- 0.018
e_e_Corn <- -1.20
e_e_Soy <- -2.50
e_e_Wheat <- -0.85
e_e_Rice <- -2.62
e_e_Peanuts <- -1.00
e_i_Corn <- 0.50
e_i_Soy <- 0.50
e_i_Wheat <- 0.50
e_i_Rice <- 0.40
e_i_Peanuts <- 0.50
e_s_AOS_cc <- 0.20
e_s_AOS_cs <- -0.11
e_s_AOS_cw <- -0.00
e_s_AOS_cr <-0
e_s_AOS_cp <- 0
e_s_AOS_sc <- -0.17
e_s_AOS_ss <- 0.15
e_s_AOS_sw <- -0.01
e_s_AOS_sr <- -0.00
e_s_AOS_sp <- 0
e_s_AOS_wc <- -0.15
e_s_AOS_ws <- -0.11
e_s_AOS_ww <- 0.20
e_s_AOS_wr <- -0.00
e_s_AOS_wp <- 0
e_s_AOS_rc <- -0.16
e_s_AOS_rs <- -0.12
e_s_AOS_rw <- -0.01
e_s_AOS_rr <- 0.24
e_s_AOS_rp <- 0
e_s_AOS_pc <- 0
e_s_AOS_ps <- 0
e_s_AOS_pw <- 0
e_s_AOS_pr <- 0
e_s_AOS_pp <- 0.35
e_s_FRS_cc <- 0.33
e_s_FRS_cs <- -0.04
e_s_FRS_cw <- -0.00
e_s_FRS_cr <- -0.03
e_s_FRS_cp <- 0
e_s_FRS_sc <- -0.03
e_s_FRS_ss <- 0.19
e_s_FRS_sw <- -0.01
e_s_FRS_sr <- -0.10
e_s_FRS_sp <- 0
e_s_FRS_wc <- -0.02
e_s_FRS_ws <- -0.05
e_s_FRS_ww <- 0.33
e_s_FRS_wr <- -0.04
e_s_FRS_wp <- 0
e_s_FRS_rc <- -0.01
e_s_FRS_rs <- -0.05
e_s_FRS_rw <- -0.00
e_s_FRS_rr <- 0.47
e_s_FRS_rp <- 0
e_s_FRS_pc <- 0
e_s_FRS_ps <- 0
e_s_FRS_pw <- 0
e_s_FRS_pr <- 0
e_s_FRS_pp <- 0.35
sympy(
'eqns = [
Eq(EP_corn * e_d_corn + (EP_corn) * (ss_exports_corn * e_e_Corn - ss_imports_corn *e_i_Corn), ((ss_FRS_corn * (e_s_FRS_cc * EP_corn + e_s_FRS_cs * EP_soy + e_s_FRS_cw * EP_wheat + e_s_FRS_cr * EP_rice + e_s_FRS_cp * EP_peanut + B_FRS_c)) + (ss_AOS_corn * (e_s_AOS_cc * EP_corn + e_s_AOS_cs * EP_soy + e_s_AOS_cw * EP_wheat + e_s_AOS_cr * EP_rice + e_s_AOS_cp * EP_peanut + B_AOS_c)))),
Eq(EP_soy * e_d_soy + (EP_soy) * (ss_exports_soy * e_e_Soy - ss_imports_soy *e_i_Soy), ((ss_FRS_soy * (e_s_FRS_sc * EP_corn + e_s_FRS_ss * EP_soy + e_s_FRS_sw * EP_wheat + e_s_FRS_sr * EP_rice + e_s_FRS_sp * EP_peanut + B_FRS_s)) + (ss_AOS_soy * (e_s_AOS_sc * EP_corn + e_s_AOS_ss * EP_soy + e_s_AOS_sw * EP_wheat + e_s_AOS_sr * EP_rice + e_s_AOS_sp * EP_peanut + B_AOS_s)))),
Eq(EP_wheat * e_d_wheat + (EP_wheat) * (ss_exports_wheat * e_e_Wheat - ss_imports_wheat *e_i_Wheat), ((ss_FRS_wheat * (e_s_FRS_wc * EP_corn + e_s_FRS_ws * EP_soy + e_s_FRS_ww * EP_wheat + e_s_FRS_wr * EP_rice + e_s_FRS_wp * EP_peanut + B_FRS_w)) + (ss_AOS_wheat * (e_s_AOS_wc * EP_corn + e_s_AOS_ws * EP_soy + e_s_AOS_ww * EP_wheat + e_s_AOS_wr * EP_rice + e_s_AOS_wp * EP_peanut + B_AOS_w)))),
Eq(EP_rice * e_d_peanut + (EP_rice) * (ss_exports_rice * e_e_Rice - ss_imports_rice *e_i_Rice), ((ss_FRS_rice * (e_s_FRS_rc * EP_corn + e_s_FRS_rs * EP_soy + e_s_FRS_rw * EP_wheat + e_s_FRS_rr * EP_rice + e_s_FRS_rp * EP_peanut + B_FRS_r)) + (ss_AOS_rice * (e_s_AOS_rc * EP_corn + e_s_AOS_rs * EP_soy + e_s_AOS_rw * EP_wheat + e_s_AOS_rr * EP_rice + e_s_AOS_rp * EP_peanut + B_AOS_r)))),
Eq(EP_peanut * e_d_peanut + (EP_peanut) * (ss_exports_peanut * e_e_Peanuts - ss_imports_peanut *e_i_Peanuts), ((ss_FRS_peanuts * (e_s_FRS_pc * EP_corn + e_s_FRS_ps * EP_soy + e_s_FRS_pw * EP_wheat + e_s_FRS_pr * EP_rice + e_s_FRS_pp * EP_peanut + B_FRS_p)) + (ss_AOS_peanuts * (e_s_AOS_pc * EP_corn + e_s_AOS_ps * EP_soy + e_s_AOS_pw * EP_wheat + e_s_AOS_pr * EP_rice + e_s_AOS_pp * EP_peanut + B_AOS_p)))) ]'
)
sympy('corn = Eq(EP_corn * e_d_corn + (EP_corn) * (ss_exports_corn * e_e_Corn - ss_imports_corn *e_i_Corn), ((ss_FRS_corn * (e_s_FRS_cc * EP_corn + e_s_FRS_cs * EP_soy + e_s_FRS_cw * EP_wheat + e_s_FRS_cr * EP_rice + e_s_FRS_cp * EP_peanut + B_FRS_c)) + (ss_AOS_corn * (e_s_AOS_cc * EP_corn + e_s_AOS_cs * EP_soy + e_s_AOS_cw * EP_wheat + e_s_AOS_cr * EP_rice + e_s_AOS_cp * EP_peanut + B_AOS_c))))')
sympy('soy = Eq(EP_soy * e_d_soy + (EP_soy) * (ss_exports_soy * e_e_Soy - ss_imports_soy *e_i_Soy), ((ss_FRS_soy * (e_s_FRS_sc * EP_corn + e_s_FRS_ss * EP_soy + e_s_FRS_sw * EP_wheat + e_s_FRS_sr * EP_rice + e_s_FRS_sp * EP_peanut + B_FRS_s)) + (ss_AOS_soy * (e_s_AOS_sc * EP_corn + e_s_AOS_ss * EP_soy + e_s_AOS_sw * EP_wheat + e_s_AOS_sr * EP_rice + e_s_AOS_sp * EP_peanut + B_AOS_s))))')
sympy('wheat = Eq(EP_wheat * e_d_wheat + (EP_wheat) * (ss_exports_wheat * e_e_Wheat - ss_imports_wheat *e_i_Wheat), ((ss_FRS_wheat * (e_s_FRS_wc * EP_corn + e_s_FRS_ws * EP_soy + e_s_FRS_ww * EP_wheat + e_s_FRS_wr * EP_rice + e_s_FRS_wp * EP_peanut + B_FRS_w)) + (ss_AOS_wheat * (e_s_AOS_wc * EP_corn + e_s_AOS_ws * EP_soy + e_s_AOS_ww * EP_wheat + e_s_AOS_wr * EP_rice + e_s_AOS_wp * EP_peanut + B_AOS_w))))')
sympy('rice = Eq(EP_rice * e_d_peanut + (EP_rice) * (ss_exports_rice * e_e_Rice - ss_imports_rice *e_i_Rice), ((ss_FRS_rice * (e_s_FRS_rc * EP_corn + e_s_FRS_rs * EP_soy + e_s_FRS_rw * EP_wheat + e_s_FRS_rr * EP_rice + e_s_FRS_rp * EP_peanut + B_FRS_r)) + (ss_AOS_rice * (e_s_AOS_rc * EP_corn + e_s_AOS_rs * EP_soy + e_s_AOS_rw * EP_wheat + e_s_AOS_rr * EP_rice + e_s_AOS_rp * EP_peanut + B_AOS_r))))')
sympy('peanut = Eq(EP_peanut * e_d_peanut + (EP_peanut) * (ss_exports_peanut * e_e_Peanuts - ss_imports_peanut *e_i_Peanuts), ((ss_FRS_peanuts * (e_s_FRS_pc * EP_corn + e_s_FRS_ps * EP_soy + e_s_FRS_pw * EP_wheat + e_s_FRS_pr * EP_rice + e_s_FRS_pp * EP_peanut + B_FRS_p)) + (ss_AOS_peanuts * (e_s_AOS_pc * EP_corn + e_s_AOS_ps * EP_soy + e_s_AOS_pw * EP_wheat + e_s_AOS_pr * EP_rice + e_s_AOS_pp * EP_peanut + B_AOS_p))))')
sympy('corn = corn.subs([
(e_d_corn,-0.696), (e_d_soy,-0.065), (e_d_wheat,-0.202), (e_d_rice,-0.065), (e_d_peanut,-0.235),
(ss_AOS_corn,0.94), (ss_FRS_corn,0.06),
(ss_AOS_soy,0.88), (ss_FRS_soy,0.12),
(ss_AOS_wheat,0.90), (ss_FRS_wheat,0.10),
(ss_AOS_rice,0.24), (ss_FRS_rice,0.76),
(ss_AOS_peanuts,0.03), (ss_FRS_peanuts,0.97),
(ss_imports_corn,0.01), (ss_imports_soy,0.02), (ss_imports_wheat,0.12), (ss_imports_rice,0.17), (ss_imports_peanut,0.03),
(ss_exports_corn,0.14), (ss_exports_soy,0.83), (ss_exports_wheat,0.80), (ss_exports_rice,0.84), (ss_exports_peanut,0.23),
(B_AOS_c,0),(B_AOS_s,0),(B_AOS_w,0),(B_AOS_r,0),(B_AOS_p,0),
(B_FRS_c,0.0147),(B_FRS_s,0.005),(B_FRS_w,0.0166),(B_FRS_r,0.0046),(B_FRS_p,0.018),
(e_e_Corn,-1.20),(e_e_Soy,-2.50),(e_e_Wheat,-0.85),(e_e_Rice,-2.62),(e_e_Peanuts,-1.00),
(e_i_Corn,0.50),(e_i_Soy,0.50),(e_i_Wheat,0.50),(e_i_Rice,0.40),(e_i_Peanuts,0.50),
(e_s_AOS_cc,0.20),(e_s_AOS_cs,-0.11),(e_s_AOS_cw,-0.00),(e_s_AOS_cr,0),(e_s_AOS_cp,0),
(e_s_AOS_sc,-0.17),(e_s_AOS_ss,0.15),(e_s_AOS_sw,-0.01),(e_s_AOS_sr,-0.00),(e_s_AOS_sp,0),
(e_s_AOS_wc,-0.15),(e_s_AOS_ws,-0.11),(e_s_AOS_ww,0.20),(e_s_AOS_wr,-0.00),(e_s_AOS_wp,0),
(e_s_AOS_rc,-0.16),(e_s_AOS_rs,-0.12),(e_s_AOS_rw,-0.01),(e_s_AOS_rr,0.24),(e_s_AOS_rp,0),
(e_s_AOS_pc,0),(e_s_AOS_ps,0),(e_s_AOS_pw,0),(e_s_AOS_pr,0),(e_s_AOS_pp,0.35),
(e_s_FRS_cc,0.33),(e_s_FRS_cs,-0.04),(e_s_FRS_cw,-0.00),(e_s_FRS_cr,-0.03),(e_s_FRS_cp,0),
(e_s_FRS_sc,-0.03),(e_s_FRS_ss,0.19),(e_s_FRS_sw,-0.01 ),(e_s_FRS_sr,-0.10 ),(e_s_FRS_sp,0),
(e_s_FRS_wc,-0.02),(e_s_FRS_ws,-0.05 ),(e_s_FRS_ww,0.33),(e_s_FRS_wr,-0.04 ),(e_s_FRS_wp,0),
(e_s_FRS_rc,-0.01 ), (e_s_FRS_rs,-0.05), (e_s_FRS_rw,-0.00 ), (e_s_FRS_rr,0.47),(e_s_FRS_rp,0),
(e_s_FRS_pc,0),(e_s_FRS_ps,0),(e_s_FRS_pw,0),(e_s_FRS_pr,0),(e_s_FRS_pp,0.35)
])')
sympy('soy = soy.subs([
(e_d_corn,-0.696), (e_d_soy,-0.065), (e_d_wheat,-0.202), (e_d_rice,-0.065), (e_d_peanut,-0.235),
(ss_AOS_corn,0.94), (ss_FRS_corn,0.06),
(ss_AOS_soy,0.88), (ss_FRS_soy,0.12),
(ss_AOS_wheat,0.90), (ss_FRS_wheat,0.10),
(ss_AOS_rice,0.24), (ss_FRS_rice,0.76),
(ss_AOS_peanuts,0.03), (ss_FRS_peanuts,0.97),
(ss_imports_corn,0.01), (ss_imports_soy,0.02), (ss_imports_wheat,0.12), (ss_imports_rice,0.17), (ss_imports_peanut,0.03),
(ss_exports_corn,0.14), (ss_exports_soy,0.83), (ss_exports_wheat,0.80), (ss_exports_rice,0.84), (ss_exports_peanut,0.23),
(B_AOS_c,0),(B_AOS_s,0),(B_AOS_w,0),(B_AOS_r,0),(B_AOS_p,0),
(B_FRS_c,0.0147),(B_FRS_s,0.005),(B_FRS_w,0.0166),(B_FRS_r,0.0046),(B_FRS_p,0.018),
(e_e_Corn,-1.20),(e_e_Soy,-2.50),(e_e_Wheat,-0.85),(e_e_Rice,-2.62),(e_e_Peanuts,-1.00),
(e_i_Corn,0.50),(e_i_Soy,0.50),(e_i_Wheat,0.50),(e_i_Rice,0.40),(e_i_Peanuts,0.50),
(e_s_AOS_cc,0.20),(e_s_AOS_cs,-0.11),(e_s_AOS_cw,-0.00),(e_s_AOS_cr,0),(e_s_AOS_cp,0),
(e_s_AOS_sc,-0.17),(e_s_AOS_ss,0.15),(e_s_AOS_sw,-0.01),(e_s_AOS_sr,-0.00),(e_s_AOS_sp,0),
(e_s_AOS_wc,-0.15),(e_s_AOS_ws,-0.11),(e_s_AOS_ww,0.20),(e_s_AOS_wr,-0.00),(e_s_AOS_wp,0),
(e_s_AOS_rc,-0.16),(e_s_AOS_rs,-0.12),(e_s_AOS_rw,-0.01),(e_s_AOS_rr,0.24),(e_s_AOS_rp,0),
(e_s_AOS_pc,0),(e_s_AOS_ps,0),(e_s_AOS_pw,0),(e_s_AOS_pr,0),(e_s_AOS_pp,0.35),
(e_s_FRS_cc,0.33),(e_s_FRS_cs,-0.04),(e_s_FRS_cw,-0.00),(e_s_FRS_cr,-0.03),(e_s_FRS_cp,0),
(e_s_FRS_sc,-0.03),(e_s_FRS_ss,0.19),(e_s_FRS_sw,-0.01 ),(e_s_FRS_sr,-0.10 ),(e_s_FRS_sp,0),
(e_s_FRS_wc,-0.02),(e_s_FRS_ws,-0.05 ),(e_s_FRS_ww,0.33),(e_s_FRS_wr,-0.04 ),(e_s_FRS_wp,0),
(e_s_FRS_rc,-0.01 ), (e_s_FRS_rs,-0.05), (e_s_FRS_rw,-0.00 ), (e_s_FRS_rr,0.47),(e_s_FRS_rp,0),
(e_s_FRS_pc,0),(e_s_FRS_ps,0),(e_s_FRS_pw,0),(e_s_FRS_pr,0),(e_s_FRS_pp,0.35)
])')
sympy('wheat = wheat.subs([
(e_d_corn,-0.696), (e_d_soy,-0.065), (e_d_wheat,-0.202), (e_d_rice,-0.065), (e_d_peanut,-0.235),
(ss_AOS_corn,0.94), (ss_FRS_corn,0.06),
(ss_AOS_soy,0.88), (ss_FRS_soy,0.12),
(ss_AOS_wheat,0.90), (ss_FRS_wheat,0.10),
(ss_AOS_rice,0.24), (ss_FRS_rice,0.76),
(ss_AOS_peanuts,0.03), (ss_FRS_peanuts,0.97),
(ss_imports_corn,0.01), (ss_imports_soy,0.02), (ss_imports_wheat,0.12), (ss_imports_rice,0.17), (ss_imports_peanut,0.03),
(ss_exports_corn,0.14), (ss_exports_soy,0.83), (ss_exports_wheat,0.80), (ss_exports_rice,0.84), (ss_exports_peanut,0.23),
(B_AOS_c,0),(B_AOS_s,0),(B_AOS_w,0),(B_AOS_r,0),(B_AOS_p,0),
(B_FRS_c,0.0147),(B_FRS_s,0.005),(B_FRS_w,0.0166),(B_FRS_r,0.0046),(B_FRS_p,0.018),
(e_e_Corn,-1.20),(e_e_Soy,-2.50),(e_e_Wheat,-0.85),(e_e_Rice,-2.62),(e_e_Peanuts,-1.00),
(e_i_Corn,0.50),(e_i_Soy,0.50),(e_i_Wheat,0.50),(e_i_Rice,0.40),(e_i_Peanuts,0.50),
(e_s_AOS_cc,0.20),(e_s_AOS_cs,-0.11),(e_s_AOS_cw,-0.00),(e_s_AOS_cr,0),(e_s_AOS_cp,0),
(e_s_AOS_sc,-0.17),(e_s_AOS_ss,0.15),(e_s_AOS_sw,-0.01),(e_s_AOS_sr,-0.00),(e_s_AOS_sp,0),
(e_s_AOS_wc,-0.15),(e_s_AOS_ws,-0.11),(e_s_AOS_ww,0.20),(e_s_AOS_wr,-0.00),(e_s_AOS_wp,0),
(e_s_AOS_rc,-0.16),(e_s_AOS_rs,-0.12),(e_s_AOS_rw,-0.01),(e_s_AOS_rr,0.24),(e_s_AOS_rp,0),
(e_s_AOS_pc,0),(e_s_AOS_ps,0),(e_s_AOS_pw,0),(e_s_AOS_pr,0),(e_s_AOS_pp,0.35),
(e_s_FRS_cc,0.33),(e_s_FRS_cs,-0.04),(e_s_FRS_cw,-0.00),(e_s_FRS_cr,-0.03),(e_s_FRS_cp,0),
(e_s_FRS_sc,-0.03),(e_s_FRS_ss,0.19),(e_s_FRS_sw,-0.01 ),(e_s_FRS_sr,-0.10 ),(e_s_FRS_sp,0),
(e_s_FRS_wc,-0.02),(e_s_FRS_ws,-0.05 ),(e_s_FRS_ww,0.33),(e_s_FRS_wr,-0.04 ),(e_s_FRS_wp,0),
(e_s_FRS_rc,-0.01 ), (e_s_FRS_rs,-0.05), (e_s_FRS_rw,-0.00 ), (e_s_FRS_rr,0.47),(e_s_FRS_rp,0),
(e_s_FRS_pc,0),(e_s_FRS_ps,0),(e_s_FRS_pw,0),(e_s_FRS_pr,0),(e_s_FRS_pp,0.35)
])')
sympy('rice = rice.subs([
(e_d_corn,-0.696), (e_d_soy,-0.065), (e_d_wheat,-0.202), (e_d_rice,-0.065), (e_d_peanut,-0.235),
(ss_AOS_corn,0.94), (ss_FRS_corn,0.06),
(ss_AOS_soy,0.88), (ss_FRS_soy,0.12),
(ss_AOS_wheat,0.90), (ss_FRS_wheat,0.10),
(ss_AOS_rice,0.24), (ss_FRS_rice,0.76),
(ss_AOS_peanuts,0.03), (ss_FRS_peanuts,0.97),
(ss_imports_corn,0.01), (ss_imports_soy,0.02), (ss_imports_wheat,0.12), (ss_imports_rice,0.17), (ss_imports_peanut,0.03),
(ss_exports_corn,0.14), (ss_exports_soy,0.83), (ss_exports_wheat,0.80), (ss_exports_rice,0.84), (ss_exports_peanut,0.23),
(B_AOS_c,0),(B_AOS_s,0),(B_AOS_w,0),(B_AOS_r,0),(B_AOS_p,0),
(B_FRS_c,0.0147),(B_FRS_s,0.005),(B_FRS_w,0.0166),(B_FRS_r,0.0046),(B_FRS_p,0.018),
(e_e_Corn,-1.20),(e_e_Soy,-2.50),(e_e_Wheat,-0.85),(e_e_Rice,-2.62),(e_e_Peanuts,-1.00),
(e_i_Corn,0.50),(e_i_Soy,0.50),(e_i_Wheat,0.50),(e_i_Rice,0.40),(e_i_Peanuts,0.50),
(e_s_AOS_cc,0.20),(e_s_AOS_cs,-0.11),(e_s_AOS_cw,-0.00),(e_s_AOS_cr,0),(e_s_AOS_cp,0),
(e_s_AOS_sc,-0.17),(e_s_AOS_ss,0.15),(e_s_AOS_sw,-0.01),(e_s_AOS_sr,-0.00),(e_s_AOS_sp,0),
(e_s_AOS_wc,-0.15),(e_s_AOS_ws,-0.11),(e_s_AOS_ww,0.20),(e_s_AOS_wr,-0.00),(e_s_AOS_wp,0),
(e_s_AOS_rc,-0.16),(e_s_AOS_rs,-0.12),(e_s_AOS_rw,-0.01),(e_s_AOS_rr,0.24),(e_s_AOS_rp,0),
(e_s_AOS_pc,0),(e_s_AOS_ps,0),(e_s_AOS_pw,0),(e_s_AOS_pr,0),(e_s_AOS_pp,0.35),
(e_s_FRS_cc,0.33),(e_s_FRS_cs,-0.04),(e_s_FRS_cw,-0.00),(e_s_FRS_cr,-0.03),(e_s_FRS_cp,0),
(e_s_FRS_sc,-0.03),(e_s_FRS_ss,0.19),(e_s_FRS_sw,-0.01 ),(e_s_FRS_sr,-0.10 ),(e_s_FRS_sp,0),
(e_s_FRS_wc,-0.02),(e_s_FRS_ws,-0.05 ),(e_s_FRS_ww,0.33),(e_s_FRS_wr,-0.04 ),(e_s_FRS_wp,0),
(e_s_FRS_rc,-0.01 ), (e_s_FRS_rs,-0.05), (e_s_FRS_rw,-0.00 ), (e_s_FRS_rr,0.47),(e_s_FRS_rp,0),
(e_s_FRS_pc,0),(e_s_FRS_ps,0),(e_s_FRS_pw,0),(e_s_FRS_pr,0),(e_s_FRS_pp,0.35)
])')
sympy('peanut = peanut.subs([
(e_d_corn,-0.696), (e_d_soy,-0.065), (e_d_wheat,-0.202), (e_d_rice,-0.065), (e_d_peanut,-0.235),
(ss_AOS_corn,0.94), (ss_FRS_corn,0.06),
(ss_AOS_soy,0.88), (ss_FRS_soy,0.12),
(ss_AOS_wheat,0.90), (ss_FRS_wheat,0.10),
(ss_AOS_rice,0.24), (ss_FRS_rice,0.76),
(ss_AOS_peanuts,0.03), (ss_FRS_peanuts,0.97),
(ss_imports_corn,0.01), (ss_imports_soy,0.02), (ss_imports_wheat,0.12), (ss_imports_rice,0.17), (ss_imports_peanut,0.03),
(ss_exports_corn,0.14), (ss_exports_soy,0.83), (ss_exports_wheat,0.80), (ss_exports_rice,0.84), (ss_exports_peanut,0.23),
(B_AOS_c,0),(B_AOS_s,0),(B_AOS_w,0),(B_AOS_r,0),(B_AOS_p,0),
(B_FRS_c,0.0147),(B_FRS_s,0.005),(B_FRS_w,0.0166),(B_FRS_r,0.0046),(B_FRS_p,0.018),
(e_e_Corn,-1.20),(e_e_Soy,-2.50),(e_e_Wheat,-0.85),(e_e_Rice,-2.62),(e_e_Peanuts,-1.00),
(e_i_Corn,0.50),(e_i_Soy,0.50),(e_i_Wheat,0.50),(e_i_Rice,0.40),(e_i_Peanuts,0.50),
(e_s_AOS_cc,0.20),(e_s_AOS_cs,-0.11),(e_s_AOS_cw,-0.00),(e_s_AOS_cr,0),(e_s_AOS_cp,0),
(e_s_AOS_sc,-0.17),(e_s_AOS_ss,0.15),(e_s_AOS_sw,-0.01),(e_s_AOS_sr,-0.00),(e_s_AOS_sp,0),
(e_s_AOS_wc,-0.15),(e_s_AOS_ws,-0.11),(e_s_AOS_ww,0.20),(e_s_AOS_wr,-0.00),(e_s_AOS_wp,0),
(e_s_AOS_rc,-0.16),(e_s_AOS_rs,-0.12),(e_s_AOS_rw,-0.01),(e_s_AOS_rr,0.24),(e_s_AOS_rp,0),
(e_s_AOS_pc,0),(e_s_AOS_ps,0),(e_s_AOS_pw,0),(e_s_AOS_pr,0),(e_s_AOS_pp,0.35),
(e_s_FRS_cc,0.33),(e_s_FRS_cs,-0.04),(e_s_FRS_cw,-0.00),(e_s_FRS_cr,-0.03),(e_s_FRS_cp,0),
(e_s_FRS_sc,-0.03),(e_s_FRS_ss,0.19),(e_s_FRS_sw,-0.01 ),(e_s_FRS_sr,-0.10 ),(e_s_FRS_sp,0),
(e_s_FRS_wc,-0.02),(e_s_FRS_ws,-0.05 ),(e_s_FRS_ww,0.33),(e_s_FRS_wr,-0.04 ),(e_s_FRS_wp,0),
(e_s_FRS_rc,-0.01 ), (e_s_FRS_rs,-0.05), (e_s_FRS_rw,-0.00 ), (e_s_FRS_rr,0.47),(e_s_FRS_rp,0),
(e_s_FRS_pc,0),(e_s_FRS_ps,0),(e_s_FRS_pw,0),(e_s_FRS_pr,0),(e_s_FRS_pp,0.35)
])')
sympy('eqns = [corn,soy,wheat,rice,peanut]')
sympy('solve(eqns, EP_corn, EP_soy, EP_wheat, EP_rice, EP_peanut)')
jholderieath/rEDM documentation built on Sept. 28, 2018, 12:25 a.m.
R Package Documentation
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Note that we can't provide technical support on individual packages. You should contact the package authors for that.
find_q_chg <- function(A,B,X,...) {
ainv <- solve(A)
ainv %*% B %*% X
}
number_of_commodities <- 5
imports <- TRUE
exports <- TRUE
ed <- matrix(data = c(
-0.696, -0.289, -0.094, -0.024, -0.172,
-0.382, -0.536, 0.031, -0.021, -0.046,
-1.665, 0.498, -0.202, 0.056, 0.591,
-0.18, -0.027, 0.114, -0.065, 0.477,
-0.191, 0.108, 0.127, -0.008, -0.235
),nrow = number_of_commodities,ncol = number_of_commodities)
esa <- matrix(data = c(
0.201, -0.108, -0.004, 0, 0,
-0.167, 0.153, -0.005, -0.001, 0,
-0.155, -0.110, 0.201, -0.001, 0,
-0.164, -0.117, -0.006, 0.238, 0,
0, 0, 0, 0, 0.350
),nrow = number_of_commodities,ncol = number_of_commodities)
esw <- matrix(data = c(
0.326, -0.036, -0.003, -0.034, 0,
-0.031, 0.191, -0.008, -0.095, 0,
-0.016, -0.047, 0.331, -0.045, 0,
-0.015, -0.050, -0.004, 0.473, 0,
0, 0, 0, 0, 0.35
),nrow = number_of_commodities,ncol = number_of_commodities)
e0 <- matrix(data = 0,nrow = number_of_commodities,ncol = number_of_commodities)
ed0 <- cbind(ed,e0,e0)
esa0 <- cbind(e0,esa,e0)
esw0 <- cbind(e0,e0,esw)
A <- rbind(ed0,esa0,esw0)
rm(e0,ed0,esa0,esw0)
X <- matrix(data = c(0,0,0,0,0,
0,0,0,0,0,
0.0147,
0.005,
0.0166,
0.0046,
0.018),nrow=15,ncol = 1)
library(rSymPy)
EP_corn <- Var('EP_corn')
EP_soy <- Var('EP_soy')
EP_wheat <- Var('EP_wheat')
EP_rice <- Var('EP_rice')
EP_peanut <- Var('EP_peanut')
e_d_corn <- Var('e_d_corn')
e_d_soy <- Var('e_d_soy')
e_d_wheat <- Var('e_d_wheat')
e_d_rice <- Var('e_d_rice')
e_d_peanut <- Var('e_d_peanut')
ss <- c('ss_AOS_corn', 'ss_FRS_corn',
'ss_AOS_soy', 'ss_FRS_soy',
'ss_AOS_wheat', 'ss_FRS_wheat',
'ss_AOS_rice', 'ss_FRS_rice',
'ss_AOS_peanuts', 'ss_FRS_peanuts',
'ss_imports_corn', 'ss_imports_soy', 'ss_imports_wheat', 'ss_imports_rice', 'ss_imports_peanut',
'ss_exports_corn', 'ss_exports_soy', 'ss_exports_wheat', 'ss_exports_rice', 'ss_exports_peanut'
)
for (i in ss) {
assign(noquote(i),Var(i))
}
B <- c('B_AOS_c','B_AOS_s','B_AOS_w','B_AOS_r','B_AOS_p',
'B_FRS_c', 'B_FRS_s', 'B_FRS_w', 'B_FRS_r', 'B_FRS_p')
for (i in B) {
assign(noquote(i),Var(i))
}
elast <- c(
'e_e_Corn', 'e_e_Soy', 'e_e_Wheat', 'e_e_Rice', 'e_e_Peanuts',
'e_i_Corn', 'e_i_Soy', 'e_i_Wheat', 'e_i_Rice', 'e_i_Peanuts',
'e_s_AOS_cc', 'e_s_AOS_cs', 'e_s_AOS_cw', 'e_s_AOS_cr', 'e_s_AOS_cp',
'e_s_AOS_sc', 'e_s_AOS_ss', 'e_s_AOS_sw', 'e_s_AOS_sr', 'e_s_AOS_sp',
'e_s_AOS_wc', 'e_s_AOS_ws', 'e_s_AOS_ww', 'e_s_AOS_wr', 'e_s_AOS_wp',
'e_s_AOS_rc', 'e_s_AOS_rs', 'e_s_AOS_rw', 'e_s_AOS_rr', 'e_s_AOS_rp',
'e_s_AOS_pc', 'e_s_AOS_ps', 'e_s_AOS_pw', 'e_s_AOS_pr', 'e_s_AOS_pp',
'e_s_FRS_cc', 'e_s_FRS_cs', 'e_s_FRS_cw', 'e_s_FRS_cr', 'e_s_FRS_cp',
'e_s_FRS_sc', 'e_s_FRS_ss', 'e_s_FRS_sw', 'e_s_FRS_sr', 'e_s_FRS_sp',
'e_s_FRS_wc', 'e_s_FRS_ws', 'e_s_FRS_ww', 'e_s_FRS_wr', 'e_s_FRS_wp',
'e_s_FRS_rc', 'e_s_FRS_rs', 'e_s_FRS_rw', 'e_s_FRS_rr', 'e_s_FRS_rp',
'e_s_FRS_pc', 'e_s_FRS_ps', 'e_s_FRS_pw', 'e_s_FRS_pr', 'e_s_FRS_pp'
)
for (i in elast) {
assign(noquote(i),Var(i))
}
##--------------------
e_d_corn = -0.696
e_d_soy = -0.065
e_d_wheat =-0.202
e_d_rice = -0.065
e_d_peanut = -0.235
ss_AOS_corn <- 0.94
ss_FRS_corn <- 0.06
ss_AOS_soy <- 0.88
ss_FRS_soy <- 0.12
ss_AOS_wheat <- 0.90
ss_FRS_wheat <- 0.10
ss_AOS_rice <- 0.24
ss_FRS_rice <- 0.76
ss_AOS_peanuts <- 0.03
ss_FRS_peanuts <- 0.97
ss_imports_corn <- 0.01
ss_imports_soy <- 0.02
ss_imports_wheat <- 0.12
ss_imports_rice <- 0.17
ss_imports_peanut <- 0.03
ss_exports_corn <- 0.14
ss_exports_soy <- 0.83
ss_exports_wheat <- 0.80
ss_exports_rice <- 0.84
ss_exports_peanut <- 0.23
B_AOS_c <- 0
B_AOS_s <- 0
B_AOS_w <- 0
B_AOS_r <- 0
B_AOS_p <- 0
B_FRS_c <- 0.0147
B_FRS_s <- 0.005
B_FRS_w <- 0.0166
B_FRS_r <- 0.0046
B_FRS_p <- 0.018
e_e_Corn <- -1.20
e_e_Soy <- -2.50
e_e_Wheat <- -0.85
e_e_Rice <- -2.62
e_e_Peanuts <- -1.00
e_i_Corn <- 0.50
e_i_Soy <- 0.50
e_i_Wheat <- 0.50
e_i_Rice <- 0.40
e_i_Peanuts <- 0.50
e_s_AOS_cc <- 0.20
e_s_AOS_cs <- -0.11
e_s_AOS_cw <- -0.00
e_s_AOS_cr <-0
e_s_AOS_cp <- 0
e_s_AOS_sc <- -0.17
e_s_AOS_ss <- 0.15
e_s_AOS_sw <- -0.01
e_s_AOS_sr <- -0.00
e_s_AOS_sp <- 0
e_s_AOS_wc <- -0.15
e_s_AOS_ws <- -0.11
e_s_AOS_ww <- 0.20
e_s_AOS_wr <- -0.00
e_s_AOS_wp <- 0
e_s_AOS_rc <- -0.16
e_s_AOS_rs <- -0.12
e_s_AOS_rw <- -0.01
e_s_AOS_rr <- 0.24
e_s_AOS_rp <- 0
e_s_AOS_pc <- 0
e_s_AOS_ps <- 0
e_s_AOS_pw <- 0
e_s_AOS_pr <- 0
e_s_AOS_pp <- 0.35
e_s_FRS_cc <- 0.33
e_s_FRS_cs <- -0.04
e_s_FRS_cw <- -0.00
e_s_FRS_cr <- -0.03
e_s_FRS_cp <- 0
e_s_FRS_sc <- -0.03
e_s_FRS_ss <- 0.19
e_s_FRS_sw <- -0.01
e_s_FRS_sr <- -0.10
e_s_FRS_sp <- 0
e_s_FRS_wc <- -0.02
e_s_FRS_ws <- -0.05
e_s_FRS_ww <- 0.33
e_s_FRS_wr <- -0.04
e_s_FRS_wp <- 0
e_s_FRS_rc <- -0.01
e_s_FRS_rs <- -0.05
e_s_FRS_rw <- -0.00
e_s_FRS_rr <- 0.47
e_s_FRS_rp <- 0
e_s_FRS_pc <- 0
e_s_FRS_ps <- 0
e_s_FRS_pw <- 0
e_s_FRS_pr <- 0
e_s_FRS_pp <- 0.35
sympy(
'eqns = [
Eq(EP_corn * e_d_corn + (EP_corn) * (ss_exports_corn * e_e_Corn - ss_imports_corn *e_i_Corn), ((ss_FRS_corn * (e_s_FRS_cc * EP_corn + e_s_FRS_cs * EP_soy + e_s_FRS_cw * EP_wheat + e_s_FRS_cr * EP_rice + e_s_FRS_cp * EP_peanut + B_FRS_c)) + (ss_AOS_corn * (e_s_AOS_cc * EP_corn + e_s_AOS_cs * EP_soy + e_s_AOS_cw * EP_wheat + e_s_AOS_cr * EP_rice + e_s_AOS_cp * EP_peanut + B_AOS_c)))),
Eq(EP_soy * e_d_soy + (EP_soy) * (ss_exports_soy * e_e_Soy - ss_imports_soy *e_i_Soy), ((ss_FRS_soy * (e_s_FRS_sc * EP_corn + e_s_FRS_ss * EP_soy + e_s_FRS_sw * EP_wheat + e_s_FRS_sr * EP_rice + e_s_FRS_sp * EP_peanut + B_FRS_s)) + (ss_AOS_soy * (e_s_AOS_sc * EP_corn + e_s_AOS_ss * EP_soy + e_s_AOS_sw * EP_wheat + e_s_AOS_sr * EP_rice + e_s_AOS_sp * EP_peanut + B_AOS_s)))),
Eq(EP_wheat * e_d_wheat + (EP_wheat) * (ss_exports_wheat * e_e_Wheat - ss_imports_wheat *e_i_Wheat), ((ss_FRS_wheat * (e_s_FRS_wc * EP_corn + e_s_FRS_ws * EP_soy + e_s_FRS_ww * EP_wheat + e_s_FRS_wr * EP_rice + e_s_FRS_wp * EP_peanut + B_FRS_w)) + (ss_AOS_wheat * (e_s_AOS_wc * EP_corn + e_s_AOS_ws * EP_soy + e_s_AOS_ww * EP_wheat + e_s_AOS_wr * EP_rice + e_s_AOS_wp * EP_peanut + B_AOS_w)))),
Eq(EP_rice * e_d_peanut + (EP_rice) * (ss_exports_rice * e_e_Rice - ss_imports_rice *e_i_Rice), ((ss_FRS_rice * (e_s_FRS_rc * EP_corn + e_s_FRS_rs * EP_soy + e_s_FRS_rw * EP_wheat + e_s_FRS_rr * EP_rice + e_s_FRS_rp * EP_peanut + B_FRS_r)) + (ss_AOS_rice * (e_s_AOS_rc * EP_corn + e_s_AOS_rs * EP_soy + e_s_AOS_rw * EP_wheat + e_s_AOS_rr * EP_rice + e_s_AOS_rp * EP_peanut + B_AOS_r)))),
Eq(EP_peanut * e_d_peanut + (EP_peanut) * (ss_exports_peanut * e_e_Peanuts - ss_imports_peanut *e_i_Peanuts), ((ss_FRS_peanuts * (e_s_FRS_pc * EP_corn + e_s_FRS_ps * EP_soy + e_s_FRS_pw * EP_wheat + e_s_FRS_pr * EP_rice + e_s_FRS_pp * EP_peanut + B_FRS_p)) + (ss_AOS_peanuts * (e_s_AOS_pc * EP_corn + e_s_AOS_ps * EP_soy + e_s_AOS_pw * EP_wheat + e_s_AOS_pr * EP_rice + e_s_AOS_pp * EP_peanut + B_AOS_p)))) ]'
)
sympy('corn = Eq(EP_corn * e_d_corn + (EP_corn) * (ss_exports_corn * e_e_Corn - ss_imports_corn *e_i_Corn), ((ss_FRS_corn * (e_s_FRS_cc * EP_corn + e_s_FRS_cs * EP_soy + e_s_FRS_cw * EP_wheat + e_s_FRS_cr * EP_rice + e_s_FRS_cp * EP_peanut + B_FRS_c)) + (ss_AOS_corn * (e_s_AOS_cc * EP_corn + e_s_AOS_cs * EP_soy + e_s_AOS_cw * EP_wheat + e_s_AOS_cr * EP_rice + e_s_AOS_cp * EP_peanut + B_AOS_c))))')
sympy('soy = Eq(EP_soy * e_d_soy + (EP_soy) * (ss_exports_soy * e_e_Soy - ss_imports_soy *e_i_Soy), ((ss_FRS_soy * (e_s_FRS_sc * EP_corn + e_s_FRS_ss * EP_soy + e_s_FRS_sw * EP_wheat + e_s_FRS_sr * EP_rice + e_s_FRS_sp * EP_peanut + B_FRS_s)) + (ss_AOS_soy * (e_s_AOS_sc * EP_corn + e_s_AOS_ss * EP_soy + e_s_AOS_sw * EP_wheat + e_s_AOS_sr * EP_rice + e_s_AOS_sp * EP_peanut + B_AOS_s))))')
sympy('wheat = Eq(EP_wheat * e_d_wheat + (EP_wheat) * (ss_exports_wheat * e_e_Wheat - ss_imports_wheat *e_i_Wheat), ((ss_FRS_wheat * (e_s_FRS_wc * EP_corn + e_s_FRS_ws * EP_soy + e_s_FRS_ww * EP_wheat + e_s_FRS_wr * EP_rice + e_s_FRS_wp * EP_peanut + B_FRS_w)) + (ss_AOS_wheat * (e_s_AOS_wc * EP_corn + e_s_AOS_ws * EP_soy + e_s_AOS_ww * EP_wheat + e_s_AOS_wr * EP_rice + e_s_AOS_wp * EP_peanut + B_AOS_w))))')
sympy('rice = Eq(EP_rice * e_d_peanut + (EP_rice) * (ss_exports_rice * e_e_Rice - ss_imports_rice *e_i_Rice), ((ss_FRS_rice * (e_s_FRS_rc * EP_corn + e_s_FRS_rs * EP_soy + e_s_FRS_rw * EP_wheat + e_s_FRS_rr * EP_rice + e_s_FRS_rp * EP_peanut + B_FRS_r)) + (ss_AOS_rice * (e_s_AOS_rc * EP_corn + e_s_AOS_rs * EP_soy + e_s_AOS_rw * EP_wheat + e_s_AOS_rr * EP_rice + e_s_AOS_rp * EP_peanut + B_AOS_r))))')
sympy('peanut = Eq(EP_peanut * e_d_peanut + (EP_peanut) * (ss_exports_peanut * e_e_Peanuts - ss_imports_peanut *e_i_Peanuts), ((ss_FRS_peanuts * (e_s_FRS_pc * EP_corn + e_s_FRS_ps * EP_soy + e_s_FRS_pw * EP_wheat + e_s_FRS_pr * EP_rice + e_s_FRS_pp * EP_peanut + B_FRS_p)) + (ss_AOS_peanuts * (e_s_AOS_pc * EP_corn + e_s_AOS_ps * EP_soy + e_s_AOS_pw * EP_wheat + e_s_AOS_pr * EP_rice + e_s_AOS_pp * EP_peanut + B_AOS_p))))')
sympy('corn = corn.subs([
(e_d_corn,-0.696), (e_d_soy,-0.065), (e_d_wheat,-0.202), (e_d_rice,-0.065), (e_d_peanut,-0.235),
(ss_AOS_corn,0.94), (ss_FRS_corn,0.06),
(ss_AOS_soy,0.88), (ss_FRS_soy,0.12),
(ss_AOS_wheat,0.90), (ss_FRS_wheat,0.10),
(ss_AOS_rice,0.24), (ss_FRS_rice,0.76),
(ss_AOS_peanuts,0.03), (ss_FRS_peanuts,0.97),
(ss_imports_corn,0.01), (ss_imports_soy,0.02), (ss_imports_wheat,0.12), (ss_imports_rice,0.17), (ss_imports_peanut,0.03),
(ss_exports_corn,0.14), (ss_exports_soy,0.83), (ss_exports_wheat,0.80), (ss_exports_rice,0.84), (ss_exports_peanut,0.23),
(B_AOS_c,0),(B_AOS_s,0),(B_AOS_w,0),(B_AOS_r,0),(B_AOS_p,0),
(B_FRS_c,0.0147),(B_FRS_s,0.005),(B_FRS_w,0.0166),(B_FRS_r,0.0046),(B_FRS_p,0.018),
(e_e_Corn,-1.20),(e_e_Soy,-2.50),(e_e_Wheat,-0.85),(e_e_Rice,-2.62),(e_e_Peanuts,-1.00),
(e_i_Corn,0.50),(e_i_Soy,0.50),(e_i_Wheat,0.50),(e_i_Rice,0.40),(e_i_Peanuts,0.50),
(e_s_AOS_cc,0.20),(e_s_AOS_cs,-0.11),(e_s_AOS_cw,-0.00),(e_s_AOS_cr,0),(e_s_AOS_cp,0),
(e_s_AOS_sc,-0.17),(e_s_AOS_ss,0.15),(e_s_AOS_sw,-0.01),(e_s_AOS_sr,-0.00),(e_s_AOS_sp,0),
(e_s_AOS_wc,-0.15),(e_s_AOS_ws,-0.11),(e_s_AOS_ww,0.20),(e_s_AOS_wr,-0.00),(e_s_AOS_wp,0),
(e_s_AOS_rc,-0.16),(e_s_AOS_rs,-0.12),(e_s_AOS_rw,-0.01),(e_s_AOS_rr,0.24),(e_s_AOS_rp,0),
(e_s_AOS_pc,0),(e_s_AOS_ps,0),(e_s_AOS_pw,0),(e_s_AOS_pr,0),(e_s_AOS_pp,0.35),
(e_s_FRS_cc,0.33),(e_s_FRS_cs,-0.04),(e_s_FRS_cw,-0.00),(e_s_FRS_cr,-0.03),(e_s_FRS_cp,0),
(e_s_FRS_sc,-0.03),(e_s_FRS_ss,0.19),(e_s_FRS_sw,-0.01 ),(e_s_FRS_sr,-0.10 ),(e_s_FRS_sp,0),
(e_s_FRS_wc,-0.02),(e_s_FRS_ws,-0.05 ),(e_s_FRS_ww,0.33),(e_s_FRS_wr,-0.04 ),(e_s_FRS_wp,0),
(e_s_FRS_rc,-0.01 ), (e_s_FRS_rs,-0.05), (e_s_FRS_rw,-0.00 ), (e_s_FRS_rr,0.47),(e_s_FRS_rp,0),
(e_s_FRS_pc,0),(e_s_FRS_ps,0),(e_s_FRS_pw,0),(e_s_FRS_pr,0),(e_s_FRS_pp,0.35)
])')
sympy('soy = soy.subs([
(e_d_corn,-0.696), (e_d_soy,-0.065), (e_d_wheat,-0.202), (e_d_rice,-0.065), (e_d_peanut,-0.235),
(ss_AOS_corn,0.94), (ss_FRS_corn,0.06),
(ss_AOS_soy,0.88), (ss_FRS_soy,0.12),
(ss_AOS_wheat,0.90), (ss_FRS_wheat,0.10),
(ss_AOS_rice,0.24), (ss_FRS_rice,0.76),
(ss_AOS_peanuts,0.03), (ss_FRS_peanuts,0.97),
(ss_imports_corn,0.01), (ss_imports_soy,0.02), (ss_imports_wheat,0.12), (ss_imports_rice,0.17), (ss_imports_peanut,0.03),
(ss_exports_corn,0.14), (ss_exports_soy,0.83), (ss_exports_wheat,0.80), (ss_exports_rice,0.84), (ss_exports_peanut,0.23),
(B_AOS_c,0),(B_AOS_s,0),(B_AOS_w,0),(B_AOS_r,0),(B_AOS_p,0),
(B_FRS_c,0.0147),(B_FRS_s,0.005),(B_FRS_w,0.0166),(B_FRS_r,0.0046),(B_FRS_p,0.018),
(e_e_Corn,-1.20),(e_e_Soy,-2.50),(e_e_Wheat,-0.85),(e_e_Rice,-2.62),(e_e_Peanuts,-1.00),
(e_i_Corn,0.50),(e_i_Soy,0.50),(e_i_Wheat,0.50),(e_i_Rice,0.40),(e_i_Peanuts,0.50),
(e_s_AOS_cc,0.20),(e_s_AOS_cs,-0.11),(e_s_AOS_cw,-0.00),(e_s_AOS_cr,0),(e_s_AOS_cp,0),
(e_s_AOS_sc,-0.17),(e_s_AOS_ss,0.15),(e_s_AOS_sw,-0.01),(e_s_AOS_sr,-0.00),(e_s_AOS_sp,0),
(e_s_AOS_wc,-0.15),(e_s_AOS_ws,-0.11),(e_s_AOS_ww,0.20),(e_s_AOS_wr,-0.00),(e_s_AOS_wp,0),
(e_s_AOS_rc,-0.16),(e_s_AOS_rs,-0.12),(e_s_AOS_rw,-0.01),(e_s_AOS_rr,0.24),(e_s_AOS_rp,0),
(e_s_AOS_pc,0),(e_s_AOS_ps,0),(e_s_AOS_pw,0),(e_s_AOS_pr,0),(e_s_AOS_pp,0.35),
(e_s_FRS_cc,0.33),(e_s_FRS_cs,-0.04),(e_s_FRS_cw,-0.00),(e_s_FRS_cr,-0.03),(e_s_FRS_cp,0),
(e_s_FRS_sc,-0.03),(e_s_FRS_ss,0.19),(e_s_FRS_sw,-0.01 ),(e_s_FRS_sr,-0.10 ),(e_s_FRS_sp,0),
(e_s_FRS_wc,-0.02),(e_s_FRS_ws,-0.05 ),(e_s_FRS_ww,0.33),(e_s_FRS_wr,-0.04 ),(e_s_FRS_wp,0),
(e_s_FRS_rc,-0.01 ), (e_s_FRS_rs,-0.05), (e_s_FRS_rw,-0.00 ), (e_s_FRS_rr,0.47),(e_s_FRS_rp,0),
(e_s_FRS_pc,0),(e_s_FRS_ps,0),(e_s_FRS_pw,0),(e_s_FRS_pr,0),(e_s_FRS_pp,0.35)
])')
sympy('wheat = wheat.subs([
(e_d_corn,-0.696), (e_d_soy,-0.065), (e_d_wheat,-0.202), (e_d_rice,-0.065), (e_d_peanut,-0.235),
(ss_AOS_corn,0.94), (ss_FRS_corn,0.06),
(ss_AOS_soy,0.88), (ss_FRS_soy,0.12),
(ss_AOS_wheat,0.90), (ss_FRS_wheat,0.10),
(ss_AOS_rice,0.24), (ss_FRS_rice,0.76),
(ss_AOS_peanuts,0.03), (ss_FRS_peanuts,0.97),
(ss_imports_corn,0.01), (ss_imports_soy,0.02), (ss_imports_wheat,0.12), (ss_imports_rice,0.17), (ss_imports_peanut,0.03),
(ss_exports_corn,0.14), (ss_exports_soy,0.83), (ss_exports_wheat,0.80), (ss_exports_rice,0.84), (ss_exports_peanut,0.23),
(B_AOS_c,0),(B_AOS_s,0),(B_AOS_w,0),(B_AOS_r,0),(B_AOS_p,0),
(B_FRS_c,0.0147),(B_FRS_s,0.005),(B_FRS_w,0.0166),(B_FRS_r,0.0046),(B_FRS_p,0.018),
(e_e_Corn,-1.20),(e_e_Soy,-2.50),(e_e_Wheat,-0.85),(e_e_Rice,-2.62),(e_e_Peanuts,-1.00),
(e_i_Corn,0.50),(e_i_Soy,0.50),(e_i_Wheat,0.50),(e_i_Rice,0.40),(e_i_Peanuts,0.50),
(e_s_AOS_cc,0.20),(e_s_AOS_cs,-0.11),(e_s_AOS_cw,-0.00),(e_s_AOS_cr,0),(e_s_AOS_cp,0),
(e_s_AOS_sc,-0.17),(e_s_AOS_ss,0.15),(e_s_AOS_sw,-0.01),(e_s_AOS_sr,-0.00),(e_s_AOS_sp,0),
(e_s_AOS_wc,-0.15),(e_s_AOS_ws,-0.11),(e_s_AOS_ww,0.20),(e_s_AOS_wr,-0.00),(e_s_AOS_wp,0),
(e_s_AOS_rc,-0.16),(e_s_AOS_rs,-0.12),(e_s_AOS_rw,-0.01),(e_s_AOS_rr,0.24),(e_s_AOS_rp,0),
(e_s_AOS_pc,0),(e_s_AOS_ps,0),(e_s_AOS_pw,0),(e_s_AOS_pr,0),(e_s_AOS_pp,0.35),
(e_s_FRS_cc,0.33),(e_s_FRS_cs,-0.04),(e_s_FRS_cw,-0.00),(e_s_FRS_cr,-0.03),(e_s_FRS_cp,0),
(e_s_FRS_sc,-0.03),(e_s_FRS_ss,0.19),(e_s_FRS_sw,-0.01 ),(e_s_FRS_sr,-0.10 ),(e_s_FRS_sp,0),
(e_s_FRS_wc,-0.02),(e_s_FRS_ws,-0.05 ),(e_s_FRS_ww,0.33),(e_s_FRS_wr,-0.04 ),(e_s_FRS_wp,0),
(e_s_FRS_rc,-0.01 ), (e_s_FRS_rs,-0.05), (e_s_FRS_rw,-0.00 ), (e_s_FRS_rr,0.47),(e_s_FRS_rp,0),
(e_s_FRS_pc,0),(e_s_FRS_ps,0),(e_s_FRS_pw,0),(e_s_FRS_pr,0),(e_s_FRS_pp,0.35)
])')
sympy('rice = rice.subs([
(e_d_corn,-0.696), (e_d_soy,-0.065), (e_d_wheat,-0.202), (e_d_rice,-0.065), (e_d_peanut,-0.235),
(ss_AOS_corn,0.94), (ss_FRS_corn,0.06),
(ss_AOS_soy,0.88), (ss_FRS_soy,0.12),
(ss_AOS_wheat,0.90), (ss_FRS_wheat,0.10),
(ss_AOS_rice,0.24), (ss_FRS_rice,0.76),
(ss_AOS_peanuts,0.03), (ss_FRS_peanuts,0.97),
(ss_imports_corn,0.01), (ss_imports_soy,0.02), (ss_imports_wheat,0.12), (ss_imports_rice,0.17), (ss_imports_peanut,0.03),
(ss_exports_corn,0.14), (ss_exports_soy,0.83), (ss_exports_wheat,0.80), (ss_exports_rice,0.84), (ss_exports_peanut,0.23),
(B_AOS_c,0),(B_AOS_s,0),(B_AOS_w,0),(B_AOS_r,0),(B_AOS_p,0),
(B_FRS_c,0.0147),(B_FRS_s,0.005),(B_FRS_w,0.0166),(B_FRS_r,0.0046),(B_FRS_p,0.018),
(e_e_Corn,-1.20),(e_e_Soy,-2.50),(e_e_Wheat,-0.85),(e_e_Rice,-2.62),(e_e_Peanuts,-1.00),
(e_i_Corn,0.50),(e_i_Soy,0.50),(e_i_Wheat,0.50),(e_i_Rice,0.40),(e_i_Peanuts,0.50),
(e_s_AOS_cc,0.20),(e_s_AOS_cs,-0.11),(e_s_AOS_cw,-0.00),(e_s_AOS_cr,0),(e_s_AOS_cp,0),
(e_s_AOS_sc,-0.17),(e_s_AOS_ss,0.15),(e_s_AOS_sw,-0.01),(e_s_AOS_sr,-0.00),(e_s_AOS_sp,0),
(e_s_AOS_wc,-0.15),(e_s_AOS_ws,-0.11),(e_s_AOS_ww,0.20),(e_s_AOS_wr,-0.00),(e_s_AOS_wp,0),
(e_s_AOS_rc,-0.16),(e_s_AOS_rs,-0.12),(e_s_AOS_rw,-0.01),(e_s_AOS_rr,0.24),(e_s_AOS_rp,0),
(e_s_AOS_pc,0),(e_s_AOS_ps,0),(e_s_AOS_pw,0),(e_s_AOS_pr,0),(e_s_AOS_pp,0.35),
(e_s_FRS_cc,0.33),(e_s_FRS_cs,-0.04),(e_s_FRS_cw,-0.00),(e_s_FRS_cr,-0.03),(e_s_FRS_cp,0),
(e_s_FRS_sc,-0.03),(e_s_FRS_ss,0.19),(e_s_FRS_sw,-0.01 ),(e_s_FRS_sr,-0.10 ),(e_s_FRS_sp,0),
(e_s_FRS_wc,-0.02),(e_s_FRS_ws,-0.05 ),(e_s_FRS_ww,0.33),(e_s_FRS_wr,-0.04 ),(e_s_FRS_wp,0),
(e_s_FRS_rc,-0.01 ), (e_s_FRS_rs,-0.05), (e_s_FRS_rw,-0.00 ), (e_s_FRS_rr,0.47),(e_s_FRS_rp,0),
(e_s_FRS_pc,0),(e_s_FRS_ps,0),(e_s_FRS_pw,0),(e_s_FRS_pr,0),(e_s_FRS_pp,0.35)
])')
sympy('peanut = peanut.subs([
(e_d_corn,-0.696), (e_d_soy,-0.065), (e_d_wheat,-0.202), (e_d_rice,-0.065), (e_d_peanut,-0.235),
(ss_AOS_corn,0.94), (ss_FRS_corn,0.06),
(ss_AOS_soy,0.88), (ss_FRS_soy,0.12),
(ss_AOS_wheat,0.90), (ss_FRS_wheat,0.10),
(ss_AOS_rice,0.24), (ss_FRS_rice,0.76),
(ss_AOS_peanuts,0.03), (ss_FRS_peanuts,0.97),
(ss_imports_corn,0.01), (ss_imports_soy,0.02), (ss_imports_wheat,0.12), (ss_imports_rice,0.17), (ss_imports_peanut,0.03),
(ss_exports_corn,0.14), (ss_exports_soy,0.83), (ss_exports_wheat,0.80), (ss_exports_rice,0.84), (ss_exports_peanut,0.23),
(B_AOS_c,0),(B_AOS_s,0),(B_AOS_w,0),(B_AOS_r,0),(B_AOS_p,0),
(B_FRS_c,0.0147),(B_FRS_s,0.005),(B_FRS_w,0.0166),(B_FRS_r,0.0046),(B_FRS_p,0.018),
(e_e_Corn,-1.20),(e_e_Soy,-2.50),(e_e_Wheat,-0.85),(e_e_Rice,-2.62),(e_e_Peanuts,-1.00),
(e_i_Corn,0.50),(e_i_Soy,0.50),(e_i_Wheat,0.50),(e_i_Rice,0.40),(e_i_Peanuts,0.50),
(e_s_AOS_cc,0.20),(e_s_AOS_cs,-0.11),(e_s_AOS_cw,-0.00),(e_s_AOS_cr,0),(e_s_AOS_cp,0),
(e_s_AOS_sc,-0.17),(e_s_AOS_ss,0.15),(e_s_AOS_sw,-0.01),(e_s_AOS_sr,-0.00),(e_s_AOS_sp,0),
(e_s_AOS_wc,-0.15),(e_s_AOS_ws,-0.11),(e_s_AOS_ww,0.20),(e_s_AOS_wr,-0.00),(e_s_AOS_wp,0),
(e_s_AOS_rc,-0.16),(e_s_AOS_rs,-0.12),(e_s_AOS_rw,-0.01),(e_s_AOS_rr,0.24),(e_s_AOS_rp,0),
(e_s_AOS_pc,0),(e_s_AOS_ps,0),(e_s_AOS_pw,0),(e_s_AOS_pr,0),(e_s_AOS_pp,0.35),
(e_s_FRS_cc,0.33),(e_s_FRS_cs,-0.04),(e_s_FRS_cw,-0.00),(e_s_FRS_cr,-0.03),(e_s_FRS_cp,0),
(e_s_FRS_sc,-0.03),(e_s_FRS_ss,0.19),(e_s_FRS_sw,-0.01 ),(e_s_FRS_sr,-0.10 ),(e_s_FRS_sp,0),
(e_s_FRS_wc,-0.02),(e_s_FRS_ws,-0.05 ),(e_s_FRS_ww,0.33),(e_s_FRS_wr,-0.04 ),(e_s_FRS_wp,0),
(e_s_FRS_rc,-0.01 ), (e_s_FRS_rs,-0.05), (e_s_FRS_rw,-0.00 ), (e_s_FRS_rr,0.47),(e_s_FRS_rp,0),
(e_s_FRS_pc,0),(e_s_FRS_ps,0),(e_s_FRS_pw,0),(e_s_FRS_pr,0),(e_s_FRS_pp,0.35)
])')
sympy('eqns = [corn,soy,wheat,rice,peanut]')
sympy('solve(eqns, EP_corn, EP_soy, EP_wheat, EP_rice, EP_peanut)')
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