model_name = "mmm_0_5"
# Price-setting + Job Guarantee model, revised with:
#   * a productivity-aware nominal wage anchor,
#   * a positive target inflation rate,
#   * endogenous private wage bidding against the JG buffer,
#   * lagged private investment,
#   * a real-goods inventory cycle,
#   * finite JG enrolment speed rather than an exact algebraic mirror of firm employment.
#
# Units:
#   time   = year
#   labour = worker-years
#   nominal stocks/flows = currency units
#   V      = real private-goods inventory stock
#
# This remains a stylized MMT/post-Keynesian model, not a calibrated economy.

[parameters]
# ---------------------------------------------------------------------------
# Population and productivity
# ---------------------------------------------------------------------------
N0 = 100.0
beta = 0.01

A_F0 = 1.0
A_G0 = 1.0
A_JG0 = 0.5

alpha_F = 0.02
alpha_G = 0.02
alpha_JG = 0.01

# ---------------------------------------------------------------------------
# Nominal anchor and inflation objective
# ---------------------------------------------------------------------------
# The old fixed nominal JG wage combined with rising productivity forced
# unit labour cost downward and therefore generated persistent deflation.
# Here the policy wage grows with productivity + the target inflation rate.
w_JG0 = 0.60
pi_star = 0.02

# Regular public-service wage premium above the JG wage.
premium_G = 0.80

# Firms bid above the JG wage.  The premium rises when the JG buffer becomes
# small, representing tighter recruitment conditions.
premium_F_min = 0.35
premium_F_tight = 0.40
jg_wage_scale = 0.05
kappa_w = 1.0

p_goods_factor = 1.20

# ---------------------------------------------------------------------------
# Regular public services and procurement
# ---------------------------------------------------------------------------
q_G_pc0 = 0.12
gamma_G_service = 0.02
q_goods_pc = 0.10

# ---------------------------------------------------------------------------
# Taxes and household demand
# ---------------------------------------------------------------------------
r_H = 0.15
r_F = 0.05
c_w = 0.80
c_m = 0.02

# ---------------------------------------------------------------------------
# Private price setting, employment and investment
# ---------------------------------------------------------------------------
monopoly = 0.20
eta_p = 0.20
tau_P = 0.50

u_F_target = 0.90
kappa_L = 1.50

# Investment is now a state variable.  Its desired share responds to
# utilization, but only with a lag.
iota_base = 0.08
eta_I = 3.0
kappa_I = 0.30

# ---------------------------------------------------------------------------
# Inventory-cycle mechanism
# ---------------------------------------------------------------------------
# Firms hold a desired inventory equal to inventory_ratio years of current
# real private demand.  Production responds to inventory gaps with a lag.
# This is the principal endogenous business-cycle mechanism in this version.
inventory_ratio = 0.20
kappa_V = 0.80

# ---------------------------------------------------------------------------
# JG enrolment friction
# ---------------------------------------------------------------------------
# rho_JG is the fraction of otherwise-idle workers actually enrolled in JG.
# A high target preserves the guarantee interpretation while allowing a small
# open-unemployment/administrative transition margin.
rho_JG_target = 0.98
kappa_JG = 2.0


# ---------------------------------------------------------------------------
# Model-owned admissibility limits
# ---------------------------------------------------------------------------
[limits.parameters.u_F_target]
min = 0.0
min_inclusive = false
max = 1.0
description = "Target private-sector utilization must lie in (0,1]"

[limits.parameters.iota_base]
min = 0.0
max = 1.0
description = "Baseline gross investment share must lie in [0,1]"

[limits.parameters.rho_JG_target]
min = 0.0
max = 1.0
description = "Target JG enrolment fraction must lie in [0,1]"

[limits.initial_conditions.lambda_F]
min = 0.0
max = 1.0
description = "Initial firm-employment fraction must lie in [0,1]"

[limits.initial_conditions.rho_JG]
min = 0.0
max = 1.0
description = "Initial JG enrolment fraction must lie in [0,1]"

[limits.initial_conditions.iota_F]
min = 0.0
max = 1.0
description = "Initial investment share must lie in [0,1]"


[variables]
# P          private price level
# lambda_F   fraction of non-regular-government labour employed by firms
# w_F        nominal private wage
# iota_F     gross real investment share
# rho_JG     fraction of residual slack enrolled in the JG
# V          real private-goods inventory stock
# F_D,W_D    private financial positions
# G_N        signed consolidated government net financial position
names = ["P", "lambda_F", "w_F", "iota_F", "rho_JG", "V", "F_D", "W_D", "G_N"]


[initial_conditions]
P = 1.10
lambda_F = 0.95
w_F = 0.90
iota_F = 0.08
rho_JG = 0.95
V = 15.0
F_D = 100.0
W_D = 100.0
G_N = -200.0


[equations.auxiliary]
# ---------------------------------------------------------------------------
# Demography and productivity
# ---------------------------------------------------------------------------
N = "N0 * exp(beta*t)"
A_F = "A_F0 * exp(alpha_F*t)"
A_G = "A_G0 * exp(alpha_G*t)"
A_JG = "A_JG0 * exp(alpha_JG*t)"

# ---------------------------------------------------------------------------
# Government wage / price anchor
# ---------------------------------------------------------------------------
# A productivity-aware nominal anchor avoids automatic secular deflation.
w_JG = "w_JG0 * exp((alpha_F + pi_star)*t)"
w_G = "(1 + premium_G)*w_JG"
P_G = "p_goods_factor*w_JG/A_F"

# ---------------------------------------------------------------------------
# Regular public employment
# ---------------------------------------------------------------------------
q_G_pc = "q_G_pc0 * exp(gamma_G_service*t)"
Q_G_des = "q_G_pc*N"
L_G = "Q_G_des/A_G"

N_res = "N - L_G"
L_F = "lambda_F*N_res"
U3 = "N_res - L_F"

# JG is no longer an exact algebraic mirror of U3: rho_JG adjusts dynamically.
L_JG = "rho_JG*U3"
U_open = "U3 - L_JG"

L_total = "L_F + L_G + L_JG"

lambda_G = "L_G/N"
lambda_JG = "L_JG/N"
lambda_open = "U_open/N"
lambda_regular = "(L_F + L_G)/N"

# ---------------------------------------------------------------------------
# Private wage bidding against the buffer stock
# ---------------------------------------------------------------------------
# When the JG pool is small, firms face tighter recruitment conditions and
# bid a higher wage premium.  With a large JG buffer, the premium relaxes.
jg_tightness = "exp(-lambda_JG/jg_wage_scale)"
w_F_target = "w_JG*(1 + premium_F_min + premium_F_tight*jg_tightness)"

# ---------------------------------------------------------------------------
# Real output
# ---------------------------------------------------------------------------
Q_F = "A_F*L_F"
Q_G = "A_G*L_G"
Q_JG = "A_JG*L_JG"
Q_total = "Q_F + Q_G + Q_JG"

# ---------------------------------------------------------------------------
# Government spending
# ---------------------------------------------------------------------------
G_G = "w_G*L_G"
G_JG = "w_JG*L_JG"

Q_goods = "q_goods_pc*N"
G_goods = "P_G*Q_goods"
G_total = "G_G + G_JG + G_goods"

# ---------------------------------------------------------------------------
# Household income and consumption
# ---------------------------------------------------------------------------
W_F = "w_F*L_F"
W_all = "W_F + G_G + G_JG"

T_H = "r_H*W_all"
C = "c_w*(W_all - T_H) + c_m*W_D"

# ---------------------------------------------------------------------------
# Private investment and effective demand
# ---------------------------------------------------------------------------
I_real = "iota_F*Q_F"
I_nom = "P*I_real"

Sales_external = "C + G_goods"
Taxable_F = "Sales_external + I_nom"
T_F = "r_F*Taxable_F"
T_total = "T_H + T_F"

Q_demand = "C/P + Q_goods + I_real"
u_F = "Q_demand/Q_F"

# Desired investment share rises when utilization is above its normal level,
# and falls when utilization is weak.  Exponential form keeps the target > 0.
iota_target = "iota_base*exp(eta_I*(u_F - u_F_target))"

# ---------------------------------------------------------------------------
# Inventory cycle
# ---------------------------------------------------------------------------
V_target = "inventory_ratio*Q_demand"

# Firms produce for current demand plus an inventory-restocking correction.
Q_plan = "Q_demand + kappa_V*(V_target - V)"
Q_required = "Q_plan/u_F_target"

# Normalized labour-demand pressure.
excess = "(Q_required - Q_F)/(A_F*N_res)"

# ---------------------------------------------------------------------------
# Private pricing
# ---------------------------------------------------------------------------
P_unit_cost = "w_F/A_F"
P_target = "(1 + monopoly)*P_unit_cost*exp(eta_p*excess)"
pi_rate = "f_P/P"

# ---------------------------------------------------------------------------
# Fiscal / welfare diagnostics
# ---------------------------------------------------------------------------
S_NG = "G_total - T_total"
NFA_private = "F_D + W_D"

Y_exp_nom = "C + I_nom + G_goods + G_G + G_JG"
Y_real_pc = "Y_exp_nom/(P*N)"
C_real_pc = "C/(P*N)"


[godley]
# [source account, destination account, nominal flow/year, description]
# Investment remains an intra-firm-sector purchase at this aggregation level.
T1 = ["F_D", "W_D", "W_F", "Firm wages"]
T2 = ["G_N", "W_D", "G_G", "Regular public-service payroll"]
T3 = ["G_N", "W_D", "G_JG", "JG buffer payroll"]
T4 = ["G_N", "F_D", "G_goods", "Government purchases of private goods"]
T5 = ["W_D", "F_D", "C", "Household consumption purchases"]
T6 = ["W_D", "G_N", "T_H", "Household wage-income tax"]
T7 = ["F_D", "G_N", "T_F", "Firm turnover tax"]


[equations.ode]
# Price adjustment around private cost + markup.
f_P = "tau_P*(P_target - P)"

# Firm employment responds to demand plus inventory-restocking pressure.
f_lambda_F = "kappa_L*lambda_F*(1 - lambda_F)*excess"

# Private wages respond with a finite lag to buffer-stock tightness.
f_w_F = "kappa_w*(w_F_target - w_F)"

# Investment has its own accelerator/adjustment lag.
f_iota_F = "kappa_I*(iota_target - iota_F)"

# JG enrolment is rapid but not instantaneous.
f_rho_JG = "kappa_JG*(rho_JG_target - rho_JG)"

# Real inventory accumulation is production minus final private demand.
f_V = "Q_F - Q_demand"

# f_F_D, f_W_D and f_G_N are supplied from [godley].


[tspan]
t0 = 0.0
t1 = 50.0


[solver]
dt = 0.05
method = "Tsit5"
adaptive = false
output_dt = 0.1
abstol = 1e-8
reltol = 1e-6


[plots]
time_series = [
    "P", "pi_rate",
    "lambda_F", "lambda_JG",
    "lambda_G", "lambda_open",
    "u_F", "iota_F",
    "V", "V_target",
    "Y_real_pc", "C_real_pc",
    "F_D", "W_D"
]
combine_stability_lyapunov_plots = false


[eigenvalues]
all = false


[lyapunov]
enabled = true
renormalize_dt = 0.5
transient = 5.0