# ============================================
# 關稅衝擊 + 投入產出 (Leontief) 經濟連鎖效應 模型
> []
關稅衝擊 + 投入產出 (Leontief) 經濟連鎖效應 模型# 作者：風海自知命
# ============================================

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

# ======== 模型參數 ========
# 技術係數矩陣 A (3產業toy示例，可自行替換為真實IO表數據)
A = np.array([
[0.2, 0.1, 0.0],
[0.05, 0.3, 0.1],
[0.0, 0.05, 0.25]
])

# 初始出口額 (sector0: 100, sector1: 50, sector2: 30)
export_values = np.array([100.0, 50.0, 30.0])

# 關稅檔位 (百分比)
tariff_rates = np.array([0.10, 0.15, 0.20, 0.25, 0.30, 0.35])

# 彈性情境 (低 / 中 / 高)
elasticities = [-0.8, -1.5, -2.5]

# ======== Leontief 逆矩陣 ========
I = np.eye(len(A))
L = np.linalg.inv(I - A) # Leontief inverse

# ======== 計算函數 ========
def calc_impact(tariff, elasticity, sector=0):
"""
tariff: 關稅 (小數)
elasticity: 貿易彈性 (負值)
sector: 出口衝擊發生在哪個產業
"""
# 出口下降百分比
delta_percent = elasticity * tariff
# 出口下降金額
delta_export = np.zeros(len(export_values))
delta_export[sector] = export_values[sector] * delta_percent
# 最終需求變動
delta_x = L.dot(delta_export)
return delta_percent*100, delta_x, delta_x.sum()

# ======== 計算所有情境 ========
results = []
for e in elasticities:
for t in tariff_rates:
pct, dx_vec, dx_sum = calc_impact(t, e, sector=0)
results.append({
"Elasticity": e,
"TariffRate": f"{int(t*100)}%",
"ExportChange(%)": round(pct, 2),
"Sector0": round(dx_vec[0], 2),
"Sector1": round(dx_vec[1], 2),
"Sector2": round(dx_vec[2], 2),
"TotalOutputChange": round(dx_sum, 2)
})

df = pd.DataFrame(results)

# ======== 顯示結果表 ========
print("=== 關稅衝擊與經濟連鎖效應（Toy IO 模型） ===")
print(df)

# ======== 繪圖 ========
fig, ax = plt.subplots(figsize=(8,6))
for e in elasticities:
subset = df[df["Elasticity"] == e]
ax.plot(subset["TariffRate"], subset["TotalOutputChange"], marker='o', label=f"Elasticity={e}")
ax.set_xlabel("Tariff Rate")
ax.set_ylabel("Total Output Change")
ax.set_title("Tariff Impact on Total Output (Toy IO Model)")
ax.legend()
plt.grid(True)
plt.show()