A model for interprovincial air pollution control based on futures prices

Figures & data

Table 1. Definitions of the variables and parameters

Variables and Parameters	Definition
Ri	Annual air pollution reduction quantity for province; i = 1, 2, …, N
R0i	Annual air pollutant quantity produced by province; i = 1, 2, …, N
R1i	Annual industrial air pollutant quantity produced by province; i = 1, 2, …, N
Qi	Air pollutant quota set by the government for province; i = 1, 2, …, N
S	Spot price of annual air emission rights
hi	Air pollutant reduction quota set by the government for province; i = 1, 2, …, N; hi = P0i − Ei
πi	Total environmental cost, including the pollutant reduction cost, environmental damage cost, and the transfer tax paid for province; i = 1, 2, …, N
ACi	Cost of air pollutant reduction for province; i = 1, 2, …, N; units: 10^4 USD.
Wi	Volume of emissions for province; i = 1, 2, …, N
αi	Multiplier for the upper limit of the air pollutants emission for province; i = 1, 2, …, N
βi	The upper limit of the pollutant reduction capacity for province; i = 1, 2, …, N
γi	The lower limit of the pollutant reduction capacity for province; i = 1, 2, …, N

Table 2. Beijing, Tianjin, and Hebei SO₂ reduction cost functions

Province	Reduction Cost Function
Beijing	AC1 = 35.19R1^1.835
Tianjin	AC2 = 4.13R2^2.323
Hebei	AC3 = 72.77R3^1.251

Notes: The unit for AC_i is 10⁴ USD; that for R_i is 10⁴ t.

Table 3. Benefit allocation to Beijing in 2013

S	Beijing	Beijing, Hebei
V(S)	0	3.19
V(S – {Beijing})	0	0
V(S) – V(S – {Beijing})	0	3.19
|S|	1	2
W(|S|)	1/2	1/2
W(|S|)[V(S) – V(S – {Beijing})]	0	1.60

Table 4. Benefit allocation to Hebei in 2013

S	Hebei	Hebei, Beijing
V(S)	0	3.19
V(S – {Hebei})	0	0
V(S) – V(S – {Hebei})	0	3.19
|S|	1	2
W(|S|)	1/2	1/2
W(|S|)[V(S) – V(S – {Hebei})]	0	1.60

Table 5. Comparison of the pollutant (SO₂) reduction costs in 2009

Parameter	Beijing	Tianjin	Hebei	Total
Current reduction (hi; 10^4 t)	7.2	24.8	117.5	149.5
Current environmental reduction cost (A; 10^4 $)	1317.08	7168.77	28287.06	36772.90
Optimal reduction in our model (pi*; 10^4 t)	7.2	17.5	124.8	149.5
Environmental reduction cost in the present model (B; 10^4 $)	1308.35	6174.47	27526.13	35008.95
A − B (10^4 $)	8.73	994.30	760.93	1763.95

Table 6. Sensitivity analysis for futures price

Futures Price Volatility	Futures Price ($/t)	Beijing (10^4 t)	Tianjin (10^4 t)	Hebei (10^4 t)	Total (10^4 $)	Saving
−20%	327.13	7.17	17.5	124.83	35008.07	4.80%
−10%	368.02	7.2	17.5	124.8	35008.95	4.80%
0.00%	408.91	7.2	17.5	124.8	35008.95	4.80%
10%	449.80	7.2	17.5	124.8	35008.95	4.80%
20%	490.69	7.2	18.59	123.71	35156.65	4.40%