Optimal Fare, Vacancy Rate, and Subsidies under Log-Linear Demand with the Consideration of Externalities for a Cruising Taxi Market

Table 2

Optimization results.

Variables	Solutions
	With no consideration of externality			With the consideration of externality
				e = 0.2779			e = 1.7680
Price elasticity of taxi demand ()	−1.4	−1	−0.78	−1.4	−1	−0.78	−1.4	−1	−0.78
Occupied distance (); (km/day)	5,756,306	22,657,728	44,971,503	5,780,323	22,726,929	45,083,479	5,914,402	23,113,859	45,711,208
Vacant distance (); (km/day)	826,300	3,711,662	7,907,173	821,311	3,686,661	7,851,246	796,573	3,562,023	7,571,859
Total operation distance; (km/day)	6,582,606	26,369,390	52,878,676	6,601,634	26,413,590	52,934,725	6,710,975	26,675,882	53,283,067
Vacancy rate () (%)	12.55	14.08	14.95	12.44	13.96	14.83	11.87	13.35	14.21
Fare (); (NTD/veh.-km)	20.416	20.416	20.416	20.350	20.350	20.350	19.994	19.994	19.994
Waiting time (); (min.)	2.141	2.021	0.949	9.132	2.034	0.955	9.415	2.106	0.991
Social welfare (); (NTD/day)	2.141 × 10^8	8.895 × 10^8	1.821 × 10^9	2.145 × 10^8	8.905 × 10^8	1.822 × 10^9	2.170 × 10^8	8.965 × 10^8	1.830 × 10^9
Net external benefit; (NTD/day)
e = 1.7680	9.467 × 10^6	3.726 × 10^7	7.396 × 10^7	9.506 × 10^6	3.738 × 10^7	7.414 × 10^7	9.727 × 10^6	3.801 × 10^7	7.518 × 10^7
e = 0.2779	1.488 × 10^6	5.857 × 10^6	1.163 × 10^7	1.494 × 10^6	5.875 × 10^6	1.165 × 10^7	1.529 × 10^6	5.975 × 10^6	1.182 × 10^7
Net external benefit difference (NTD/day)
e = 1.7680	0	0	0	3.951 × 10^4	1.139 × 10^5	1.842 × 10^5	2.601 × 10^5	7.504 × 10^5	1.217 × 10^6
e = 0.2779	0	0	0	6.210 × 10^3	1.790 × 10^4	2.896 × 10^4	4.088 × 10^4	1.180 × 10^5	1.91 × 10^5
Average operation cost; (NTD/veh.-km)	23.347	23.760	24.006	23.317	23.728	23.971	23.166	23.562	23.798
Subsidy (); (NTD/km)	2.931	3.344	3.590	2.967	3.378	3.622	3.172	3.568	3.804

Compared with the corresponding net external benefit without considering externality.