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Reports:

Bus subsidy simulation study

Appendix D: Profit Maximising Positions

This study has considered the incentive effects of the switch from FDR to a inactive IPP. In order to consider incentives it is necessary to consider the objectives of the organisations - in this case, the bus companies - that are facing the incentives.

We have done this by considering how IPP would move the operator away from their existing position - the crucial feature is the direction and strength of the move. In order to assess the strength of the incentive we have to find the point at which the firm would be maximising profits, either subject to a constraint such as fare or frequency fixed, or with fare, frequency and service quality all variable. From this point, we can then assess the strength of the move.

This Appendix provides the background to the discussion in Section 4.4 of the main text of the report. In Section 4.4 of the main report we indicated the "Day 1" change in profit maximising position starting, not as in Section 4.3 with the present profitmaximising position, but with profit-maximising positions predicted by our model under different constraints. In this Appendix we provide some additional background on those profit maximising positions.

It should be stressed that the key result is the extent to which profits increase once the operator changes its behaviour in response to the change in subsidy regime, and hence the extent to which this causes the operator to reduce fare and change frequency and service quality, so as to increase the demand for bus services.

Figure D.1 shows the situation where the operator is free to change fare, frequency and service quality. Figure D.2 shows the situation where fare is fixed. Figure D.3 shows the situation where frequency is fixed. Figure D.4 shows a comparison of the per cent change in profits for each route under each of these three situations. In general, the operators can best increase profits when they are free to vary all variables. However, if frequency is fixed (and it may well be relatively "sticky" in practice because frequency is not normally continuously variable), then the firm's profit-maximising profitability is in most (but not all) cases not strongly reduced. If fares are fixed, then the opportunity for the firm to increase profits from the initial, "Day 1", position is much reduced - and in this case where fares do not fall the switch from FDR to IPP will not have its main incentive effect. On the other hand, with frequencies fixed, but fares falling, the incentive effect of a fall in fares is reinforced with all the services which actually become less profitable with the subsidy switch.

Tables D.1, D.2 and D.3 below contain, respectively, the impact without constraints, the impact with fares constrained at their present level and the impact with frequency constrained at its present level. For each analysis and route, the following is shown:

  • Fares, frequency, quality, demand and profit under the current (FDR) position.
  • The current (FDR) profit-maximising combination of fares, frequency, quality, demand and profit.
  • The Day 1 impact on profits of a move from FDR to IPP. Only profits change in the Day 1 impact as the operator has not yet adjusted fares and service levels.
  • The profit-maximising combination of fares, frequency, quality, demand and profit under a per-passenger subsidy.

Table D.1: Detailed Modelled Operator Response - No Constraints


Average
revenue
per
passenger		Frequency
(buses
per
hour)		Quality levelPassengersProfit
Busy urban 1 Current position (FDR) £0.63 8.0 1.50 256919 £50,364
FDR profit maximising £0.80 6.1 2.69 190030 £66,087
Day 1 impact on profits £0.80 6.1 2.69 190030 £75,104
IPP profit maximising £0.76 6.4 2.75 207013 £75,644






Busy urban 2 Current position (FDR) £0.93 6.0 1.50 51583 3108
FDR profit maximising £1.17 4.2 1.74 32944 8080
Day 1 impact on profits £1.17 4.2 1.74 32944 8060
IPP profit maximising £1.14 4.1 1.75 33780 8098






Medium urban Current position (FDR) £0.90 3.0 1.50 37978 2983
FDR profit maximising £1.11 2.1 1.62 24667 6077
Day 1 impact on profits £1.11 2.1 1.62 24667 6077
IPP profit maximising £1.08 2.2 1.64 25935 6807






Marginal urban Current position (FDR) £1.02 5.0 1.00 31238 -£2,957
FDR profit maximising £1.36 3.0 1.63 17495 £3,806
Day 1 impact on profits £1.36 3.0 1.63 17495 £3,064
IPP profit maximising £1.34 2.9 1.62 17295 £3,086






Busy interurban 1 Current position (FDR) £0.86 1.0 1.00 43812 £4,457
FDR profit maximising £1.03 0.9 1.86 36364 £7,326
Day 1 impact on profits £1.03 0.9 1.86 36364 £6,013
IPP profit maximising £1.01 0.9 1.86 36376 £6,083






Busy interurban 2 Current position (FDR) £1.23 2.0 1.00 67888 £26,299
FDR profit maximising £1.43 2.2 2.45 68363 £33,927
Day 1 impact on profits £1.43 2.2 2.45 68363 £29,434
IPP profit maximising £1.42 2.1 2.44 67136 £29,618






Marginal interurban Current position (FDR) £0.82 2.0 2.00 59465 £1,223
FDR profit maximising £0.95 1.7 1.93 44574 £3,127
Day 1 impact on profits £0.95 1.7 1.93 44574 £2,437
IPP profit maximising £0.92 1.7 1.94 45777 £2,519






Loss-making interurban Current position (FDR) £2.28 1.0 1.50 9334 -£3,989
FDR profit maximising £2.72 0.7 1.55 5921 -£2,000
Day 1 impact on profits £2.72 0.7 1.55 5921 -£4,854
IPP profit maximising £2.66 0.6 1.51 5162 -£4,674






Rural Current position (FDR) £0.88 1.0 2.00 19206 £3,170
FDR profit maximising £1.01 0.8 1.52 14117 £4,221
Day 1 impact on profits £1.01 0.8 1.52 14117 £3,895
IPP profit maximising £0.98 0.8 1.53 14398 £3,923






Table D.2: Detailed Modelled Operator Response - Fares Constrained at Present Level


Average
revenue
per
passenger		Frequency
(buses
per
hour)		Quality levelPassengersProfit
Busy urban 1 Current position (FDR) £0.63 8.0 1.50 256919 £50,364
FDR profit maximising £0.63 7.5 2.39 265967 £54,943
Day 1 impact on profits £0.63 7.5 2.39 265967 £68,492
IPP profit maximising £0.63 7.6 2.55 269966 £68,590






Busy urban 2 Current position (FDR) £0.93 6.0 1.50 51583 3108
FDR profit maximising £0.93 4.6 1.44 44308 4747
Day 1 impact on profits £0.93 4.6 1.44 44308 5179
IPP profit maximising £0.93 4.6 1.46 44440 5180






Medium urban Current position (FDR) £0.90 3.0 1.50 37978 2983
FDR profit maximising £0.90 2.3 1.41 32605 4032
Day 1 impact on profits £0.90 2.3 1.41 32605 5185
IPP profit maximising £0.90 2.4 1.45 33324 5196






Marginal urban Current position (FDR) £1.02 5.0 1.00 31238 -£2,957
FDR profit maximising £1.02 1.8 1.27 13130 £311
Day 1 impact on profits £1.02 1.8 1.27 13130 -£83
IPP profit maximising £1.02 1.8 1.28 12819 -£80






Busy interurban 1 Current position (FDR) £0.86 1.0 1.00 43812 £4,457
FDR profit maximising £0.86 1.0 1.64 45188 £5,516
Day 1 impact on profits £0.86 1.0 1.64 45188 £4,506
IPP profit maximising £0.86 0.9 1.63 43814 £4,534






Busy interurban 2 Current position (FDR) £1.23 2.0 1.00 67888 £26,299
FDR profit maximising £1.23 2.4 2.31 82978 £31,300
Day 1 impact on profits £1.23 2.4 2.31 82978 £26,965
IPP profit maximising £1.23 2.3 2.27 80721 £27,090






Marginal interurban Current position (FDR) £0.82 2.0 2.00 59465 £1,223
FDR profit maximising £0.82 1.7 1.73 51063 £1,831
Day 1 impact on profits £0.82 1.7 1.73 51063 £1,644
IPP profit maximising £0.82 1.7 1.77 50788 £1,650






Loss-making interurban Current position (FDR) £2.28 1.0 1.50 9334 -£3,989
FDR profit maximising £2.28 0.7 1.41 6170 -£2,675
Day 1 impact on profits £2.28 0.7 1.41 6170 -£5,262
IPP profit maximising £2.28 0.6 1.41 5026 -£5,055






Rural Current position (FDR) £0.88 1.0 2.00 19206 £3,170
FDR profit maximising £0.88 0.9 1.45 16366 £3,859
Day 1 impact on profits £0.88 0.9 1.45 16366 £3,684
IPP profit maximising £0.88 0.8 1.46 16096 £3,687






Table D.3: Detailed Modelled Operator Response - Frequency Constrained at Current Level


Average
revenue
per
passenger		Frequency
(buses
per
hour)		Quality levelPassengersProfit
Busy urban 1 Current position (FDR) £0.63 8.0 1.50 256919 £50,364
FDR profit maximising £0.74 8.0 2.83 232310 £60,705
Day 1 impact on profits £0.74 8.0 2.83 232310 £71,089
IPP profit maximising £0.70 8.0 2.87 246350 £71,729






Busy urban 2 Current position (FDR) £0.93 6.0 1.50 51583 3108
FDR profit maximising £1.09 6.0 1.88 44746 4780
Day 1 impact on profits £1.09 6.0 1.88 44746 4522
IPP profit maximising £1.05 6.0 1.90 46444 £4596






Medium urban Current position (FDR) £0.90 3.0 1.50 37978 2983
FDR profit maximising £1.04 3.0 1.72 32981 £3978
Day 1 impact on profits £1.04 3.0 1.72 32981 £4786
IPP profit maximising £1.00 3.0 1.74 34359 £4849






Marginal urban Current position (FDR) £1.02 5.0 1.00 31238 -£2,957
FDR profit maximising £1.22 5.0 1.81 27476 -£540
Day 1 impact on profits £1.22 5.0 1.81 27476 -£1,936
IPP profit maximising £1.19 5.0 1.82 28228 -£1,906






Busy interurban 1 Current position (FDR) £0.86 1.0 1.00 43812 £4,457
FDR profit maximising £1.02 1.0 1.90 39225 £7,168
Day 1 impact on profits £1.02 1.0 1.90 39225 £5,710
IPP profit maximising £0.99 1.0 1.91 40563 £5,762






Busy interurban 2 Current position (FDR) £1.23 2.0 1.00 67888 £26,299
FDR profit maximising £1.45 2.0 2.40 62709 £33,410
Day 1 impact on profits £1.45 2.0 2.40 62709 £29,428
IPP profit maximising £1.43 2.0 2.41 64060 £29,471






Marginal interurban Current position (FDR) £0.82 2.0 2.00 59465 £1,223
FDR profit maximising £0.94 2.0 2.01 51477 £2,459
Day 1 impact on profits £0.94 2.0 2.01 51477 £1,602
IPP profit maximising £0.90 2.0 2.03 53669 £1,698






Loss-making interurban Current position (FDR) £2.28 1.0 1.50 9334 -£3,989
FDR profit maximising £2.68 1.0 1.64 7987 -£3,209
Day 1 impact on profits £2.68 1.0 1.64 7987 -£7,110
IPP profit maximising £2.66 1.0 1.65 8036 -£7,109






Rural Current position (FDR) £0.88 1.0 2.00 19206 £3,170
FDR profit maximising £0.99 1.0 1.56 16393 £3,957
Day 1 impact on profits £0.99 1.0 1.56 16393 £3,546
IPP profit maximising £0.96 1.0 1.57 17091 £3,577






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