The equity effect of road charges: 
calculating Lorenz curve differentials through sample enumeration  

By 
Lasse Fridstrøm, Ph.D., Managing Director
Harald Minken, Cand. Oecon., Chief Research Economist
Arild Vold, Dr. Scient., Senior Research Engineer 

Institute of Transport Economics (TØI)
Gaustadalléen 21
N-0349 Oslo, NORWAY

The equity effect of road charges: 
calculating Lorenz curve differentials through sample enumeration  

By 
Lasse Fridstrøm, Harald Minken, and Arild Vold
Institute of Transport Economics (TØI)
Gaustadalléen 21
N-0349 Oslo, NORWAY

Abstract
To investigate the equity effect of road pricing, a realistic transportation network modeling exercise has been undertaken, simulating a first-best road pricing strategy as well as various second-best strategies as implemented in the Oslo toll ring. The model predicts trip generation, destination choice, mode split, and route assignment, separately for the peak and off-peak periods. Relying on the prototypical sample enumeration technique, we subdivide the population in each zone into eight brackets defined in terms of household income per consumption unit. We compute costs, benefits, and demand effects within each income bracket and show how equity impacts can be described in terms of differential Lorenz curves and Gini coefficients.

1. INTRODUCTION 

A frequently cited argument against congestion charging and other forms of road tolls is that it is unfair to the less affluent, as these are less able to afford the extra cost imposed and hence more likely to suffer a deadweight loss in the event of higher costs of road use. To investigate the tenability of this argument, we use a realistic transportation network model to simulate a first-best road pricing strategy as well as various second-best strategies as implemented in the Oslo toll ring. The main purpose of this paper is to show how equity impacts can be assessed and interpreted in terms of differential Lorenz curves and Gini coefficients.

2. METHODOLOGY

The AFFORD project for the European Commission aimed to investigate the economic efficiency and equity effects of urban marginal cost pricing in transport, as well as its public, political and corporate acceptability. To this purpose, strategic and tactical transport model simulations have been run for the cities of Edinburgh, Helsinki, and Oslo (Fridstrøm et al 1999, 2000, 2001; Vold et al 2001a, b). In this paper, we focus on the general framework for equity impact assessment as illustrated by the Oslo case study.

2.1 Modeling framework
The RETRO model for the greater Oslo area is operated by the Institute of Transport Economics (TØI) in Norway. The model covers the city of Oslo and the municipalities of the surrounding county of Akershus, exhibiting 49 zones of residence and employment. The RETRO model predicts license holding and private car ownership. It also predicts – separately for the peak and off-peak periods – trip generation, destination choice, mode split, and route assignment. Being based on a disaggregate travel behavior survey, the model allows for the calculation of travel demand and economic welfare response indicators within separate population subgroups, through the so-called prototypical sample enumeration technique. 
In essence, this means that for each zone in the network, a set of weights is defined, in such a way that when these weights are applied to the disaggregate units (respondents) of a travel survey, the sample becomes «representative» of the zonal population in the sense of reproducing, at least approximately, the true zonal income distribution, as recorded in official statistics. A total of eight income brackets are defined and used in the calculations. 
Network assignment (route choice) is done by means of an EMME/2 application run in an iterative loop with the car ownership/travel demand submodel of RETRO. The EMME/2 network includes a total of 438 zones. The model base case is representative of the year 1995, and assume that cordon toll charges – if any – are collected at the same toll plazas that are currently in use. Note that these plazas have been located so as to maximize revenue rather than to optimize congestion charges.

2.2 First-best and second-best marginal cost pricing 
By definition, the first-best pricing policy is the unconstrained welfare optimum, in which one imagines that each traveler is charged the true marginal social cost of road use, as given by the level of congestion, environmental and accident costs generated by the marginal road user exactly there and then. 
By equating the marginal social cost to the marginal private cost, the first-best pricing policy induces all individual decision makers to make the socially most profitable choice, whenever they maximize their own utility or profit. This first-best pricing solution, however, presupposes a very sophisticated, real-time revenue collection and information system, in which road user charges vary instantaneously in space and time, i e between all road links and for every single minute, depending on the current level of congestion etc. 
This ideal road pricing scheme is only a theoretical construct, infeasible in practice. It can, however, be mimicked in a network simulation model, so that one may derive the theoretically optimal level of road user charges and their hypothetical effect on traveler behavior. To do this, we simply run a network assignment task in which, rather than the average private cost, we use the marginal social cost function as our volume-delay relationship. The equilibrium solution thus generated will also be a system optimum. 
Thus, although it is hard to imagine schemes by which true marginal cost pricing could be imposed on the road users in practice, it is – in principle – perfectly possible to describe such a situation with the help of a network assignment model. 
We use this theoretical first-best solution as an interesting benchmark case, against which the various feasible, second-best solutions – based on real-world policy instruments – can be judged. How far in the direction of the ideal, first-best solution are we able to move, when constrained by the pricing instruments actually available to policy makers? 
In general, by a second-best policy package we shall understand the optimal combination of policy instruments under the constraints represented by technology, geography, legislation, and institutional barriers.
These constraints may, of course, be defined in various ways, depending on the temporal and spatial horizon. In this paper we limit our attention to one particular second-best scenario, labeled second-best under current institutions. In this solution, economic efficiency is maximized with respect to cordon toll rates and time-differentiated parking charges. In Norway, both of these instruments are, in principle, available to the local government, hence their use requires no legislative changes or institutional reform. 

2.3 Efficiency assessment principles
The general methodological framework of this modeling exercise is an adaptation of standard cost-benefit analysis. Cost-benefit accounts are drawn up relative to a base case scenario. To find the optimal combination of second-best policy instruments, transport model output is used to calculate the elements of the cost-benefit accounts, and an optimization procedure is used to tune the policy instruments available to the levels that maximize the overall economic efficiency function. 
The general optimization principle applied is that of maximizing economic efficiency EE in the presence of externalities 
(1)	,
where UB is the benefit to transport users (consumer surplus), PSPS is the production surplus of private sector transport providers, EC denotes environmental costs (accidents, noise and pollution), NGS is net government surplus, i e the net financial benefit of the policy to government and publicly owned parking, tolling and public transport companies, and  denotes the «shadow price of public funds», i e the cost – in terms of economic efficiency – of raising one unit of public revenue through tax schemes other than road pricing. All terms are measured relative to the base case scenario and are net present values over 30 years.
Empirical estimates of the shadow price of public funds range at least from –0.2 to +0.8. In the analysis presented here, we have used the assumption , meaning that the distortionary cost of taxation is € 0.25 per euro levied. This is broadly in line with official guidelines in the Scandinavian countries at present.
In the subsequent cost-benefit analysis, we attempt to decompose the user benefit between various types of agents as shown in Table 1. Consumer surplus changes are calculated by means of the simplifying «rule-of-a-half». This widely used practice is a linear approximation to the change in consumer surplus. When dealing with strongly non-linear demand relations and large changes in market behavior, such as a massive shift from private to public transport, the rule-of-a-half may yield rather inaccurate results.
It has, however, the advantage that, if the generalized cost of travel (, say) takes the form of a linear combination of monetary and non-monetary terms, 
(2)	, 
then the rule-of-a-half can be written as an additively separable sum of monetary and non-monetary elements:
(3)	
Here,  and are the monetary and non-monetary (i e, time) costs, respectively, in situation k,  is the quantity demanded (i e, the amount of travel), and  is the conversion factor between time and money – the «value of time». 
It is, in other words, possible to calculate «money savings» and «time savings» as two separate quantities.
(Table 1 here)

2.4 Equity assessment principles
Having subdivided the population into eight brackets defined in terms of household income per consumption unit, we compute costs, benefits, and demand effects within each income bracket. Adding the consumer surplus (or deficit) generated to the initial mean income, we compute a «partial generalized income» (see below) before and after road pricing within each income bracket, and calculate the respective Lorenz curves and their associated Gini coefficient values in the respective scenarios.
The Lorenz curve, due to Lorenz (1905), relates the cumulative proportion of income units (x-axis) to the cumulative proportion of income received (y-axis), when units are arranged in ascending order of their income. It takes the form of a straight line through the origin with slope 1 (45-degree angle) if and only if all units in the population receive the same income. In all other cases the curve is a monotonously increasing, upward-bending line located beneath the straight line with a 45-degree angle. The lower the Lorenz curve, the more income is concentrated in the upper income brackets, and the less «equitable» is the distribution.
To fix ideas, we show – as an example – the Lorenz curve for Oslo-Akershus in the benchmark scenario (Figure 1). Income levels are grouped into 8 brackets, generally NOK 50 000 per annum wide. (NOK 8 = appr € 1.) The lowest bracket runs from zero to NOK 99, while the uppermost bracket includes incomes from NOK 300 000 upwards. 
(Figure 1 here.)
As shown by the Lorenz curve, the lowest 40 per cent of the adult population earn only 10 per cent of the total income.
Note, however, that this picture is conditioned by the fact that we use individual rather than household income. Many persons with low or zero income (students, housewives, etc) live in families with a fairly large household income. An analysis based on household income would most probably provide a less alarming picture of income inequality. 
Thus, in the equity analyses based in the Oslo model, for which disaggregate data are available on household income as well as on individual income, we prefer to draw the Lorenz curves in terms of household income per consumption unit, defined as follows. Each household member is assigned a weight, given by 1 for the household head (or the «first» adult person in the household), by 0.7 for any additional adult, and by 0.5 for children up to 17. With small variations, these weights are in line with international (OECD) recommendations for household consumer surveys. The number of consumption units is given by the sum of the weights assigned to all members of the household. 
When two distinct populations exhibit Lorenz curves such that one is uniformly located above the other, the former distribution (corresponding to the upper curve) is unambiguously more equitable. However, if the two Lorenz curves intersect, one inevitably needs to «trade» one segment of the income scale against another, in order to conclude which distribution is «more equitable».
One way to summarize the information contained in the Lorenz curve is by way of the Gini coefficient, due to Gini (1912). It is equal to twice the area between the 45-degree straight line and the Lorenz curve. The higher the Gini-coefficient, the larger is the «gap» between the actual and the maximally equitable distribution, and the less «equitable» is – in a sense – the distribution at hand. The Gini coefficient is bounded between zero and one: .
In Figure 1, we also show – for purposes of illustration – the impact of a hypothetical NOK 10 000 increase in annual income for all individuals (except those with zero income), as measured in terms of the Lorenz curve. One notes that the area between the Lorenz curve and the straight line has been slightly diminished – indicating a certain improvement in the income distribution.
The diagram in Figure 1 can be made more easily readable by rotating the curves 45 degrees clockwise (Figure 2).
(Figure 2 here)
Here, the «perfect equality» Lorenz curve takes the form of a straight line along the horizontal axis.
In most cases, the interest is not in comparing some empirical distribution to an ideal «perfect equality», but rather to compare two plausible, real-world situations. To this end, a diagram in which the «new» distribution is compared to an «old» («empirical») would bring out the differences even more clearly, as in Figure 3.
(Figure 3 here.)
Here, the old «empirical distribution» Lorenz curve takes the form of a straight line along the horizontal axis.
In the sequel, we shall apply this method of graphical illustration to show the equity impacts of the respective scenarios and of various way of recycling the toll and tax revenue to the population. 
We shall do this by first adding to the income of each bracket the monetary savings obtained by peak hour travelers (a+b in Table 1), then – in this order – the money savings accruing to off-peak travelers (f+g), the time savings of peak hour car drivers (c), the time savings of other travelers (d+e+h+i+j), and finally the toll and tax revenue redistributed to the tax payers according to some more or less progressive scheme. This stepwise, cumulative calculation is illustrated graphically in Figures 4 through 10 below.   
In doing this, we make the simplifying assumption that redistributing the revenue has only negligible feedback effects on behavioral choice. In a rigorous analysis, one would have to take into account that large income transfers will affect consumer behavior, notably in the labor market, and to a considerable extent also the choices made in the transport sector, such as car ownership and use. Such an analysis would, however, require a full-fledged general equilibrium model of the urban economy, something which has been beyond the scope of the present analysis. 
In general, the income increments and transfers simulated in our analyses are small compared to the initial levels of income. Thus the assumption of negligible feedback is probably an innocuous one.
It may be argued that it makes little sense to add together nominal gross income and some measure of consumer surplus, which includes all sorts of non-monetary benefits and utility components, such as time gains. In so doing, we implicitly define a kind of  partial generalized income, made up by the initial, nominal income and the consumer surplus changes generated by our policy. This is, of course, a simplified measure of welfare, in that the consumer surplus generated in the reference scenario is not included in the initial (generalized) income measure. We are therefore not able to say anything about the relative changes in welfare affecting the various income groups. However, as long as we restrict attention to differential effects on generalized income, the argument may be considered valid, if not at the ratio level of measurement, so at least on an interval scale. 

3. RESULTS

3.1 Economic efficiency 
Under the assumption of a 0.25 shadow price of public funds, the welfare gain obtainable from an ideal, first-best marginal cost road pricing scheme in Oslo has been calculated at € 199 per capita per annum over a 30-year period, starting in 1995.  
The second-best solution under current institutions for Oslo invokes the use of  cordon toll rates and parking charges, both of them differentiated between peak and off-peak. This policy achieves a € 56 per capita annual benefit, or 28 per cent of the first-best solution. 
This rather discouraging result must, however, be interpreted with some caution. We cannot rule out certain methodological explanations, such as the fact that our model specifies only two, rather crude travel time periods («peak» and «off-peak») and does not allow for substitution between them. Nor can we exclude the possibility that these results are strongly tainted by the particular traffic conditions in Oslo, notably by the location of the cordon toll ring, which is such as to maximize revenue rather than to restrain the traffic, and by the fact the toll revenue has facilitated massive improvement in the road network, to a point where congestion, as of 1995, was kept at a fairly moderate level.
In both scenarios, a major part of the social surplus is attributable to the value of additional public revenue: 65 per cent in the first-best case and no less than 96 per cent in second best scenario. If it were not for the extra value attached to these funds, the second best marginal cost pricing policy studied would have only modest welfare effects (see Fridstrøm et al 1999 for more details).  
Both scenarios are characterized by a negative travelers’ surplus before revenue recycling. If one assumes, however, that the net public revenue flow (toll, parking, and public transport operators’ surplus) is somehow (and costlessly) redistributed to the private consumers, even the second-best solution would imply a certain welfare improvement for the travelers. 

3.2 Equity effects 
3.2.1 First-best pricing 
A first impression of the equity impact of the first-best scenario for Oslo is given in Figure 4. Income brackets are defined in terms of household income per consumption unit, and the brackets are delimited in such a way that each group covers approximately one eighth of the adult population. That is, bracket 1 runs from zero income to the 12.5 income percentile, bracket 2 from the 12.5 to the 25th percentile, and so on.  
(Figure 4 here.)  
Under the assumption that the public revenue from road pricing is not redistributed to private consumers, but kept by the public authority, all income groups suffer a welfare loss as measured by the change in consumer surplus. The public authority, on the other hand, obtains a surplus which is larger than the total economic benefit arising.
In Figure 5, where the differential effects on «partial generalized income» are shown, this is brought out more clearly. Here, we have also added a last column representing the added net income accruing to all income groups if the revenue from road pricing is redistributed to the households in amounts proportional to each household initial income, i e as a constant percentage point tax relief to all income earners. 
(Figure 5 here.)
One notes that the monetary welfare loss incurred during the peak hour period, in terms of road charge expenditure and reduced amounts of travel, are larger in the higher income brackets (first bar in each group in Figure 5 – «Money savings peak added» – corresponding to items a and b of Table 1). The more affluent people are to a larger extent hit by peak hour road pricing. The off-peak charges, however, are much more evenly distributed between income groups, so that when all monetary costs are summed up (as in the second bar in Figure 5 – «All money savings added» – corresponding to items a and b plus items f and g of Table 1), the differences between income segments become less pronounced. Indeed, the third income bracket ends up incurring almost as large a monetary cost as the uppermost bracket. 
In the third column if Figure 5 («Road time savings peak also added»), we compound the monetary savings of column two and the peak hour time savings for motorists (item c of Table 1) in the various income groups. As might be expected, these time savings are generally larger among the more affluent. 
In the fourth column («All time and money savings added»), the entire consumer surplus change is included. By and large, the upper income brackets are seen to incur a larger welfare loss (prior to revenue recycling) due to first-best marginal cost pricing than do the lower income groups, at least in terms of absolute willingness-to-pay. 
Note, however, that our analyses do not take account of differences in the marginal utility of money. Since the marginal utility of money is generally higher among the less affluent, it may be argued that our efficiency and equity analyses, based as they are on a willingness-to-pay criterion, tend to be inherently biased against the interests of the poor. 
On the other hand, since transport time is a generic variable in the model, our analyses do not take into account the fact that the members of different income groups may exhibit different subjective values of time. Typically, on might imagine that high income earners value time at a higher rate than do low income earners. A recent ex ante study of the road pricing experiment in Stockholm (Eliasson and Mattsson 2006) suggests, however, that value of time differences are of minor importance to the equity impacts of road pricing in Stockholm. It is thought that this result would apply also in the Oslo context.
When the (differential) revenue and profit collected by the public treasury and operators are redistributed to the households in amounts proportional to each household’s initial income, i e as a given percentage point income tax relief, the upper income brackets are seen to reap a net welfare gain, while the opposite is true of the low income groups. 
These equity effects are also clearly visible in terms of Lorenz curve differentials, as shown in Figure 6, which is tailored to the standard introduced by Figure 3 above. The monetary welfare loss incurred by peak hour travelers has an only moderately adverse distributional effect, the Gini coefficient going from 0.19014 to 0.19105, while a much larger, adverse effect is due to off-peak traveling. The time gains, on the other hand, tend to reduce the adverse equity effect, shifting the Lorenz curve upwards compared to the situation before time benefits have been taken into account, and the changing Gini coefficient from 0.19502 to 0.19405. 
(Figure 6 here.)
Note that, by definition, a proportional redistribution of revenue does not change the Lorenz curve or the Gini coefficient. Thus Figure 6 also represents the situation after proportional redistribution, as shown in Figure 5.   
In Figures 7 and 8, however, we show the results of an alternative redistribution scheme, in which all individuals receive the same nominal amount of money, large enough (after tax) to exactly deplete the revenue generated by the road pricing policy. We shall refer to this redistribution scheme as a «poll transfer» or «flat» recycling.
(Figure 7 here.)
(Figure 8 here.)
With this kind of redistribution, all income groups receive a net welfare gain, and the lower income groups receive the largest gain, in relative as well as in absolute terms.  
This is indicated by a very clear improvement in the Gini index, which changes from 0.19405 to 0.18574 after flat redistribution of revenue. Thus, in terms of the Gini index, the poll transfer leads to an improvement in the income distribution which is more than twice as large as the deterioration due to marginal cost pricing (0.19405 – 0.19014), and about 9 times larger than the effect of the monetary consumer deficit (= 0.19105 –0.19014). 
Put otherwise, it would be sufficient to redistribute only a certain share of the revenue, in order to keep all income groups at least equally well off and the income distribution at least as even as before (in terms of the Gini coefficient). 
One might, however, question the coherence of an analysis which assumes flat revenue redistribution to the households, and at the same time includes a (non-zero) shadow value of public funds in the efficiency measure. Several interpretations are possible here.
If the redistribution is done in such a way that distortionary taxation is not reduced, there is no rationale for including the shadow value of public funds in the efficiency measure. In this case, we are faced with a clear-cut trade-off between efficiency and equity: the equity can be improved through redistribution, but only at the expense of more than half the efficiency gain obtained from the first-best marginal cost pricing strategy.  
If, on the other hand, the redistribution does contribute to reduce the incidence of distortionary taxation, at a rate equal to the assumed, average shadow price of public funds, the efficiency measure has been correctly calculated and will not be altered through the redistribution. In this case, the redistribution of income will improve efficiency in other markets, the total efficiency gain throughout the economy being given – precisely – by the shadow value of the public funds being redistributed. 
This relates to the argument given towards the end of Section 2.4 above, on the feedback effects generated from the rest of the economy. One might say that, by not correcting the efficiency measure for the recycling of revenue, we include in our policy assessment a summary measure of the efficiency gains obtainable from shifting the tax burden from distortionary taxation to road user charges. 
To the extent that the marginal tax on labor is distortionary, a redistribution scheme which lowers the marginal tax rate by a given number of percentage points, as in a «proportional» recycling scheme, would seem to qualify as a scheme which does not reduce overall efficiency. But this redistribution scheme does nothing to correct the income distribution. 
The «flat» redistribution scheme, on the other hand, would give equal amounts to all income brackets and hence not affect the marginal tax rate at all. This scheme certainly improves the income distribution, but hardly the allocative efficiency of the general economy. Indeed, it is quite possible that such a scheme might even worsen efficiency, to the extent, e g, that the poll transfer serves to reduce the supply of labor. In such a case, the relevant shadow price of public revenue would be negative.   
The trade-off between equity and efficiency thus seems to come back on us. It may seem that «good» (effective) redistribution schemes are bound to take something away from efficiency. 
It is fair to say, however, that – judging by the results obtained by the RETRO model for Oslo – the equity impact of first-best marginal cost pricing is relatively modest. It could, in principle, be neutralized through the redistribution of (part of) the public revenue generated. 

3.2.2 Second-best pricing
The equity impacts of another scenario for Oslo – the second-best under current  institutions – are illustrated in Figures 9 through 11.
Thus, in Figure 9 we show the differential effects of second-best pricing given a 0.25 shadow price of public funds and a proportional recycling scheme. This policy package, too, keeps the upper income groups at least equally well off, while the low income groups lose. The changes in welfare are generally smaller than under first-best pricing (confer Figure 5).  
(Figure 9 here.)
(Figure 10 here.)
On the other hand, income distribution effects are less severe (compare Figures 10 and 6). The Gini coefficient increases from 0.19014 to 0.19273 – an unfavourable but rather modest income distribution effect. 

3.3 Travel demand
In Figure 11, we show relative changes in the demand for car trips, public transport, and walking/bicycling, respectively, under the second-best scenario, i e under optimally time differentiated toll rates and parking charges.  
(Figure 11 here.)
Interestingly, our model simulation results show no indication that (second-best) marginal cost pricing affects the mobility of low income groups to a larger extent than people in the higher income brackets. The percentage change in travel by car is similar between all income brackets – in fact slightly higher in the upper income area. 
Since the upper income groups have a much higher car travel frequency to start with, especially during the rush hour, these relative changes translate into absolute changes in mobility that are even more disproportionate, in the sense of hitting the more affluent people «harder» than the low income groups. 
Also, the more affluent people tend to convert to public transport, walking or bicycling to a much larger extent than the poorer.

4. CONCLUDING REMARKS

It may be argued that road pricing schemes are unfair to the less affluent, who may not have the means to pay their way out of the situation and therefore incur a disproportionately large loss in the form of reduced mobility. Or, if they do find it worthwhile to pay the road price, they do so at a higher rate, in terms of utility, than the more affluent, because their marginal utility of income is higher than the average. They have to spend a larger share of their income in order to maintain the level of mobility. How tenable is this argument?
We have set out to provide a general framework for answering this question. The main elements of our approach are the following:  (i) We use a standard disaggregate travel demand modeling system distinguishing between (at least) two periods of travel per day. (ii)  Prototypical sample enumeration is used to account for the distribution of income groups in the respective zones. (iii) Account is taken of the marginal cost of public funds, as its affects the welfare optimum as well as any possible revenue redistribution scheme. (iv) The distributional effects of road pricing are described and analyzed through differential Lorenz curves and Gini coefficients, as defined in terms of household income per consumption unit before and after revenue redistribution. 
In our case, the analysis shows that road pricing does indeed have adverse income distribution effects, but that these effects can, in principle, be avoided if all or part of the road pricing revenue is redistributed to the households in a certain way. 
If the revenue is redistributed proportionately by personal income, i e as a given percentage point relief in the income tax rate, the Gini coefficient of income inequality is – by definition – unaltered from the level attained as a result of road pricing. If, on the other hand, the redistribution is done by means of a «poll transfer», i e by recycling the same, absolute amount of money to each adult individual, the Gini coefficient not only improves considerably, but even ends up at a much more favorable level than before the road pricing measures were implemented. 
Marginal cost road pricing has the double effect of discouraging congestion and raising public revenue. To the extent that public funds are a scarce resource, the latter effect may well be the more important as seen in an economic efficiency perspective. This is at least the case for optimal road pricing in a less heavily congested city like Oslo. 
If toll revenue is redistributed to the public in such a way, e g by a poll transfer, that it does not also reduce the excess burden of taxation, a major part of the economic benefit derived from marginal cost pricing will most probably be wasted. There is thus a real conflict between economic efficiency and equity objectives in the design of road pricing schemes. To enhance the acceptability of marginal cost pricing systems, it may, however, be necessary to envisage schemes by which the revenue collected from private motorists is at least partly redistributed to the public, in a way perceived as fair and equitable in relation to the income distribution. 
Interestingly, our modeling results show no indication that (second-best) marginal cost pricing affects the mobility of low income groups to a larger extent than people in the higher income brackets. The percentage change in travel by car is similar between all income brackets. In absolute terms, i e when counting the numbers of car trips suppressed per person, the high income families actually carry the larger burden. 
Thus, according to the Oslo model simulations, the unfavorable income distribution effect of road pricing is due, in its entirety, to the fact that the out-of-pocket expenditure on road charges represents a higher share of the household income in the low income groups than among the more affluent. 
Since transport time is a generic variable in the Oslo model, our analysis is unable to take account of the fact that the value of time varies between people in different income brackets. A recent ex ante study of the road pricing experiment in Stockholm suggests, however, that value of time differences are of minor importance to the equity impacts of road pricing in Stockholm. It is thought that this result would apply also in the Oslo context. 

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Table 1: Components of user benefits  

Trips	Money savings	                Time savings	
	Road	Public transport	Road	Public transport	Walking & cycling	
Peak hours	a	b	c	d	e	
Off peak	f	g	h	i	j	

CAPTIONS TO ILLUSTRATIONS

Figure 1: Lorenz curves for the adult population in Oslo-Akershus 1992. «New distribution» = NOK 10 000 annual increment for all. 
Figure 2: Rotated Lorenz curves for the adult population in Oslo-Akershus 1992. «New distribution» = NOK 10 000 annual increment for all. 
Figure 3: Lorenz curve differentials between the empirical distribution for Oslo-Akershus 1992 and a «new distribution» given by a NOK 10 000 annual increment for everyone. 
Figure 4: Effects of first-best marginal cost pricing, by partial generalized household income per consumption unit, assuming no redistribution of revenue. 
Figure 5: Differential effects of first-best marginal cost pricing, by partial generalized household income per consumption unit, assuming proportional redistribution of revenue. 
Figure 6: First-best scenario assuming no or proportional redistribution of revenue. Lorenz curve differentials defined in terms of partial generalized income. 
Figure 7: Differential effects of first-best marginal cost pricing, by partial generalized household income per consumption unit, assuming flat redistribution of revenue (poll transfer).
Figure 8: First-best scenario assuming flat redistribution of revenue (poll transfer). Lorenz curve differentials defined in terms of partial generalized income. 
Figure 9: Differential effects of second-best pricing under current institutions, by partial generalized household income per consumption unit, assuming proportional redistribution of revenue. 
Figure 10: Second-best scenario, assuming no or proportional redistribution of revenue. Lorenz curve differentials defined in terms of partial generalized income.  
Figure 11: Changes in trip frequency, by mode and income bracket, under the second-best scenario 

Figure 1: Lorenz curves for the adult population in Oslo-Akershus 1992. «New distribution» = NOK 10 000 annual increment for all. 

Figure 2: Rotated Lorenz curves for the adult population in Oslo-Akershus 1992. «New distribution» = NOK 10 000 annual increment for all. 

Figure 3: Lorenz curve differentials between the empirical distribution for Oslo-Akershus 1992 and a «new distribution» given by a NOK 10 000 annual increment for everyone. 

Figure 4: Effects of first-best marginal cost pricing, by partial generalized household income per consumption unit, assuming no redistribution of revenue. 

Figure 5: Differential effects of first-best marginal cost pricing, by partial generalized household income per consumption unit, assuming proportional redistribution of revenue. 

First best without redistribution 

-0.01

-0.008

-0.006

-0.004

-0.002

0

0.002

0.004

0.006

0.008

0.01

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Share of adult population

Share of income

Money savings peak added

All money savings added

All time and money savings added

Initial Gini=0.19014

Gini=0.19105

Gini=0.19502

Gini=0.19405

Figure 6: First-best scenario assuming no or proportional redistribution of revenue. Lorenz curve differentials defined in terms of partial generalized income. 

Figure 7: Differential effects of first-best marginal cost pricing, by partial generalized household income per consumption unit, assuming flat redistribution of revenue (poll transfer).

First best with flat redistribution (poll transfer) 

 

-0.01

-0.008

-0.006

-0.004

-0.002

0

0.002

0.004

0.006

0.008

0.01

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Share of adult population

Share of income

Money savings peak added

All money savings added

All time and money savings added

Flat redistribution

Gini=0.18574

Initial Gini =0.19014

Figure 8: First-best scenario assuming flat redistribution of revenue (poll transfer). Lorenz curve differentials defined in terms of partial generalized income,

 
Figure 9: Differential effects of second-best pricing under current institutions, by partial generalized household income per consumption unit, assuming proportional redistribution of revenue. 

Second best without redistribution

-0.016

-0.014

-0.012

-0.01

-0.008

-0.006

-0.004

-0.002

0

0.002

0.004

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Share of adult population

Share of income

Money savings peak added

All money savings added

All time and money savings added

Initial Gini=0.19014

Gini=0.19059

Gini=0.19319

Gini=0.19273

Figure 10: Second-best scenario, assuming no or proportional redistribution of revenue. Lorenz curve differentials defined in terms of partial generalized income. 

Figure 11: Changes in trip frequency, by mode and income bracket, under the second-best scenario 

FOOTNOTES