Andrew Nutter Economics Dr. Sällström
amfn2@cam.ac.uk 25/11/11
Part II: Paper 1, Microeconomics
Marginal Cost Pricing
a. ‘In a public enterprise such as the postal service, marginal cost pricing is irrelevant, since
production is characterised by increasing returns to scale.’ Discuss
From the founding work on marginal cost pricing of Harold Hotelling and Jules Dupuit’s writings on the
subject of maximising the benefits derived from public works, the polemical area of these two overlapping
themes has been one of great interest and activity. Generally speaking, public enterprises owe their
existence to market failures of some sort, where pricing systems fail to allocate resources “correctly”.
Juxtaposed to this concept is the idea that to maximise welfare, goods must be priced at marginal cost to be
“correctly” equated to marginal benefit. The two, it is advocated, should be combined to reach an optimal
arrangement. Just as a note, it strikes me that it is strange to use a type of method that is source of economic
failure to combat and redress the original failure, i.e. use a pricing mechanism to redress a problem caused
by the failure of a pricing mechanism. Either way, the supported theories rapidly run into difficulties,
notably when being applied to industries displaying increasing returns to scale. A service such as the Post
Office would, it seems, face increasing returns to scale and thus have a marginal cost curve that is always
below the average cost curve, and would operate at a loss were it to implement marginal cost pricing
without alternative sources of financing. Is marginal cost pricing therefore irrelevant in this specific
context? I will reach an answer by first starting at the basics of public enterprises and the theories of
marginal cost pricing and then looking at the feasibility of linking the two.
First, a public enterprise is loosely defined as being an organisation producing and selling goods or
services, and whose assets are not owned by private shareholders, but by a public agency 1. Rees argues that
there are four reasons why a public enterprise might exist. These are to correct market failure, to alter the
structure of payoffs in the economy, to facilitate long-term economic planning and to change the nature of
the economy from a capitalist to a socialist one. In a capitalist framework, only the first two of the four
reasons is significant. Alternatives to public enterprise are taxes and subsidies, anti-trust policy and
regulatory bodies. Recently, the emphasis in Western Europe and developed countries has been to shift the
balance onto the private sector, but keep some strings linked to central control through regulatory bodies
and other such systems. In the UK, the post office, alongside the London Underground and air traffic
control, remains one of the last true public enterprises standing and is thus an interesting case study. The
crucial defining feature we are interested in here is that many public enterprises are monopolies and the
Post office is a monopoly for a certain range of goods.
Second, in situations where prices are not equal to marginal cost, it is advocated that instigating a marginal
cost pricing structure can increase general welfare. A very basic derivation of the concept is as follows:
The objective is welfare W optimisation through the maximisation of the social benefits SB minus social
costs SC. We assume the public enterprise is seeking to maximise
W=SB-SC
We also assume that SC is equal to Total costs TC (i.e. that the enterprise faces a perfectly elastic supply
curve for all its factors of production) and that the social benefit is simply the sum of total revenues TR and
the consumer surplus CS. Therefore
W=TR+CS-TC
Differentiating with respect to quantity Q and setting to 0
W
(TR TS ) (TC ) 0
Q Q Q
1
Rees, Public Enterprise Economics
Andrew Nutter Economics Dr. Sällström
amfn2@cam.ac.uk 25/11/11
Since the TR+CS is simply the area under the Price, Cost
uncompensated demand curve and (TC ) is the
Q
marginal cost, we now have
Q
Q
P(Q)dQ MC 0
0
P’
B MC
Transfer
from
or P=MC consumers Deadweight
to firm loss E
P’’
This is an intuitive result, replicated graphically in A
D
figure 1.1 for the case of a monopoly, with extensive MR
implications. Graphically, we can see that, for a Q’’
monopolist, marginal cost pricing is the only type of
Q’ Output
Figure 1.1
pricing that does not generate a deadweight loss.
For the specific case of a public enterprise with increasing returns to scale, the situation is represented in
figure 1.2 below. Whereas a profit motivated monopolist would chose to limit production to Q’ and reap
CAEP’ worth of profits, marginal cost pricing
would bring output to Q’’, without actually Price, Cost
covering the costs of production. The enterprise
would therefore be operating at a loss of the
shaded area in the diagram.
Is it necessary to write off marginal cost pricing
P’ E
for public enterprises such as the Post Office? An
answer depends on three things. What the
purpose of marginal pricing was in the first place C A
and whether its application yields the required AC
results? Whether it is possible to retain marginal P’’ MC
cost pricing and fill the shortfall through other MR D
means? Whether alternative pricing structures
reach these aims or “satisfactory” second-best Q’ Q’’ Output
Figure 2.1
solutions?
We’ve already determined that the purpose of marginal cost pricing was to maximise welfare, which we
would assume explains the existence of the Post Office. Advocates of the theory, Lerner, Meade, Reder and
Vickrey have argued that the marginal cost pricing structure should stay in place and the deficit be financed
through other means, but failed to fully recognise the implications of such actions. Hotelling initially
suggested the deficit should be financed by taxes on inheritance, rent of land and incomes, since these are
all lump-sum taxation. However, true lump sum taxes fall on either consumer or producer surplus and,
whilst taxes on inheritance and rent of land fall under this category, it is dubious whether income taxes are
a pure lump sum tax. This was supported by the analogy of income taxes as excise taxes on certain factors
of production, which may prevent marginal conditions from being met. A more stringent hindrance to
financing deficits through taxation is the lack of methods of instantaneously making interpersonal
comparisons of utility. Whilst this lack of interpersonal comparison of utility has been used to attack the
foundations of marginal cost pricing theory on many occasions, the problem is magnified when advocating
deficit financing. Clearly, on the one hand, the tax may not be collected from those benefiting of the
consumption of the subsidised good and on the other, this system favours those consuming goods and
services originating from decreasing cost industries.
These questions dent some of the theoretical potency of marginal cost theory in decreasing cost industries.
Obviously, further questions arise undermining the marginal cost theory at its very core, such as whether:
Andrew Nutter Economics Dr. Sällström
amfn2@cam.ac.uk 25/11/11
- companies actually know their marginal cost curves and the cost of them discovering or failing to
ascertain marginal costs correctly
- there are resulting losses due to the lack of profit-incentives (companies could be meeting their social
goals whilst making losses year after year) and the longer term loss of welfare due to the arising
inefficiency.
- the model is flexible enough to deal with dynamics of demand and supply. Etc…
If marginal cost pricing suffers from all these “hindrances”, we are half way to answering the question. We
must now see if there are usable and relevant alternatives to marginal cost pricing. I shall briefly look at
two of the most commonly put forward. The first was proposed by Frisch, Meade and Nordin at various
points in time and suggests that to plug the deficit whilst keeping marginal conditions, prices need only be
proportional to marginal cost. This is silly in the sense that doing so would either
a) increase both factor and finished good prices by the same proportional amount, negating the proposed
improvement in finances.
b) Change the relationship between the ratio of consumer good price to marginal prices and the ratio of
factors to their marginal products, hence changing marginal conditions throughout the system through
the choice between work and leisure channel.
So actual equality is necessary to maintain the same optimum level of welfare at marginal cost pricing.
However, I do feel the issues is too complex to identify the exact shifts in welfare under varying
circumstances.
The second proposition, attributable to E.W.Clemens, is to perfect price discrimination instead of marginal
cost pricing. He showed that the marginal conditions would hold and that an ideal point of welfare would
still be reached. However, the practical implications of this theoretical work can almost immediately be
discredited due to the impossibility of implementing such a practice (unless some sort of perfect auction
could be engineered that would reveal everyone’s true demand for the good or service). So we are
apparently left with no practical method of pricing goods in a decreasing cost public enterprise so as to
achieve an optimal level of welfare.
To conclude, I have decided to reach the rather lame conclusion that there is no direct answer to the
question; marginal cost pricing provides a tool for reaching higher levels of welfare under certain
circumstances. The evaluation of applications of such pricing must take into account a colossal amount of
information, taking into account all alternatives, and must be done on a case by case basis.
In decreasing cost public industries, methods exist to finance the deficit left by marginal cost pricing and
such a combination may offer an optimal welfare solution. Rather than foolishly search for the panacea of
all pricing strategy, better to use what tools are available to reach specific conclusions; “Every pricing
system results in a some sort of redistribution of income, and no substantial redistribution of income is
possible without changing that pricing system”.
In the case of the Post Office, the situation is changing so rapidly, notably in terms of purpose being eroded
by electronic alternatives, that it would be almost impossible to price its products according to marginal
cost at the moment.
b. What should determine the level and structure of tolls on new road bridges, such as the Dartford
Crossing in East London or the Skye bridge in Scotland?
Jules Dupuit’s incisive insight into welfare and public works suggest that tolls on new road bridges should
be zero. The argument put forward is that using the bridge incurs no marginal cost and any toll imposed
would immediately reduce benefits. This is an increasing-returns-to-scale problem, but this time with the
average cost curve above the demand curve. Yet, bridges need to be built as they generate direct benefits to
users and positive externalities in terms of trade and free movement off capital. Two confronting examples
of toll bridge are the Skye Bridge and the Dartford Crossing. The former, seen by many as a contentious
and expensive piece of scenery. The latter, seen as a busy and efficient alternative to the tunnels below the
Andrew Nutter Economics Dr. Sällström
amfn2@cam.ac.uk 25/11/11
Thames. The arguments as to why marginal cost pricing would be beneficial and its implications have been
elucidated in the previous question.
The question here starts on the presumption that a toll is in place and purely leaves us to determine the
structure and level of toll? We are not attempting to determine whether it is the correct form of financing
the deficit.
The building of new road bridges is now being decentralised as a means of injecting the vigour of private
enterprise into the equation. Under the Public Finance Initiative, private companies tender for projects such
as bridge building and expect to recoup their investment under predefined terms. The purpose is clearly one
of efficiency for the government (as well as providing some neat accounting tricks to reduce apparent
public expenditure). The imposition of tolls on bridges to recoup sunk costs, meet running costs and make a
profit as an incentive is contentious from more than just the marginal cost pricing point of view. It is also
clear that there is an obvious space for a divergence of social and private benefits and costs in this case. The
most pertinent example of this is the Skye Bridge. The bridge cost between £25 and £37 million and has
some of the highest tolls in Europe, with single trip down the couple of hundred meters standing at a hefty
£4.70 and £27.90 for tourist buses. (Compare this to the £11+ for crossing the massive Oresund bridge +
artificial island which is 16 km long). Locals are appearing before courts for refusing to pay these amounts
and pressure groups are going to the European courts to argue that they have been cut off and the bridge
restricts their right to free movement (the government abolished the competing ferry service). Meanwhile,
the bridge has already cost the government £15 million and the Bank of America is making a hefty profit
on the situation. The list seems to go on and opens to reveal a can of worms if looked at too closely.
A suggested way to redress the sub-optimality of the Skye Bridge toll system would be to implement a
“shadow toll”, i.e. measure how many cars cross the bridge and get the government to pay the cost of
buying back the bridge. This concept is supposedly being implemented in recent PFI projects.
The Dartford Crossing on the other hand, is quite different in its toll policy and the circumstances of the
structure. The crossing was built to ease congestion on the two tunnels below it and provide a continuous
link to the M25. The 4 lane carriageway is meant to be one of the busiest toll in the world, carrying over 50
million cars every year. A toll in this case may have a beneficial purpose, given the amount of traffic
flowing over the bridge, the charge is only £1 for a car and the private company can recoup its sunk costs,
whilst improving social benefit by controlling traffic flow.
An intuitive attempt at ascertaining what should determine the level and structure of tolls is makes more
sense in the case of the Dartford Crossing rather than the Skye Bridge. Assuming the company can only
just break-free and meet its maintenance costs, it should have a flexible menu of toll prices that would
achieve the necessary revenue over time.
First, distinction are made between the types of vehicles using the bridge, generally small ones paying less,
and HGVs paying more, reflecting the sensitivities of these vehicles to costs and environmental
dammage/speed/length. The structure should also include elements of flexibility such as electronic passes
that reduce the cost of use and speed up the flow of traffic. Most importantly though, I believe the real use
of tolls should be in changing prices according to the flow of traffic. At peak times, prices should be
increased to maintain the flow of traffic and simultaneously address environmental issues (marginal
environmental costs increase disproportionately with increased congestion). Furthermore, this comes a step
towards installing the elusive “perfect” price discrimination policy and reaching our nirvana of marginal
conditions. Increasing tolls limits the customers to those who value it at the price or more than the price.
Also, the surplus revenue gained in these peak time periods can serve to cross subsidise the off peak time.
Such a toll framework could be engineered, assuming there is enough traffic, to keep the combination of
traffic and revenues flowing at an optimal rate, whilst keeping the welfare loss of the departure from
marginal pricing minimal.
To conclude, the Skye Bridge is a bad example of how to set tolls, build bridges and use the PFI, the
Dartford crossing a good example. The essential intuitive result we are looking for is that the toll should be
set such that private cost should be equal to marginal social cost. This varies throughout the day and
according to the nature of the vehicle, variables that a well-defined toll should be able to cope with