Elasticities: a New Application

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Australasian Journal of Economics EducationVol. 5. Numbers 1 & 2, 2008

AN ILLUSTRATION OF THE IMPORTANCE OF ELASTICITIESIN MICROECONOMIC POLICY

Jerry Mushin

VictoriaUniversity of Wellington

New Zealand

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ABSTRACT

Applying supply-and-demand theory to graffiti production explains why this problem is difficult to solve and illustrates that elasticities are interesting concepts.When, in a competitive market, demand is inelastic, a significant change in output requires a very substantial shift in the supply curve or a much smaller shift in the demand curve.In this situation, therefore, a government that wishes to influence the level of output of a particular commodity should use demand-side policies and not supply-side policies.

Keywords: demand elasticity, supply elasticity

JEL Classification: A21, A22

Graffiti, which are defined as the unauthorised defacements and decorations of buildings and other structures, are widespread in many cities. The production of graffiti, which is also known as tagging, is generally seen as a problem because there are substantial externalities.These include the costs of cleaning and of repairs. The externalities also include the cost of installingand operating measures that are intended to discourage it. Perhaps more important than these measurable costs is the damaging effect of graffiti on the morale of the overwhelming majority of the population.

The use of supplyanddemand diagrams gives new insightsinto issues, including policy responses, that are related to graffiti. This application of familiar theory can also assist students. Elasticities of supply and of demand are theoretical devices that have been taught to students of economics for more than one hundred years. Despite this, they are not always seen by beginning students as relevant to the understanding of realworld issues.Teachers and lecturers who illustrate this topic by referring to graffitiproduction might find that they arouse the interest of additional students inthe meaning and importance of elasticities and in other aspects of supplyanddemand theory.

Although there are no customers who pay for the output, tagging can be analysed as if it is a type of production. Resources are diverted from other uses and,while their value cannot be measured in money terms,the producers receive benefits.In addition to the use of their time, the costs to the tagger are the payments for paint and for tools (brushes, ladders, etc). Additional costs to the tagger are the risk of being caught and punished and the risk of injury. The benefits to the tagger, which are intangible and impossible to measure, include fame among his/her peers, the satisfaction of showing defiance to authority, and the relief of boredom.Assuming rational behaviour, taggers will vary the quantity of graffiti that is produced each week until the marginal cost is equal to the marginal benefit.

The marginal benefit to the tagger of additional graffiti will decrease as the level of production increases. The usual principle of diminishing marginal utility will apply. The precise shape of the graph is, of course, impossible to determine but it is likely to be steep. Tagging might be comparable to addictive behaviour in which there is a target level beyond which additional satisfaction is low or negligible. The marginal benefit curve, as a function of the quantity produced, is the tagger’s demand curve. He/she will want to produce additional graffiti until the additional satisfaction from additional output is equal to the price that has to be paid for it. If the marginal benefit falls sharply as the production level increases, as is probable, a tagger’s demand curve is inelastic.

The marginal cost to the tagger of additional graffiti will increase as the level of production increases. The tagger will deface the most accessible locations first and will then move on to increasingly difficult places. This increases the marginal cost of graffiti production by increasing the time needed to complete a tag and by increasing the risk of injury and the risk of being prosecuted. The increase in marginal cost, following an increase in graffiti production is, however, likely to be small. Every city has a very large number of very accessible locations. Since there are no barriers to entry, it can be assumed that graffiti production is a competitive industry. It follows that the marginal cost function of an individual tagger is his/her supply curve. Since the marginal cost probably increases by a very small amount when graffiti production increases (even by a large amount), a tagger’s supply curve is elastic.

Figure 1 shows the marginal benefit function (demand curve) and the marginal cost function (supply curve) of graffiti production. The equilibrium production quantity [Qe]of graffiti is at the intersection of the demand curve, which is shown as almost vertical, and the supply curve, which is shown as almost horizontal. Of course, this diagram ignores the negative externalities of graffiti, which impose severe burdens, both financial and nonfinancial, on the community. To identify the social optimum output level of graffiti, which is probably zero, the supply curve (or marginal cost function) should be shifted upwards by the amount of the external costs (including the nonfinancial costs).

To decrease the output of graffiti, governments can attempt to shift the supply curve to the left, or they can attempt to shift the demand curve to the left, or a combination of these. Anaxiom that appears in introductory textbooks is that, on a supplydemand diagram, the effect of a shift of one of the curves depends on the elasticity of the other curve. This is why elasticities are important. In this case, where the demand curve is inelastic and the supply curve is elastic, a significant decrease in the equilibrium level of graffiti production will need a very substantial shift in the supply curve or a small shift in the demand curve. On Figure1, a shift of the demand curve leads to a (large) decrease in graffiti output fromQe to Q1and a shift of the supply curve leads to a (small) decrease in graffiti output from Qe to Q2. Of course, it is impossible, on a diagram of this kind, to compare the magnitudes of the stimuli that produced each of these shifts.

Many governments have attempted to increase taggers’ costs and thus to shift the supply curve upwards (and to the left). At the time of writing of this article (2008), for example, the New Zealand government is proposing to introduce a dramatic increase in the fine for which convicted taggers are liable. In addition, many privatesector owners of buildings have attempted to deter taggers, or to increase the chance of apprehending them, by employing security staff and by installing lighting, barbed wire, cameras, etc. In addition to increasing the costs of businesses, these measures increase taggers’ costs and so also shift the supply curve upwards (and to the left). These measures have generally not beentotally (or even largely) successful at curbing the activity of taggers. The theory shows that, given the shape of the demand curve, their magnitude would need to be extremely large in order to have a substantial effect on the volume of graffiti production.

The diagram also shows that shifting the demand curve to the left, even by a small amount, is likely to be more effective at causing a useful decrease in graffiti production. This means that attempts should be made to change the attitudes and behaviour of taggers to decrease the benefit that they perceive that they receive from tagging. This task, which is not a simpleone, requires an understanding of the motives of taggers and needs the expertise of professional experts other than economists. It is probable that educational institutions have a role. Even when attempts to change taggers’ behaviour are successful, this success is likely to be very gradual. Attempts to change their behaviour might make some taggers determined not to change. The best outcome that governments and businesses should anticipate is a longterm improvement and not an immediate end to the problem of graffiti. Shifting the demand curve by a substantial amount to the left is not an objective that is easy to achieve even in the long term.

To the extent that tagging is caused or encouraged by boredom, and/or by the lack of money to pay for more acceptable (and also more expensive) activities, lower unemployment and higher aftertax wages might contribute to the shifting of the demand curve to the left.This point is a reminder that graffiti production is an inferior good. The income elasticity of demand is likely to be negative; the satisfaction derived from this activity, and hence the demand, is likely to fall when a tagger’s disposable income rises. Better housing, with less overcrowding, so that taggers have less incentive to be away from home at night, might also be helpful.

Another approach to the problem of persistent graffiti production is the immediate removal or painting over of all graffiti as they appear. If this discourages taggers, who are deprived of seeing the effect of their efforts, it will shift the demand curve to the left, and it willbe a successful policy. It would need to be applied to all of the buildings in a particular city, of course, otherwise it would merely shift the taggers’ attention to buildings where the policy does not apply. However, if the immediate removal of graffiti causes taggers to strive to replace them, the policy would shift the demand curve to the right.An understanding of taggers’ attitudes and behaviour is again needed.

The problem with the application of supplyanddemand theory to the graffiti problem is, of course, that it identifies a solution that is very difficult to implement. It does, however, enable us to understand why the combined efforts of governments and others, which have concentrated on shifting the supply curve of graffiti production and not its demand curve, have generally not been successful. It is also a reminder that there are many situations in which demandside policies are more effective than supplyside policies, and that the key to understanding this is the ratio of demand and supply elasticities. And it shows that elasticities are interesting concepts.

FIGURE 1 Equilibrium Quantity of Graffiti Production

Demand [marginal benefit]

Price

Supply [marginal cost]

Q1 Q2Qe Quantity per week