Question

Please submit a 1,000 word paper, double spaced with proper APA citations answering the following:

Since taxes distort market outcomes and efficiencies, should the government legalize currently illegal drugs which have very inelastic demand and heavily tax them to generate revenue?

Answer 1

There is no published economic analysis of  

the potential impact of drug legalization on Social Welfare. This paper treats legal and illegal drugs as different qualities of the same good, and uses price theory to analyse the social welfare effects of drug legalization and the optimal price of legal drugs. Both of these are shown to depend in an intuitive way on the relative importance of the externalities arising from drug use, such as crime and ill-health. Some simulations of the legalization of marijuana and cocaine, using reasonable parameter values,show that an increase in drug use usually results, but that the lower levels of per unit social harm in legal, as opposed to illegal, drug markets ensures that, in many cases, social welfare rises following legalization. Optimal drug policy is heavily dependent on the relationship between drug use and externalities, the inclusion of the consumer surplus from drug

consumption in social welfare, and the functional form of the demand curve. A better

understanding of these would seem necessary before any unequivocal statement about the advantages of legalization can be made.

1. Introduction.

The 'drug problem' is currently one of the most widely-discussed issues in many

countries, and consistently appears close to the top of surveys asking people what they

believe is the source of the greatest social concern. The scale of drug use is large. According

to estimates from the 1995 National Household Survey on Drug Abuse, 10 million Americans

had used marijuana in the past month, with a similar figure for cocaine of 1.5 million; and 72

million Americans aged twelve or older had tried illicit drugs at least once in their lifetime.

Of this latter, 66 million had tried marijuana and 40 million had tried some other illicit drug.

It has been estimated that revenue in the U.S. illegal drug market is one hundred billion

dollars per year (Andelman, 1994). In 1992 over one million arrests for drug-abuse violations

were reported to the FBI, and 58% of inmates in federal prisons were serving sentences for

drug offences.

Despite the issue's high profile, it has attracted only little economic analysis. This
paper considers one policy which has attracted a great deal of attention: legalization2
. It asks
whether drug legalization would increase social welfare, what price legal drugs should be
sold at, and what might be the likely effects of legalization on the quantity of drugs used,
spending on drugs, and the tax collected from drug sales.
Standard theory predicts that governments should intervene in drug markets because
of the negative externalities involved in the sale and use of drugs. However, one of the most
prevalent policies, prohibition, has apparently not worked as planned. Making drugs illegal
has not eradicated drug use,

These additional externalities include the 'environmental' effect of drug trade on
neighbourhoods, the violence associated with the illegal market (where there is no recourse to
the Law in the event of a dispute), the income-generating crime that may result from the
illegal market's high prices, the criminalization of those who purchase in the illegal market,
the possible disincentive effect of what is seen as high-profit criminal activity on schooling
and labour force participation, the health costs from adulterated and variable strength drugs,
the increased risk of infection from needle-sharing and so on. Thus Prohibition has likely
reduced the size of the drug market, but has also ensured that there are greater negative
externalities associated with each unit of drugs consumed: the balance between these two
effects is one of the key considerations in the welfare analysis of drug policy.
The paper is organized as follows. Section 2 uses a simple model of drug markets to
analyse the implications of legalization on the quantities purchased, under first the
assumption of a Perfectly Competitive illegal market and then of a Monopoly. Section 3
introduces a Social Welfare Function, which depends critically on the various externalities
linked with the drug market, and identifies the conditions under which legalization will raise
social welfare. Section 4 derives formulae for the optimal prices of legal drugs. Section 5
uses the model of the previous sections to present a number of simulations of the effect of
legalization on quantities, drug spending, tax revenue, and social welfare. Section 6
concludes.

2.optimal legal drug prices.
The price of legal drugs can be set by the government: either directly if the
government itself sells the drugs, or via taxation if drugs are supplied privately. The
expressions for welfare derived in section 3 allow formulae for the welfare-maximising legal
price to be developed; the detailed derivation is contained in the Appendix. Welfare may be
either concave or convex in cL, so that the welfare-maximising legal price may be interior or
at a corner. Under Perfect Competition and for low-price legalization under monopoly, the
concavity of W comes from tax revenue, while convexity comes from consumer surplus and
(minus) drug spending. For high-price legalization under monopoly, tax revenue is concave
but consumer surplus may be concave or convex in the legal price.
In general, the optimal legal price is higher the larger is N1 and the smaller is N2 (in
the sense of the price being higher for an interior solution and more likely at the high-price
boundary when W is concave in cL). Under low-price legalization, price is independent of N2
(as the illegal market has been priced out), although higher N2 makes low-price legalization a
more attractive policy (see above). Analogously, N1 does not affect the optimal price under high-price legalization and a competitive illegal market, as in this case legalization leads to
no change in total quantity.
The above is intuitively attractive, as the higher is the legal price, the more the market
looks like that under Prohibition, where the overall size of the drugs market is minimised,
while that of the illegal market is maximised. Both spending on drugs and tax revenue are
non-linear in the legal price, and there is no general monotonic relationship between their
importance to society and the optimal legal price.

f the illegal market is competitive, it is not welfare-maximising for the legal
and illegal markets to co-exist.
This is obviously true under low-price legalization, where the legal price is set low
enough to eliminate the illegal market; also under high-price legalization when welfare is
convex, so that the optimal price is either at the low-price boundary (where the illegal market
is just priced out) or at the high-price boundary (where no legal drugs will be purchased).
Hence, imagine that there is an optimal interior price under high-price legalization when
welfare is concave and consider the welfare effects of a small fall in the legal price. There is
no change in the size of the drug market, and hence no change in the total quantity
externality, but the size of the illegal market falls with the legal price, which raises welfare.
Total consumer surplus rises, as consumers will only switch from the illegal to the legal
market if their consumer surplus increases by doing so. All of the original legal buyers will
also see their consumer surplus rise as the legal price falls, while there is no change in
consumer surplus for those who remain in the illegal market. The rise in W due to consumer
surplus is at least as large as -)cLQL. The change in welfare from spending is -N3()cLQL
+cL)QL+ c)QI ) and the change in welfare from tax revenue is R()cLQL +(cL-c'))QL). The
sum of these three terms, remembering that )QL=-)QI as there is no change in total quantity,
is )cLQL(-1-N3+R)+)QL(-N3(cL-c)+R(cL-c')). The first term is obviously positive because R
is no greater than 1, and the second term is positive as c' is less than c and the concavity of W
requires that N3 be less than R. Total welfare thus rises and no interior price can be optimal.
A mathematical proof is contained in the Appendix.

*the illegal market is competitive and if welfare is concave in the legal price,
legalization raises welfare, and the illegal market should be priced out.
This follows from Proposition 4: if a small fall in the legal price always raises welfare,
then, starting from the high-price boundary (which is equivalent to Prohibition), welfare can
be continually raised by reducing price, up to the point at which the illegal market is
eliminated.
There is no simple relationship between the structure of the illegal market and the
level of the optimal price. As Table 2 makes clear, there is no obvious hierarchy between
high- and low-price legalization, with the choice of optimal price and policy for each market
structure depending on the values that society places on the externalities associated with
drugs. It could easily be the case that the same set of parameters implies high-price
legalization under one market structure and low-price legalization under the other. Further,
the same set of parameters may yield a convex social welfare function under one market
structure and concave welfare under the other, with the corresponding differences in the
optimal pricing of legal drugs.

3.Simulations.
The analysis of the previous sections shows that policy depends on the combination of
a large number of different variables. To illustrate the results obtained above, this section
carries out some simulations of legalization of first marijuana and then cocaine in the United
States. Few markets can be as poorly documented as that of illegal drugs, but some
information on prices and quantities is available in the Office of National Drug Control
Policy's 1995 report.
According to Table 6 of this publication, marijuana cost $341.7 per ounce in 1993 (in
1994 dollars, for purchases of 1/3 of an ounce), with 26.14 million ounces being purchased (9
million users smoking an average of 18 joints per month; one ounce of marijuana making
73.5 joints). The current price and quantity, together with an estimate of the current elasticity
of demand, allow the intercept and slope of a linear demand curve, as used above, to be calculated. The elasticity of demand for cigarettes is usually estimated to be around -0.7
(Becker, Grossman and Murphy, 1991and 1994, Chaloupka, 1991, Jones, 1989). An early
estimate of the elasticity of demand for marijuana (Nisbet and Vakil, 1972) finds it to be
somewhat higher than that for cigarettes, in the range of -1 to -1.5, perhaps because there are
more substitutes for marijuana than for cigarettes. Recent estimates of the elasticity of
demand for illicit drugs have produced some quite high numbers. Grossman, Chaloupka and
Brown (1996) use a rational addiction approach to estimate the long-run price elasticity of
demand for cocaine as -1.2. Saffer and Chaloupka (1996) find long-run demand elasticities of
-1.7 and -0.9 for heroin and cocaine respectively, while van Ours (1995) uses historical data
from the Dutch East Indies to estimate a price elasticity of demand for Opium of -118.
For the simulations an elasticity of demand of -1.1 is initially posited, for both
marijuana and cocaine19. This implies an illegal demand curve with an intercept of 652.3 and
a value of b of 11.88 (both in millions). Under competition, c equals the current illegal price
($341.7 per ounce), whereas if current price and quantity come from monopoly supply, c can
be calculated as $31.1 per ounce.

4.Conclusions
Economists have devoted an enormous amount of attention to prices and quantities in
markets, but far less to the question of whether certain goods should be prohibited. This paper
has made a start on this question, using price theory to predict quantities in the legal and
illegal drug markets, which are considered as two different qualities of the same good. Both
competition and monopoly in the current illegal drugs market are considered. The choice of
optimal policy is made by a Social Welfare function, defined over consumer surplus, tax
revenue (from a purchase tax on the legal drugs market), and three different classes of drug-
related externalities: those resulting from drug use in any market, whether legal or illegal,such as some health costs or "drugged driving"; those uniquely associated with the illegal
market, such as violence and policing costs; and those from income-generating crime.
Optimal policy depends in a natural way on the relative importance of these externalities.
To illustrate, the Social Welfare function has been parameterised for the case of
marijuana and cocaine. The model predicts that legalization of both would raise welfare, and
suggests that the latter should be effectively given away, to avoid concomitant problems of
income-generating crime. A number of experiments with different demand and externality
parameters suggest that legalization, often at a price low enough to drive out the illegal
market, has the potential to raise social welfare.
It is, however, perhaps wise not to be too sanguine about these simulation results.
First, it should be emphasised just how little we know about many of the key parameters here
and, second, the model used is a simple one. One omission relates to the use of different
kinds of policing (either of consumers or of suppliers). Enforcement, which is costly, either
pushes the demand curve inwards or raises suppliers' costs: a joint policy of legalization and
policing will be superior to one of legalization only. Although some work has considered
enforcement expenditure (Andelman, 1994, Graham, 1991, Lee, 1993, and White and
Luksetich, 1983), it has yet to be incorporated into a full-blown model of legalization.
One particular case concerns the relaxation of penalties for illegal supply after
legalization. The correct comparison is thus between prohibition with illegal cost
c and
legalization at illegal cost (c, (<1. To check, the four baseline results in Table 4 were
recalculated for (=½. The only change was that the optimum legal price for marijuana with
monopoly illegal supply dropped from $62 to $35 per oz. As seems reasonable, cheaper
illegal supply after legalization may pull down the legal price.
The current model has also said nothing about the effect of drugs on the labour
market; this would be another component of
N1. In a competitive labour market, any
productivity effect should be reflected in lower wages and is thus internalised (apart from the
impact of labour taxes). Here individuals' decisions to change the level of effort or of labour
supply, in light of their associated returns in the labour market, come from a change in
preferences. If productivity is not reflected in wages then there will be external effects. In fact, most empirical work (Gill and Michaels, 1992, Kaestner, 1993, and Sickles and
Taubman, 1991) finds that drug use is associated with higher wages, although the problems
of non-representative samples (those who drop out are not included) and of omitted variables,
most estimates being on cross-section data, should be signalled (on this latter, see Kaestner,
1994, who finds inconclusive results in NLSY panel data).
Further topics include substitution between drugs. Model (1993) considers the
prevalence of drug mentions in hospital emergency room episodes. Using the
decriminalization which occurred in twelve US cities between 1973 and 1978 as a natural
experiment, her regression analysis shows that "marijuana decriminalization was
accompanied by a significant reduction in episodes involving drugs other than marijuana and
an increase in marijuana episodes". DiNardo and Lemieux (1992) show that the rise in the
legal minimum drinking age was associated with a fall in alcohol use, but a rise in marijuana
use24. Legalization of marijuana, or of other drugs, may well bring about additional welfare
effects through changes in the menu of externality-producing goods consumed. On the supply
side, we may see the growth of a third source: home-grown. The extent to which this matters
depends obviously on the type of drug considered, on the restrictions to which it is subject
(taxed or not, how heavily policed etc.), and on market prices. It is worth noting that Table 4's
simulations yield legal marijuana prices that are mostly lower than the current illegal price,
which will reduce the incentive to grow one's own.Perhaps the most important weakness of any attempt to model the effect of
legalization on social welfare has already been mentioned: how should the consumer surplus
associated with drug use, which is predominant in calculations of social welfare, be treated?
Miron and Zwiebel note that "it is remarkable how uniformly the utility from drug
consumption is ignored in public discourse on drug policy - even by economists" (p. 182).
This may reflect some political or moral agenda, or simply that there is no consensus on how
to proceed.