Journal of Public Economics 35 (1988) 371-383. North-Holland

A SIMPLE MODEL FOR MERIT GOOD ARGUMENTS

Timothy BESLEY*

All Souls College, Oxford OXI 4AL, UK

Received April 1987, revised version received January 1988

In this paper we examine a way of representing merit goods by allowing governments to apply a specific form of correction to consumers’ preferences. The model builds upon an approach to the analysis of taste and quality change due to Fisher and Shell. We look at the first-best allocation of resources where this is done. We also consider second-best policies in which the government must charge the same price to all consumers of the merit good, and when optimal lump-sum transfers are not available.

1. Introduction

There are two main types of argument which are typically used to justify government intervention: (i) distributional arguments and (ii) market failure arguments. Both of these are well established, and have been given extensive theoretical analyses. A third class of arguments is also discussed, but its relationship with the above is often obscure. These are merit good arguments. In this paper we ask whether merit good arguments can be given a distinctively different interpretation from (i) and (ii), or whether they are most naturally subsumed into either of these categories. In particular, we seek to clarify their relationship with market failure arguments. In doing this, we offer a model of merit goods which attempts to capture the spirit of the notion first suggested by Musgrave (1959, pp. 13-14), although he does seem to vacillate between what we shall regard to be competing interpretations of the notion.

We identify a case of market failure as one in which a Pareto inefficient allocation of resources obtains. Hence, a merit good argument must justify intervention when markets work efficiently and when the distribution of income is optimised if it is to be a distinctive type of argument. In order to clarify issues further, we assume throughout that we are in regular neo- classical economy. Specifically, we assume sufficient regularity for the second

*I am grateful to David Bevan, Agnar Sandmo, Amartya Sen and an anonymous referee for comments and suggestions. Errors are mine.

0047-2727/88/$3.50 0 1988, Elsevier Science Publishers B.V. (North-Holland)

312 7: Besley, Merit good arguments

fundamental theorem of welfare economics to hold (i.e. it is possible to decentralise an optimal allocation of resources using lump-sum transfers).

Merit good arguments are difficult because they appear to challenge some central tenets of the economist’s value theory. The underpinning Utilitarian framework often elevates subjective value to a lofty status. It is taken to be all that is of intrinsic value. This can be seen transparently in the notion that ‘the consumer knows best’ embodied in the principle of consumers’ sovereignty. Anyone with minimally liberal sentiments is inclined to believe that this has some validity, i.e. there is some domain in which private choices of individuals have normative significance. Merit good arguments proceed via a pathology of individual choice, i.e. they rest upon reasons for consumers’ choices being ‘faulty’. The step to an argument for intervention is then a short one.

There are good reasons to be suspicious of the Utilitarian approach to normative analysis. It conflates what superficially are different notions. For example, it makes no distinction between the statements, ‘I desire x’, ‘I value x’ and ‘I would be happier with x’. In the simple Utilitarian model value, desire and happiness are merged into a single metric, namely utility. Despite recognising this difficulty we shall not present a thorough going alternative to it here. We accept an essentially Utilitarian framework whilst permitting the social planner to recognise that the preferences used to determine consumption may be a ‘faulty’ representation of well-being. It is this divergence upon which we pin our merit good arguments.

Before we offer an account of merit goods, we review two other approaches to merit good arguments that have gained currency. The first approach allows the quantities of some goods to enter the social welfare function directly in addition to it being a function of individuals’ utilities [see, for example, Pazner (1972)]. The motivation for this is that one can give an account of why some goods are objectively valuable, i.e. it represents a sacrifice of sub- jective value theory. We assume that it is not imperfect information that leads to this form of social welfare function for reasons that we will return to below. This approach generally has the aggregate quantities appearing in the social welfare functional. Using this leads to an immediate conflict with con- sumer sovereignty and with the Pareto principle. Consumer sovereignty is sacrificed because individual preferences are no longer respected. The weak Pareto principle goes because if everyone prefers one outcome to another, then it could still be true that the social welfare function reversed the ranking.’ The conflict of the Pareto principle with side-constraints on the social welfare function is well known. It is the essence of Sen’s liberal paradox [see Sen (1970)].

The second approach to merit goods that we shall consider proceeds by examining equilibrium under uncertainty. It exploits the distinction between

‘Sandmo (1983) makes this point.

‘I: Besley, Merit good arguments 313

ex ante and ex post efficiency, discussed by Hammond (1981). Its use in the context of merit goods has been suggested by Sandmo (1983).’ Sandmo examines a case in which individuals misperceive probabilities and which leads to the equilibrium being ex ante inefficient. There is scope, therefore, for government intervention. However, such interventions are motivated by considerations of market failures, i.e. cases in which we have a Pareto inefficient allocation of resources initially. The source of market failure is imperfect information. Providing information could make someone better off ex ante without making anyone worse off. This class of merit good argu- ments implies that in a world of costless government policy, the provision of information is needed to obtain the best possible outcome. The need to intervene directly in markets is a second-best argument based upon the costs of alternative policies.

However, if fully informed individuals did not make the appropriate choices, then imperfect information alone is not enough, and we are faced with a different kind of argument. It is important to make this distinction since it is easy for what we shall call ‘defective preference arguments’ to be disguised as imperfect information arguments to make them more palatable, when in fact their motivation is different.

To summarise: arguments for intervention based upon the existence of imperfect information may or may not be correctly labelled as merit good arguments. This is a matter of semantics. They are not, however, distinct from arguments for intervention based on market failure when we consider the ex ante efliciency of an economy.

In the next section we set up a model to analyse merit good arguments for intervention which are distinct from distributional and market failure argu- ments. In section 3 we look at the first-best allocation of resources. In section 4 second-best interventions are considered, and in section 5, we conclude.

2. The model

In our model there will be N non-merit goods xi,. . ., xN, and a single merit good denoted by y. There are H individuals indexed by h. The increasing, strictly quasi-concave, twice continuously differentiable utility function of individual h is:

Uh(Xh, yh).

We postulate the existence of a social welfare functional:

W(d(x’, y’), . ..) tP(X”, yH)).

(2.1)

(2.2) ‘Variations on this theme are presented in an analysis of health insurance with imperfect

information in Be&y (1987).

314 7: Be&y, Merit good arguments

With sufficient regularity, it is well known that the social welfare optimum can be decentralised by use of lump-sum transfers. Throughout this section we deal with an economy in which the government has sufficient information to be able to implement this allocation if it wishes. We make this assumption so as to abstract from distributional considerations and to home in directly on the merit good arguments.

To introduce the merit goods, we postulate that the social planner values y differently from private individuals. Instead of respecting the preferences of individuals, he treats them as having utilities defined by:

q75h(Xh, yh): = uh(xh, pc”(y”)). (2.3)

This formulation is intended to capture the idea that governments do respect the choices that individuals make for the x’s but not that for y. The function ph(yh) can be thought of as converting yh into efIiciency units. Hence for cigarettes, say, the government might treat ten cigarettes by its system of value as equivalent to what the individual smoking those cigarettes would regard to be twenty.3 For such a demerit good, ph(yh) < yh. Hence in utility producing units the consumer receives less than he does using his own preferences. So at a given level of consumption the planner regards the consumer to be worse off than the consumer perceives himself to be, i.e. uh(xh, ph(yh))<uh(xh, yh). Note that the form of cl”(.) might need to be constrained if the utility function is to be maintained as strictly quasi- concave. This will not trouble us here, however, since we deal with an interesting special case for the form of our merit goods function, namely

/th( yh) = yhOh. (2.4)

This gives us a simple way of classifying goods:

Oh > 1, merit good,

Oh< 1, demerit good.

Individuals misperceive the value of yh since the quantity that they believe they are consuming is different from the ‘effective’ quantity (or quantity in efficiency units).

The model proposed here is just that proposed for considering taste and quality change by Fisher and Shell (1968) [see also Muellbauer (1975)].

‘Hence using the preferences of the individual, ten cigarettes is converted into twenty. If an individual realised that he was consuming the utility equivalent of twenty, he would presumably be inclined to consume fewer.

T. Besley, Merit good arguments 375

Although special, it will enable us to achieve a basic arguments, A major convenience lies in the fact represented by $J*( .) have a dual representation with a indirect utility function is:

grasp on merit good that the preferences convenient form. The

APY 4/dh, mh)7 (2.5)

where m*= income, p =vector of the prices of the non-merit goods, and q =

price of y. This will prove useful in examining optimal taxes below. Our next step is to consider the first-best allocation of resources in an economy in which governments treat individual preferences as in (2.3) with the form given in (2.4) for the faultiness of individual preferences.

3. The first best

Since the utility function is strictly quasi-concave we need only consider the determination of two variables for the first-best allocation, an optimal lump-sum transfer m*, and the direct choice of the merit good quantity yh. Consider the partially indirect utility function:

k?Yp, yh@, m*). (3.1)

The government’s problem is:

max Wg’(p, Y’@, ml), . . . , gH(p, yHBH, mH)) Y.m

subject to

(3.2)

Setting up the appropriate Langrangian with Lagrange multiplier 1 on the constraint, yields:

m*:dW!C+~=O auh am* ’

each h,

aw ag” y*:- - e* + Aq = 0,

auh ay* each h.

(3.3)

(3.4)

Substituting (3.3) into (3.4) yields the following rule governing the choice of yh:

(3.5)

376 T. Be&y, Merit good arguments

To see what (3.5) implies, it is convenient to consider what deviations from choices of h which would be made by individuals if yh were allocated according to it. With the income distribution given by (3.3) we know that individual choices would use the rule:

82 ati -T=- ay amhq’ each h.

We can think of (3.5) as defining an implicit tax rate on y from

w 4 as” -- arnh eh =s 4(1+ zh), each h.

This gives:

l-Oh TV=-, each h.

eh

(3.6)

(3.7)

(3.8)

Eq. (3.8) gives the form of the individual specific tax rate, which enables the allocation implied by merit goods to be decentralised. Returning to our definitions from the previous section, we get the natural result that if Oh> 1 (merit good), then the good should be subsidised, while if Oh< 1 (demerit good), it should be taxed. We can think of the price q(l +zh) as the analogue of the Lindahl prices for public goods. These give the set of prices at which public goods provision can be efficiently decentralised.

More importantly, we have identified here a class of interventions that are not motivated by distributional ends or considerations of market failure. In the absence of government intervention, the economy that we consider would be perfectly efficient. The first-best (full information) outcome for social welfare involves some economic inefficiency. Marginal rates of transformation and substitution diverge in the economy under consideration. The model is based explicitly on the fact that agents’ preferences are defective in judging their own welfare when choosing quantities of the merit good y. It is a very specific paternalistic structure but does give some substance to merit good arguments. In the next section we examine some second-best policy for the model.

4. Second-best policies

Second-best government policies can be approached in a number of ways. First, governments lack the information necessary to optimise the income distribution. Secondly, they may be unable to set tax rates that vary across individuals since consumers might resell the commodity to avoid the taxes. Hence, we should consider the case in which governments have to charge the

T. Be&y, Merit good arguments 317

same price of the merit good to all consumers. We might also be interested in public expenditure policies. Some goods that are often thought of as being merit goods, e.g. health or education, are provided by the state. Even when this is true it might be impossible for the state to enforce a very specific allocation of consumption. Unwilling individuals may not be forced to take up the full amount of state provision. Although there are rules governing compulsory education, which can be regarded as being due in part to our variety of merit good arguments, there is relatively little sanction operated for failure to consume higher education which when on offer may also be undervalued. These difficulties mean that public expenditure rules will also be of a second-best kind. In this section we must strengthen the assumptions that we have required so far. We assume that the necessary conditions characterising our choice of policy variables are also sufficient.

Our first example of a second-best policy considers an economy in which we are constrained to charge a tax rate (or subsidy rate) on the merit good which is the same for all individuals. In order to make the comparison with the first best as clear as possible, we will continue to maintain the assumption that the income distribution is optimal. We also assume initially that the tax rates on the non-merit goods are zero.

The problem for the government is to choose a rate of tax r on the merit good and a vector of incomes m to maximise

WkYP, 4/Q’, ml), * *. 3 P(P, lw, 4) subject to

r T yhh 4, mh) -C mh = 0,

(4.1)

(4.2)

where @: = q + T.

Our constraint is that the government should balance its budget. The government has H+ 1 control variables: (m’, . . ., mH) and T. Setting up the Lagrangian with Lagrange multiplier J on the constraint in (4.2) yields lirst- order conditions:

(4.3)

mh:$g+l Tg(p,cj,mh)-l =O, each h. (4.4)

It is useful to define:

i aw agh ““:=jpam. (4.5)

378 T Besley, Merit good arguments

With the aid of this definition we have, by substituting (4.4) into (4.3) for each h and rearranging the resulting equations,

T_ChWhGh-Yh) 1 z- &yh - ’ &YY

where

&?TP, c?/e”, mhYW~h) 1 jh'= - dgh(p,q/Bh,mh)/dmh eh’

(4.6)

(4.7a)

(4.7b)

and

(4.8)

where c stands for ‘compensated’, i.e. this is the consumer’s demand derivative when he is compensated to stay at a given utility level.

This gives us a formula for the optimal tax on the merit good. It is inversely proportional to cyy, which is a weighted sum of the individuals’ compensated demand elasticities. This is for standard reasons when there is consideration of excess burden. The more unusual expression is the first term on the right-hand side of (4.6). We can interpret jh as the demand for the merit good that the government would choose for the individual or the individual would choose for himself if he had the ‘correct’ preferences. Call this the ‘merit quantity of yh’. The tax rate depends upon a weighted sum of the deviations of merit quantities from actual quantities. The weights are the social marginal utilities of income delined in eq. (4.5). It is interesting to note that although we have an optimal distribution of income, these weights still matter. The reason why they differ across individuals can be seen from eq.

(4.4). There is divergence from unity in so far as there is an income effect for good yh. The optimal taxes equalise net marginal utilities of income defined as:

ayh (p=Wh+T- am'

(4.9)

Returning to (4.6) we can see that if jh>yh for each h (i.e. the government believes that defective preferences lead to under-consumption of the merit good), then since EyY ~0, we have z <O and we should have a subsidy on the merit good. On the other hand, if yh is a demerit :ood we should have a tax. The outcome is ambiguous where fh > yh for some h and Jh < yh for others.

I: Besley, Merit good arguments 379

This, however, is quite an unusual case, in which preferences are incorrect in different directions for different individuals.

This tax model can be extended to the case in which there are also taxes on other goods. In this case the government’s budget constraint is:

In this case the optimal tax rule for r when mh is optimally chosen is:

A,=~hWh(Bh-Yh)

c ’ hYh

where

(4.10)

(4.11)

(4.12)

The expression in (4.12) is what Mirrlees (1976) calls an ‘index of discourage- ment’ for good y. In this case, whether we have a merit or a demerit good governs whether we have discouragement or encouragement at the tax optimum. When the t’s are non-zero, then inferences about the sign of r cannot be made, in general, for this case. It is also interesting to look at the tax rates on the non-merit goods. We have:

’ i=L...,N. (4.13)

This is an important difference with the first best when no interference with the consumption of non-merit goods is required. In this case we encourage or discourage via taxes according to whether the consumers have merit quantities of Xi above or below that chosen with the defective preferences. Suppose that Oh> 1, i.e. we have a merit good, then the effect of introducing these considerations on the consumption of x: is given by:

ax! _. ax:

aeh eh=l=-~4. (4.14)

Hence, the consumption of complements with the merit good is encouraged by moving towards the correct preferences, while substitutes are discouraged. Hence 22: is likely to be greater than x7 when the good is a gross complement with yh and less than x: when it is a gross substitute. This gives some credence to the view that one’s fiscal treatment of complements with merit goods is analogous to that for merit goods themselves. This arises because if

380 7: Besley, Merit good arguments

one cannot get a first-best allocation for merit goods, then one is inclined to encourage the consumption of complements with them to encourage their use further. This suggests that one might wish to subsidise academic books and school transport as well as education, say. This is due to second-best considerations.

We can also consider the generalisation to the case in which the income distribution is not optimal. We take the case of many taxed goods with a uniform lump-sum transfer. In this case, we have:

,y=~h~;h- l)Yh+C,Wh(jh-Yh)

hYh c hYh (4.15)

as our optimal tax rule. The first term is familiar from optimal tax theory [see, for example, Atkinson and Stiglitz (1980)]. It is the normalised covariance between the net social marginal utility of income and the demand for the merit good. The second term is now also familiar. The formula in (4.15) is conveniently additive since the terms due to merit good consider- ations are just added to those required in the ordinary optimal tax case. As one would expect for this case, the tax system for merit goods must look at the distributional effects of its policies. If the covariance is positive (con- sumers with higher distributional weights consume more of the merit good), then the distributional effects reinforce the merit good arguments. It is convenient to specialise this further to the case in which there is no taxation of non-merit goods, for which we have:

z __I -=&,,

4

(4.16)

It is clear from (4.16) how distributional and merit good arguments may reinforce or oppose each other. The case for a subsidy is unambiguous when the covariance term is positive and jj” is greater than yh for each individual. Conflicts arise with a demerit good consumed disproportionately by those with a positive covariance term (perhaps cigarettes is an example of this). There is also a conflict when a merit good is consumed predominantly by the rich (the case of opera seems appropriate here). The case for taxes or subsidies rests on the balance of these two effects4

To conclude our analysis of second-best policies, we look at a simple public expenditure model. We look at a case in which the government provides a fixed level of expenditure y to each individual. It can force all individuals to consume this amount and prevent any who wish to consume

&Related results with an analogous motivation for merit goods are given in Bevan (forthcoming, ch. 23).

7: Besley, Merit good arguments 381

more from doing so. Hence, if we take the example of education, it requires us to be able to outlaw any parallel market in education (i.e. there is no private education which is a perfect substitute for state education).

The problem for the government is,

max W(g’(p, Oly, m’), . . . , &P, BHy, m”N y,m

subject to

(4.17)

jqHy+;m”). (4.18)

We continue with the case of an optimal income distribution in order again to make comparisons with the first best transparent. The first-order con- ditions for our Lagrangian are:

aw a$ y:~y-Oh+lqH=O,

h au ay

aw agh rn":= s+A=O, each h.

Substituting (4.20) into (4.19) for each h, yields:

&$$$o”=q.

Define:

It is the virtual price of preferences, i.e. with the definition,

;pl*h=4

(4.19)

(4.20)

(4.21)

(4.22)

the merit good to a consumer without defective preferences used by the government. Using this

(4.23)

is the rule governing public expenditure provision. It says that y should be chosen so that, at the optimum, the average virtual price of the merit good (for a consumer with correct preferences) is equal to the market price. This is the analogue, for our model, of the result given by Atkinson and Stiglitz (1980, p. 499). In their case it is the virtual price associated with the

382 7: Besley, Merit good arguments

consumer’s actual preferences that should be equated with the market price of the optimum. The difference we have is that in our case, the merit preferences count.

5. Conclusions

In this paper we have examined merit good arguments using a specific model of defective preferences. The simple structure of the model has provided some understanding of the structure of first- and second-best policy devices. As we argued in the Introduction, these interventions are not based on market failure or distributional arguments, although when the govern- ment lacks sufficient information to achieve the first best, merit good arguments become intertwined with such considerations. Such effects are familiar from analyses of second-best policies.

The analysis is premised on the idea that a social planner, or politician, ‘knows best’ but chooses to correct individual preferences in a very specific way, i.e. via altering the valuation of merit goods alone. There is no violation of individual preference orderings beyond this. This attempts to capture the commodity specific nature of the merit good idea. The idea is essentially paternalistic and it is important to note that it is not based on ideas of imperfect information. Even if individual h knew the 19~ being applied by the government, he would not accept it as a basis for valuation in the terms of our model. The planner subverts individual preferences but at the same time engages in total sympathetic identification with the interests of his citizens.

The picture of Utilitarian politics that we have painted may seem objectionable, and for many is regarded as a more stringent basis for interventions than those based on distributional or market failure arguments. Nevertheless, our analysis suggests the need to spot the wolf in sheep’s garments. The imperfect information argument can easily be concealed as an argument of the kind that we are analysing. If this is a less objectionable basis for ‘correcting’ market outcomes, then we should test whether in a world with costless policies, the government would be indifferent between information provision and direct interventions. If this is not so, then we are in a world in which the model of this paper applies.

The frequency with which merit good arguments are used suggests that it is useful to have a model for the case based on defective subjective evaluation of states of affairs. Our simple structure means that we are some way short of a paradigmatic representation for merit goods: our analysis is best construed as an illustrative example. However, the gains from working with more sophisticated forms of the merit goods valuation function ph(yh) are not immediately apparent. The case of many merit goods is straight- forward, but since our aim has only been to expose the grammar of the arguments, the gains from treating this case are not very great either.

7: Be&y, Merit good arguments 383

References

Atkinson, A.B. and J.E. Stiglitz, 1980, Lectures on public economics (McGraw-Hill, New York). Besley, T.J., 1987, Information, evaluation and intervention in the nrovision for ill-health.

typescript. Bevan, D.L., Forthcoming, Accumulation and inequality (O.U.P., Oxford). Fisher, F.M. and K. Shell, 1968, Taste and quality change in the pure theory of the cost of living

index, in: J.N. Wolfe, ed., Value, capital and growth (Edinburgh University Press, Edinburgh). Hammond, P., 1981, Ex ante and ex-post welfare optimality under uncertainty, Economica 48,

235250. Mirrlees, J.A., 1976, Optimal tax theory: A synthesis, Journal of Public Economics 6, 327-358. Muellbauer, J.N.J., 1975, The cost of living and taste and quality changes, Journal of Economic

Theory 10, 269-283. Musgrave, R., 1959, The theory of public finance (McGraw-Hill, New York). Pazner, E., 1972, Merit wants and the theory of taxation, Public Finance 27, -72. Sandmo, A., 1983, Ex post welfare economics and the theory of merit goods, Economica 50,

19-33. Sen, A.K., 1970, Collective choice and social welfare (North-Holland, Amsterdam).