Corrective Taxes and Cigarette Characteristics.

HEALTH ECONOMICS Health Econ. 25: 844–859 (2016) Published online 27 April 2015 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/hec.3188

CORRECTIVE TAXES AND CIGARETTE CHARACTERISTICS PAUL CALCOTT* and VLADIMIR PETKOV School of Economics and Finance, Victoria University of Wellington, Wellington, New Zealand

SUMMARY If cigarette design was exogenous, inefficiencies arising from smoking could be addressed either with a tax per packet or with an ad valorem tax. However, it is well known that the consequences of these two instruments differ when product characteristics are endogenous. We consider three such characteristics: nicotine, tar, and flavor. Implementation of the firstbest social optimum typically requires the capacity to tax or regulate harmful ingredients. Without such a capacity, the next-best policy often combines a per-unit tax on cigarettes with an ad valorem subsidy. Copyright © 2015 John Wiley & Sons, Ltd. Received 6 March 2013; Revised 3 October 2014; Accepted 30 March 2015 JEL Classification:

KEY WORDS:

C73; D41; H21; I18

cigarette design; internalities; corrective taxes

1. INTRODUCTION This paper studies the implications of endogenous product characteristics for cigarette taxes. In particular, we investigate how the government might use a combination of policies to reduce smoking, as well as to influence product design. Incentives for consuming the optimal quantity of cigarettes could be provided with a single tax instrument that may either take a per-unit form or be applied ad valorem. Thus, when cigarette design is exogenous, there would be no need for product regulation or supplementary taxes. But when producers are able to manipulate cigarette characteristics, implementation of efficiency may require the simultaneous use of multiple instruments. Our analysis examines such combinations of instruments in a variety of models. We assume that specific and ad valorem taxes are always available to the policymaker, but consider a range of assumptions about the practicality of taxing and regulating product ingredients. Until direct government control over these ingredients becomes feasible, inefficient cigarette consumption and design can be addressed with a mix of per-unit and ad valorem taxes. Public health concerns have been expressed about three types of substance present in tobacco products (Henningfield et al., 2004). Some ingredients have harmful health consequences. To simplify the exposition, we will use tar as a representative of this group. Other product features bring satisfaction, but also contribute to addiction. They will be represented by nicotine content. Finally, cigarettes can contain components that improve the experience of smoking without causing direct harm. Some of these components are complements to harmful

Correspondence to: School of Economics and Finance, Victoria University of Wellington, Wellington, New Zealand. E-mail: [email protected]

Copyright © 2015 John Wiley & Sons, Ltd.

CORRECTIVE TAXES AND CIGARETTE CHARACTERISTICS

845

ingredients. For example, menthol and sugars can soften or disguise harshness and thus make nicotine more palatable. We will summarize these factors as ‘flavor’. There is substantial evidence that cigarette characteristics are altered by manufacturers (Wayne and Carpenter, 2009). Moreover, these characteristics can be influenced directly or indirectly by government policies. For example, the EU Parliament has voted to ban menthol in cigarettes. In the US, flavors other than menthol are already banned. In addition, the Family Smoking Prevention and Tobacco Control Act has given the FDA the ‘authority to regulate the levels of tar, nicotine, and other harmful components of tobacco products’.1 Alternatively, harmful and addictive substances might be taxed rather than regulated (Drayton, 1971; Harris, 1980; Evans and Farrelly, 1998; Cebula, 2012; Laugesen, 2012). However, such taxes have rarely been imposed in practice see Irwin and Liroff (1974) for an example. Measuring the ‘addictiveness’ or ‘harmfulness’ of cigarettes for the purpose of taxation or regulation is likely to be challenging (Kessler, 1999). Conventional methods based on ‘smoking machines’ have been unreliable and susceptible to gaming by manufacturers (Henningfield and Zeller, 2002; Wayne and Carpenter, 2009). Furthermore, general properties of cigarettes are not always attributable to a single ingredient. For example, health damage could be caused by multiple toxic substances. Similarly, nicotine may not be the only addictive ingredient (Hatsukami et al., 2010), and its absorption by smokers depends on many features of cigarettes in addition to their nicotine content (Ashley et al., 2009). Despite these difficulties, there is active research on new approaches to measurement (Watson et al., 2004), which may have future regulatory applications. Given the existing measurement issues and the recent trends in tobacco control legislation, there is a case for examining several regulatory regimes. Thus, we consider optimal taxes when the harmfulness and addictiveness of cigarettes can be controlled by the policymaker, and also when direct government control is not possible. Our paper focuses on inefficiencies due to consumption internalities. We analyze a model of addiction, in which smokers are sophisticated but present biased. Gruber and Koszegi (2001) have argued that the combination of present bias and addiction provides a potential reason to impose a substantial cigarette tax.2 They assume quadratic payoffs and consider a per-unit tax that is fixed over time. We extend their work by endogenizing product characteristics as discussed earlier. In order to distinguish between the consequences of tar and nicotine intake, we introduce separate stocks for ill-health and addiction. Moreover, our approach allows general functional forms for payoffs. Finally, we consider more flexible instruments: our corrective taxes can vary over time, and may be levied on a number of different variables. Our analysis shows that simultaneous implementation of the first-best consumption plan and cigarette design does not require flavor to be addressed, but the government must be able to influence both addictiveness and harmfulness. In one scenario that may soon become more realistic, these two characteristics can be targeted directly by the policymaker. If taxes are imposed on both, then no other instrument need be used. However, regulating these substances rather than taxing them will not be sufficient to prevent excessive smoking. A specific tax would also be required. So long as difficulties with measurement prevent the policymaker from taxing or regulating cigarette characteristics, he might rely on a combination of specific and ad valorem taxes. There is extensive research on the effects of these taxes on product design (Barzel, 1976; Sobel and Garrett, 1997; Keen, 1998).3 One result in this literature is that an ad valorem tax can create an incentive for producers to alter quality. In our model, this instrument can be used to incentivize efficient levels of a targeted ingredient. However, such a tax would also motivate smokers to adjust the number of cigarettes that they purchase. A single instrument is unlikely to promote socially optimal consumption and simultaneously ensure efficient levels of a product ingredient. Hitting both targets might be possible, however, if the ad valorem tax is accompanied by a per-unit tax.

1 2 3

Section 3, H.R. 1256 (111th): Family Smoking Prevention and Tobacco Control Act, Aug 20, 2010. O’Donoghue and Rabin (2006) also model internality taxes, albeit without accounting for addiction. Harris (1980) identifies the effects on product design from a linear per-unit tax. However, he combines nicotine and tar into a single variable and proposes a single-step-function tax rather than multiple instruments.


Health Econ. 25: 844–859 (2016) DOI: 10.1002/hec

846

P. CALCOTT AND V. PETKOV

When there are multiple characteristics that cannot be taxed or regulated, first-best efficiency is not generally attainable with just these two instruments.4 In such a setting, the government could only implement a constrained social optimum. The ad valorem tax rate should be set to strike a balance between the competing requirements for reducing the distortions associated with the different characteristics. Although we consider inefficiencies due to internalities, we could have made alternative assumptions. The specifics of corrective taxes will depend on the motives for government intervention. But our policy analysis is applicable to a wider variety of settings, because the expressions for tax rates obtained below are formulated as general functions of distortion terms. Our results can be extended to reflect other views of smoking and addiction, so long as these views generate determinate expressions for the private and the social harm from inefficient consumption and design of cigarettes. We present two such extensions in Section 7: externalities and market power. Externalities are a potential source of distortion, through side effects such as passive smoking. Another plausible source of market failure is imperfect competition in cigarette markets. However, it is assumed away in our benchmark model, so that we can isolate the impact of taxes on product quality. The previous literature has established that specific and ad valorem taxes have different effects on the exercise of market power (Delipalla and Keen, 1992; Skeath and Trandel, 1994). It is convenient to determine the effects of these policies on cigarette design in our baseline model, before examining the interaction between these effects and market power in Section 7. The remainder of the paper is structured as follows. Section 2 sets up our benchmark model of a competitive market for cigarettes. The socially optimal outcome is characterized in Section 3 . A market equilibrium with a range of taxes is examined in Section 4. General expressions for market distortions are set out in Section 5, and mapped to implementation conditions. Section 6 characterizes specific policies that would implement first-best or constrained efficiency. Extensions to the model are considered in Section 7. Section 8 presents an example, and Section 9 concludes. 2. MODEL We consider three characteristics of cigarettes. The first is tar, qb , which has harmful consequences for future health, but no effect on current utility. The second is nicotine, qa , which provides satisfaction and also contributes to addiction. Finally, flavor, qf , increases current enjoyment, but does not directly impact future well-being. Let aggregate intake of an ingredient j 2 a; b; f in period t be Qjt D qjt x t , where x t is the number of cigarettes consumed. Smoking gives rise to two stocks. The first is addiction, ka , which is formed by accumulated consumption of nicotine. The second is ill-health, kb , which results from the accumulated intake of tar. Their laws of motion are as follows: kat C1 D a kat C Qat

kbt C1 D b kbt C Qbt ;

(1)

where 1 j is the rate of decay for stock j . A representative smoker has concave period-t utility of ut D v.Qft ; Qat I kat ; kbt / C mt , where mt is current consumption of a numéraire good. We will assume that flavor improves the experience of smoking, @v t =@Qft > 0. Moreover, smokers desire a positive and finite dose of nicotine: lim @v t =@Qat D 1;

t !0 Qa

4

lim @v t =@Qat D 0:

t !1 Qa

Other barriers to first-best implementation include compensatory behavior and heterogeneity of smokers (Adda and Cornaglia, 2006; O’Donoghue and Rabin, 2006).



847


Addiction is harmful, @v t =@kat < 0, and so is illness, @v t =@kbt < 0. Thus, while tar intake does not have any immediate consequences for the smoker, it reduces her or his utility in following periods by damaging her or his future health. The addictive nature of nicotine can be acknowledged by assuming complementarities between past and current nicotine consumption, @2 v t =.@Qat @kat / > 0. Flavor may increase the marginal utility of nicotine, @2 v t =.@Qat @Qft / 0. Suppose that the consumer is present biased. In particular, she has quasi-hyperbolic time preferences. Lifetime utility from his or her viewpoint in period t is U t D ut C ˇ

1 X

.ı/st us ;

(2)

sDt C1

where 0 < ˇ 1 and 0 < ı < 1. Present bias gives rise to consumption internalities. Without precommitment, the smoker will tend to overconsume in the future (as assessed from her current viewpoint). This is because her period-t C 1 self will discount by ˇı the harm from ill-health and addiction that would be incurred in t C2. However, from her periodt perspective, the discount factor for that trade-off should be ı.5 We assume that the smoker is sophisticated: the smoker anticipates her subsequent overconsumption and takes it into account in her current decisions. Production follows constant returns to scale. Suppose that the period-t unit cost is c.qat ; qbt ; qft /. This function is assumed to be strictly convex, with an interior minimum. The interpretation is that there are natural levels of nicotine, tar, and flavor in the basic variety of tobacco that are costly for producers to depart from. Whether the equilibrium levels of these ingredients will be higher or lower than the least-cost levels may depend on how government policy is set. Cigarettes are manufactured in a competitive industry. Consequently, their prices match unit production costs: p t D c.qat ; qbt ; qft / . This allows us to write the smoker’s period-t payoff (gross of any tax payments) as w t D v qft x t ; qat x t I kat ; kbt c qat ; qbt ; qft x t : (3) 3. THE SOCIAL OPTIMUM There is some controversy about the appropriate goal for the planner that we do not wish to engage with here. Instead, we will follow a common approach in the literature and assume that the planner is concerned with the long-run well-being of consumers: he discounts future welfare exponentially by a factor ı.6 Thus, lifetime 1 P .ı/st w s : welfare as assessed in period t is given by sDt

Imagine that the planner can directly choose the smoker’s consumption, as well as regulate the design of cigarettes. Let S t D fqat ; qbt ; qft g be the set of product characteristics. The planner’s problem is represented by the following Bellman equation: n o (4) V kat ; kbt D max v Qat ; Qft I kat ; kbt c qat ; qbt ; qft C ıV a kat C Qat ; b kbt C Qbt , S t ;x t

where V is his value function. The efficient consumption plan fx t g1 t D0 solves the first-order condition: 0D

X j Da;f

5 6

X @V t C1 @v t t t q c C ı qt : j t C1 j @Qjt @k j j Da;b

(5)

In the special case when ˇ D 1, the smoker’s time preferences become exponential and her or his present bias disappears. One justification for this approach is that all but one of the period-specific preferences are in accord with the long-run approach (Bernheim and Rangel, 2007, p. 14).



848


Furthermore, the planner’s preferred level of characteristic qjt would satisfy " 0D

# @v t @c t @V t C1 t C ı t C1 x t ; @Qjt @qj @kj

(6)

where @V =@kf 0. Equations (5) and (6) suggest that the marginal benefit of any of x; qa ; qb , and qf should be balanced against the respective marginal change in production costs plus the social marginal harm in subsequent periods. Note that the instantaneous marginal utility of tar equals zero, @v=@Qb 0, and that the flavor of current cigarettes does not directly affect future payoffs. Finally, differentiating (4) with respect to stock kjt , j D a; b, yields an envelope condition: @v t @V t @V t C1 D C ı . j @kjt @kjt @kjt C1

(7)

4. MARKET EQUILIBRIUM Manufacturers choose output levels and also any product characteristics that are not subject to regulation. Let Sm S be the set of these characteristics. The planner may have several tax instruments at his disposal to influence these choices. A specific tax, xt , is paid for every cigarette purchased. It discourages the consumption of cigarettes, but does not have a direct effect on firms’ incentives to alter product characteristics. An ad valorem tax, ct , is levied in proportion to expenditure on cigarettes. It affects incentives for both the number of cigarettes sold and their characteristics. Because prices and quantities are easily observable, these two instruments are always available. Furthermore, the planner may be able to impose ingredient taxes, jt , j 2 a; b; f . They would be tied to product characteristics that may or may not be measurable and taxable in practice. When available, ingredient taxes could directly influence incentives for the design of cigarettes. To begin with, our analysis is agnostic about whether characteristics are amenable to taxation or regulation. If a characteristic j is untaxable, the relevant direct tax, jt , is necessarily zero. Taxes could be negative, that is, take the form of subsidies. The consumer correctly predicts future prices and government policies, but cannot affect them with her individual behavior. Tax rates could be set period by period with reference to the average stocks of addiction and ill-health over all smokers, or could all be determined at time t D 0. Because the market for cigarettes is assumed to be perfectly competitive, producers will set any unregulated characteristics at the levels the current smoker would have chosen. With corrective taxes in place (some of which may be zero), the consumer’s instantaneous payoff would be given by v qft x t ; qat x t I kat ; kbt 1 C ct c qat ; qbt ; qft x t xt x t

X

jt qjt x t :

(8)

j Da;b;f

As noted earlier, present bias creates an internal strategic conflict between the smoker’s current and subsequent selves. By assumption, she is aware of this conflict. Thus, we model decision making as an intra-personal dynamic game. Suppose that the players in this game follow Markovian strategies: their choices depend only on the current state. We use dynamic programming to characterize these choices. The current tax rates, t D fxt ; ct ; at ; bt ; ft g, are elements of the agents’ state, together with the stocks kat and kbt . Equilibrium cigarette output and characteristics would solve the following Bellman equation: Copyright © 2015 John Wiley & Sons, Ltd.


849


8 < U.kat ; kbt ; t / D max v qft x t ; qat x t I kat ; kbt xt x t 1 C ct c qat ; qbt ; qft x t t : fx t ;Sm g 9 = X jt qjt x t C ıˇW a kat C qat x t ; b kbt C qbt x t ; t C1 : ;

(9)

j Da;b;f

From the smoker’s period-t perspective, discounting becomes exponential after t C 1. Consequently, in equilibrium, the continuation value function W must satisfy W kat ; kbt ; t D v qft x t ; qat x t I kat ; kbt 1 C ct c qat ; qbt ; qft x t xt x t X (10) jt qjt x t C ıW a kat C qat x t ; b kbt C qbt x t ; t C1 : j Da;b;f

Differentiating (9) with respect to x t delivers a first-order condition for the number of cigarettes consumed: X j Da;f

qjt

t @v t t t t 1 C c c x @Qj

X

jt qjt C ıˇ

j Da;b;f

X

qjt

@W t C1

j Da;b

@kjt C1

D 0:

(11)

If characteristic qjt , j D a; b; f , is not fixed by regulation, its equilibrium level will satisfy t @W t C1 @v t t @c t 1 C C ıˇ D 0; c j @Qjt @qjt @kjt C1

(12)

where @W=@kf 0. The interpretation of (11) and (12) is that the smoker balances the marginal benefit of a choice variable against both his or her expenditure (including taxes) and his or her private valuation of the respective discounted future harm. Finally, differentiating (10) with respect to kjt , j D a; b, and substituting in the relevant private first-order condition yields an equation for the derivatives of the continuation value function W : X @W t @v t @W t C1 C ı.1 ˇ/ t D t C ıj t C1 @kj @kj @kj

i Da;b

where

@qit =@kjt

" qit

t @x t t @qi t Cx t @kj @kj

#

@W t C1 @kit C1

;

(13)

0 if the producer is not free to adjust qi . 5. FIRST-BEST IMPLEMENTATION

We now obtain general expressions for the distortions induced by smokers’ present bias. These expressions are then used to formulate conditions for first-best implementation. In the following section, they will help us identify optimal policies. 5.1. Distortions In the absence of government intervention, smoking would generate internalities that are mediated through the two stock variables. Specifically, inefficiencies would arise because smokers’ private valuations of the future harm from addiction and ill-health will be lower than their respective social counterparts: 0 > ıˇ.@W t C1 =@kjt C1 / > ı.@V t C1 =@kjt C1 /; j D a; b. Copyright © 2015 John Wiley & Sons, Ltd.


850


In the following discussion, it will be convenient to have compact notation for these discrepancies. Let Mj be the internality term associated with the accumulation of characteristic qj : # " t C1 t C1 @W @V ; (14) Mjt D ı ˇ t C1 @kj @kjt C1 for j D a; b. Flavor does not contribute to any stocks, so Mft 0. The planner would like to incentivize socially optimal consumption as well as efficient design of cigarettes. Thus, he wishes to implement values of four target variables: x; qa ; qb , and qf . The number of available instruments will depend on the practicality of regulations or taxes on characteristics. We first analyze a general setting in which up to five taxes are feasible, before considering implementation when characteristic taxes are not available. 5.2. Implementation conditions To implement the socially optimal number of cigarettes, x, taxes should reconcile the efficiency first-order condition, (5), with the equilibrium first-order condition, (11). Equations (5) and (11) will imply identical consumption plans when X X qj j D qj Mj : (15) x C c c C j Da;b;f

j Da;b

The additional tax obligation incurred by smoking another cigarette can have up to five components, as represented by the left-hand side of (15). The total value of this obligation should match the sum of the internalities associated with a cigarette, as set out on the right-hand side. Now, consider how product characteristics are determined. If ingredient qj is regulated, the planner will require its level to satisfy (6). Whenever qj is unregulated, its efficient level might be incentivized with taxes. They would provide correct incentives when the equilibrium conditions (from (12)) are consistent with their efficiency counterparts (from (6)). The equilibrium condition for an unregulated characteristic incorporates two taxes: the ad valorem tax and the tax on the respective ingredient (which would be zero if that ingredient is untaxable). Therefore, the reconciliation conditions for qj will balance the impact of these two instruments against the relevant internality: j C c

@c D Mj @qj

(16)

for qj 2 Sm . The aforementioned observations are summarized in the following proposition. Proposition 1 To deliver first-best implementation in a perfectly competitive setting, the tax rates must satisfy (15) and must also solve (16) for all unregulated ingredients (qj 2 Sm ). In addition, the levels of all regulated ingredients (qj … Sm ) must solve (6). 6. OPTIMAL POLICIES The planner’s choices will depend on which instruments are available. We will examine four settings that differ in their assumptions about the feasibility of taxing and regulating product characteristics. First, we consider how policy might be structured once technology permits direct government control over all harmful ingredients. In Section 6.1, these characteristics are regulated, while in Section 6.2, they are taxed. Then, Section 6.3 Copyright © 2015 John Wiley & Sons, Ltd.



851

considers intermediate cases in which the regulator cannot control all attributes directly, but full efficiency is still implementable. Finally, Section 6.4 studies a setting relevant for current policymakers, in which the first-best outcome is not attainable. 6.1. Regulation of cigarette ingredients In the absence of intervention, three of the equilibrium first-order conditions would differ from their efficiency counterparts: those with respect to qb , qa , and x. The laissez-faire first-order condition for flavor has a form that is consistent with the corresponding efficiency condition. However, the level of this characteristic may also be distorted because of complementarities with the other variables. Imagine that the government can prescribe the socially efficient levels of tar and nicotine in cigarettes as characterized in equation (6). This would leave two remaining choice variables to implement, x and qf . There are many tax combinations that could achieve this objective. However, the most straightforward way would be to just use a per-unit tax, without resorting to an ad valorem tax or a flavor tax. With the levels of tar and nicotine fixed by regulation, (16) would not apply to these two ingredients. An ad valorem tax would not be needed to incentivize their efficient levels. Moreover, if qf is unregulated, equation (16) would imply that its socially optimal value is achievable without a flavor tax or an ad valorem tax. To moderate consumption of cigarettes while keeping flavor undistorted, the government could use the specific tax. When c D a D b D f D 0, equation (15) suggests that x should be set as X x D qj Mj : (17) j Da;b

The intuition for (17) is that the specific tax would be the only penalty for consumption, and so it should account for the full extent of the internalities. Even if it becomes possible to regulate all harmful ingredients to their socially optimal levels, there will still be a role for cigarette taxes. 6.2. Feasible characteristic taxes Although policy attention has focused on regulating ingredients instead of taxing them, economists often advocate corrective taxes rather than quantity controls. When characteristic taxes are feasible, there are multiple ways to implement the first-best outcome. Even with four target variables, it is possible to incentivize efficient values for all of them with as few as two instruments. For example, the reconciliation equations (15) and (16) can be satisfied with taxes only on the two ingredients that are directly tied to internalities, nicotine and tar: a D Ma ;

b D Mb .

As the internalities are fully accounted for with a ; b , there is no need to use any other instruments: c D x D f D 0. This proposal would automatically induce the efficient output path. Note that fewer instruments are required when implementation is attained with ingredient taxes rather than with ingredient regulation. The reason is that regulations by themselves would leave consumption of cigarettes inefficiently high, but taxing tar and nicotine automatically discourages excessive smoking. 6.3. A single unregulated characteristic Now, suppose that the only taxes available to the government are the ad valorem tax, c , and the specific tax, x . The first-best outcome may be impossible to implement with only these two instruments, and it is probably not implementable in current cigarette markets. But before examining a second-best equilibrium, we first consider a simpler, if less realistic, setting in which full efficiency is still implementable. This helps us isolate the Copyright © 2015 John Wiley & Sons, Ltd.


852


implications of taxes for individual characteristics. It may also be instructive for a transitional environment in which some but not all harmful ingredients can be addressed directly. Imagine that there is only one characteristic, q1 2 fqa ; qb ; qf g, which cannot be regulated. Then, the required rates for the specific and ad valorem taxes can be found by setting characteristic taxes to zero in equations (15) and (16): M1 c D ; (18) @c=@q1 X qj Mj : (19) c c.qa ; qb ; qf / C x D j Da;b

Equation (18) reflects the need for the ad valorem tax to fully align private and social incentives for ingredient q1 in the absence of a more direct instrument. Equation (19) shows how efficient incentives for cigarette quantities should be provided by a balance of ad valorem and specific taxes. The implications of (18) and (19) depend on the identity of the targeted characteristic. 1. Unregulated flavor First, suppose that only flavor is unregulated. As argued in Section 6.2, it is not necessary to tax this ingredient. The reason is that it does not accumulate into a harmful stock. Setting @V =@kf 0 in equation (6) and recalling that the marginal utility of flavor is globally positive, it follows that @c=@qf > 0 in the social optimum. That is, resources should be expended to increase flavor above the least-cost level. As flavor does not generate an internality, Mf 0, (18) implies that the ad valorem tax should be zero: c D 0. Then, (19) yields the same specific tax as suggested in (17): x D qa Ma C qb Mb : To induce efficient output, the specific tax should again be set to the sum of internalities from smoking another cigarette. 2. Unregulated tar Second, suppose that only tar is unregulated. As qb does not impact current enjoyment, equation (6) gives us @c @V D < 0: @qb @kb In the efficient outcome, resources are expended to decrease tar below the least-cost level. Then, (18) would suggest that the ad valorem tax should be negative: c D

Mb < 0: @c=@qb

The intuition is that a subsidy for product quality reduces tar for given levels of nicotine and flavor. The specific tax should be even higher than the combined internalities from smoking another cigarette, because this instrument has to neutralize the output incentives from the ad valorem subsidy: X cMb x D qj Mj : @c=@qb j Da;b

3. Unregulated nicotine Finally, suppose that only nicotine is unregulated. Because qa affects both current enjoyment and future well-being, our assumptions do not determine unambiguously whether resources should be expended to reduce or increase the nicotine content of cigarettes. But the most plausible scenario may be that the least-cost nicotine content is too high from a social viewpoint. Then, @c=@qa < 0 holds in the Copyright © 2015 John Wiley & Sons, Ltd.



853

social optimum. If so, unregulated nicotine would also call for a combination of an ad valorem subsidy and a specific tax: c D

Ma ; @c=@qa

X

x D

qj Mj

j Da;b

cMa : @c=@qa

6.4. No characteristics regulated In the final setting, none of the product ingredients can be measured reliably enough for regulation or direct taxation. Because product ingredients will typically yield differing values of Mj =.@c=@qj /, equation (16) suggests that the first-best outcome is not attainable. In these circumstances, the planner could implement a constrained optimum with an ad valorem tax and a specific tax. The ad valorem tax now reflects a compromise between competing requirements for reducing distortions in the various characteristics.7 The specific form that this compromise takes in our model is set out in the following proposition. The proof is presented in Appendix A in the Supporting Information. Proposition 2 Let qje .x; c; ka ; kb / be the utility maximizing choices of product characteristics conditional on output, per-unit costs and stocks. The constrained optimal ad valorem tax is given by: c D

X j Da;b;f

˛j

Mj ; @c=@qj

(20)

@q e

@c j . In addition, the total tax per cigarette where the weights, ˛j , are the marginal cost shares: ˛j D @q j @c should be X X @qje cc C x D qj Mj C x Mj : (21) @x j Da;b

j Da;b

The constrained optimal ad valorem tax is a weighted average of the expressions in (18), which identified the optimal rates of this tax when a single characteristic was unregulated. However, in Section 6.3, these expressions were evaluated at the first-best outcome. In Proposition 2, they are instead evaluated at the constrained optimal outcome that is implementable in this setting. Also, note that qje , and therefore equilibrium quantities and tax rates, may now depend on whether or not the government can precommit to future policies. To interpret the marginal cost shares, ˛j , referred to in this proposition, consider how an increase in c will motivate producers to reduce unit cost. This reduction can only be achieved by altering the characteristics of cigarettes. If a marginal decrease in the required unit cost leads firms to decrease qj by @qje =@c, and a marginal change in qj has an impact on unit costs of @c=@qj , then the contribution of characteristic qj to achieving the desired reduction in unit cost is ˛j D .@c=@qj /.@qje =@c/.8 As when nicotine was the only unregulated characteristic, the sign of the constrained optimal ad valorem tax is theoretically indeterminate. And again, it seems plausible that it could be negative. So long as the constrained optimum requires manufacturers to expend resources to reduce tar and nicotine below their natural levels, @c=@qa < 0; @c=@qb < 0, the ad valorem tax rate will be a weighted average of two negative terms and one term that equals zero. Accounting for characteristics such as flavor (i.e., for which efficiency requires c D 0) would suggest that the constrained optimal value of the ad valorem tax or subsidy should be moderated.

7

A similar compromise may arise whenever the first-best outcome is not implementable. For example, this may be the case when some consumers are more addicted, more present biased or more naive X than others, but all smokers face the same tax rate. 8 Appendix A in the Supporting Information establishes that ˛j D 1. Therefore, it is legitimate to interpret the ˛j terms as shares. j 2a;b;f



854


Equation (21) is the constrained optimal counterpart to (15). It balances the additional tax payments incurred by consuming another cigarette with the impact on total internalities. However, the specific tax now indirectly affects cigarette characteristics, and so has repercussions for smoking internalities. This is acknowledged with P the new term on the right hand side of (21), x j Mj @qje =@x. 7. EXTENSIONS The distortion terms defined in Section 5 and the policies identified in Section 6 were based on a particular view about the inefficiencies arising from smoking. Next, we explore two alternative accounts. In the first alternative, the required corrective taxes are still characterized by the implementation conditions (15) and (16). However, the distortion terms Ma and Mb need to be reinterpreted, because the slopes @V =@kj and @W=@kj of the social and private continuation value functions can no longer be adequately described by equations (7) and (13). In the second alternative to be considered, there are additional distortion terms. As a result, the implementation conditions also need to be amended. 7.1. Externalities Suppose that, in addition to internalities, characteristic qj ; j D a; b, gives rise to external costs 'j .kj /. That is, smoking might impose additional costs on society in terms of health damage, 'b .kb /, and addiction, 'a .ka /, which are ignored by the individual consumer. As before, the consumer’s period-t payoff is given by (8), and the laws of motion of his or her stocks are still defined by (1). Consequently, the equilibrium conditions (11) and (12) remain unchanged. The presence of such stock externalities implies the following form for instantaneous welfare: w t D v.qft x t ; qat x t I kat ; kbt / c.qat ; qbt ; qft /x t 'a .kat / 'b .kbt /: The planner’s first-order conditions are the same as (5) and (6). However, the slope of the social value function @V =@k will be affected. The envelope condition previously given by (7) needs to be amended: @'jt @v t @V t C1 @V t D C ı ; j @kjt @kjt @kjt @kjt C1

j D a; b:

The expressions for optimal taxes in terms of Mj are the same as in Section 6, although their interpretation must now account for externalities as well as internalities. 7.2. Market power Market power is another source of inefficiency but, unlike the previous extension to the model, it leads to substantive changes in firm behavior. As a result, it is necessary to reconstruct the characterizations of optimal taxes rather than just reinterpret Mj . Imagine that i D 1; : : : ; m symmetric Cournot oligopolists compete in output xi and unregulated product characteristics qj i 2 Smi . Because there are multiple producers, aggregate consumption of ingredient j is now P P Qj D m x q . The consumer’s instantaneous payoff is v.Q ; Q I k ; k / p a a b f i i xi , and firm i’s cost is i D1 i j i c.qai ; qbi ; qf i /xi . With the departure from perfect competition, equilibrium prices are no longer equal to unit costs. As a consequence, an ad valorem tax is not equivalent to a proportional increase in production costs. In order to acknowledge this, the ad valorem tax will now be denoted with v . The consumer chooses quantities of each firm’s product: Copyright © 2015 John Wiley & Sons, Ltd.


855


8 0 1 m < X X U.kat ; kbt ; t / D max v Qat ; Qft I kat ; kbt xit @xt C 1 C vt pit C jt qjt i A t : x1t ;:::;xm i D1 j Da;b;f ) CıˇW a kat C Qat ; b kbt C Qbt ; t C1 : The first-order condition with respect to xi determines an inverse demand curve for firm i: " # X qjt i @v t @W t C1 xt t t C ıˇ : pi D j @Qjt 1 C vt @kjt C1 1 C vt

(22)

j Da;b;f

The slope of this inverse demand is @pit D @xit

X

X

tj l

lDa;b;f j Da;b;f

t qjt i qli

1 C vt

,

where tj l D

@2 v t @2 W t C1 C ıˇ : @Qjt @Qlt @kjt C1 @klt C1

Producer i realizes that her or his decisions will affect the market price. If the producer discounts future profits exponentially by a factor ı, her or his Bellman equation will be given by n o t t i .kat ; kbt ; t / D max pit xit c qai ; qbi ; qft i xit C ıi a kat C Qat ; b kbt C Qbt ; t C1 ; (23) t xit ;Smi

where pit is as specified in (22). Reconciling the social planner’s first-order condition with respect to producer i’s output, xi , and the corresponding condition derived from (23), leads to the following generalization of equation (15): xt C vt cit C

X

qjt i jt D

j Da;b;f

X

qjt i Mjt C .1 C vt /ı

j Da;b

X @t C1 i @kjt C1 j Da;b

qjt i C .1 C vt /

@pit t x : @xit i

(24)

As in the baseline model of perfect competition, the combined marginal tax burden from producing an additional cigarette is set out on the left-hand side, and should be commensurate with the combined marginal distortion. But now there are two new distortion terms in addition to the internalities on the right-hand side. One reflects the consequences for firm i’s future profits, and the other accounts for firm i’s current market power. A generalized version of (16) can be obtained by reconciling the first-order conditions with respect to qj i from the planner’s and oligopolist i’s problems: jt C vt

X @cit @t C1 t tj l qjt i xit C .1 C vt /ı tiC1 t D Mj C @qj i @kj

(25)

lDa;b;f

for qj i 2 Smi . This expression also has terms reflecting concerns about current market power and future profits. Proposition 3 To deliver first-best implementation in an oligopolistic setting, the tax rates must satisfy (24) and must also solve (25) for all unregulated ingredients (qj i 2 Smi ). In addition, the levels of all regulated ingredients (qj i … Smi ) must solve (6). Copyright © 2015 John Wiley & Sons, Ltd.


856


Table I. Parameter values.

0.1

0.6

1

1

0

a

1

1

b

1

f

1

aN

bN

a

b

ı

ˇ

1

1

0.4

0.4

0.9

0.7

Equations (24) and (25) are derived in Appendix B in the Supporting Information. 9 8. EXAMPLE Optimal tax rates will typically change over time as the stock variables accumulate or decay. This section, however, considers a special case in which these tax rates should be constant. We assume that instantaneous utility is linearly homogeneous in Qf , Qa , and ka and also linear in kb . Specifically, it takes the following form: v.Qf ; Qa I ka ; kb / D g.Qf ; Qa I ka / kb ; where g.Qf ; Qa I ka / satisfies g.Qf ; Qa I ka / D g.Qf ; Qa I ka / for any non-negative . This payoff structure implies that the optimal levels of the cigarette ingredients would be independent of both stocks, and O and fO. Finally, note that the efficient consumption rule is thus also constant. Let us denote these levels by a; O b, O a . Appendix C in the Supporting proportional to ka and independent of kb . Suppose that it is given by x D k Information provides the conditions needed to determine the equilibrium strategies and the optimal tax rates. For illustration, consider the following forms for the instantaneous utility and unit cost functions: v D Qa Qf ka1 ka kb , c.qa ; qb ; qf / D

0

C

a .qa

a/ N 2C

b .qb

N 2C b/

f

qf .

The values we assign to the parameters are presented in Table I. This specification yields first-best policies O D 0:00241; aO D 0:78661; bO D 0:29688; fO D 1:51430. The corresponding values of the internality terms are Ma D 0:41847 and Mb D 0:42188. If all ingredients could be regulated down to their efficient levels, optimal consumption would be implemented with a specific tax of x D 0:45442. An ad valorem tax need not be used. On the other hand, if the government was able to tax these ingredients, the required direct taxes would be a D 0:41847 and b D 0:42188. No other instruments would be needed. When only one ingredient cannot be taxed or regulated, the first best is still attainable with a combination of a specific and an ad valorem tax. If flavor is unregulated, efficiency requires x D 0:45442 and c D 0. If, instead, tar is unregulated, these taxes should be set at x D 1:60432 and c D 0:30000. Finally, if nicotine is unregulated, their optimal values are x D 4:21286 and c D 0:98054. In all of the aforementioned cases, the total tax obligation per cigarette is qa Ma C qb Mb D 0:45442. Now, suppose that no cigarette characteristics can be taxed or regulated. Then, full efficiency will not be attainable. The second-best outcome will generally depend on whether the government could commit to future taxes. In our example, however, commitment is irrelevant, because equilibrium taxes are independent of the stocks. Given the aforementioned parameters, the planner would impose x D 0:65455 and c D 0:04180. This would implement an equilibrium with Q D 0:00228; aQ D :94162; bQ D 0:48634; fQ D 1:59998. The total tax obligation would be x C cc D 0:49458. 9

A complete characterization of the market equilibrium would also include the firms’ envelope conditions. The exact form of these conditions will depend on the choice of equilibrium concept (feedback or open-loop). However, (24) and (25) would be valid with either choice.




857

Figure 1. Ad valorem taxes

Figure 2. Specific taxes

Figure 1 illustrates the ad valorem taxes for a number of regulatory regimes when ˇ varies between 0.7 and 1. The optimal tax rate is non-positive for all values of ˇ considered. It is zero when the government can control both nicotine and tar directly, and when flavor is the only substance that cannot be taxed or regulated. Furthermore, the ad valorem subsidy is smaller in the second-best outcome than when only tar or only nicotine are not controllable. This suggests that such a subsidy, when accompanied by a specific tax, should be relatively modest until it becomes practical to control either tar or nicotine. Then the subsidy should increase until the other harmful ingredient can be taxed or regulated, at which point this instrument is no longer needed. Figure 2 shows the corresponding specific tax rates. Their values are non-negative for the entire range of ˇ and are always zero when both tar and nicotine are taxed. Note that higher ad valorem subsidies imply higher specific taxes, as the government needs to neutralize the additional distortions to output. Copyright © 2015 John Wiley & Sons, Ltd.


858


9. CONCLUSION Cigarette consumption can be discouraged with either per-unit or ad valorem taxes. One difference between these instruments is their effects on incentives for product design. In particular, an ad valorem tax discourages firms from charging high prices, and hence from designing cigarettes that are costlier to produce. While this effect is potentially distortionary, it can also be harnessed to mitigate distortions to product characteristics when more direct instruments are unavailable. We consider three cigarette characteristics with distinct implications for payoffs. All three affect the costs of production, and thus the market price. But they have different consequences for current enjoyment and future harm. Today’s tar intake affects tomorrow’s utility via the health stock, but has no impact on instantaneous enjoyment. In contrast, flavor does not accumulate into any stock, but delivers instantaneous satisfaction. Finally, nicotine has both kinds of effect. Smokers obtain immediate relief by absorbing nicotine, but there are consequences for addiction in the future. These differences have implications for policy when characteristics are determined in the market. When harmfulness and addictiveness can be taxed directly, first-best efficiency is attainable without the need for other instruments. Moreover, a combination of a per-unit tax and an ad valorem subsidy can often implement efficiency if only one ingredient is not amenable to regulation. But with more than one such ingredient, the subsidy might reflect a compromise between the requirements for various characteristics.

REFERENCES

Adda J, Cornaglia F. 2006. Taxes, cigarette consumption, and smoking intensity. American Economic Review 96(4): 1013–1028. Ashley DL, Pankow JF, Tavakoli AD, Watson CH. 2009. Approaches, challenges, and experience in assessing free nicotine. In Nicotine Psychopharmacology. Springer: Berlin; 437–456. Barzel Y. 1976. An alternative approach to the analysis of taxation. The Journal of Political Economy 84(6): 1177–1197. Bernheim BD, Rangel A. 2007. Behavioral public economics. In Behavioral Economics and Its Applications, Diamond P, Vartiainen H (eds). Princeton University Press: Princeton, NJ; 7–84. Cebula R. 2012. A new form of federal or state-level cigarette excise taxation in the US. International Journal of Economics and Finance 4(2): 16–20. Delipalla S, Keen M. 1992. The comparison between ad valorem and specific taxation under imperfect competition. Journal of Public Economics 49(3): 351–367. Drayton W. 1971. Tar and nicotine tax: pursuing public health through tax incentives. The Yale Law Journal 81: 1487–1516. Evans WN, Farrelly MC. 1998. The compensating behavior of smokers: taxes, tar, and nicotine. The Rand Journal of Economics 29(3): 578–595. Gruber J, Koszegi B. 2001. Is addiction rational? theory and evidence. Quarterly Journal of Economics 116(4): 1261–1303. Harris J. 1980. Taxing tar and nicotine. The American Economic Review 70(3): 300–311. Hatsukami DK, Perkins KA, LeSage MG, Ashley DL, Henningfield JE, Benowitz NL, Backinger CL, Zeller M. 2010. Nicotine reduction revisited: science and future directions. Tobacco Control 19(5): e1–10. Henningfield JE, Benowitz NL, Connolly GN, Davis RM, Gray N, Myers ML, Zeller M. 2004. Reducing tobacco addiction through tobacco product regulation. Tobacco Control 13(2): 132–135. Henningfield JE, Zeller M. 2002. Could science-based regulation make tobacco products less addictive. Yale Journal of Health Policy, Law & Ethics 3: 127–138. Irwin WA, Liroff RA. 1974. Economic disincentives for pollution control, EPA. Keen M. 1998. The balance between specific and ad valorem taxation. Fiscal Studies 19(1): 1–37. Kessler DA. 1999. Regulation of tobacco: health promotion and cancer prevention. Houston Law Review 36: 1597–1603. Laugesen M. 2012. Modelling a two-tier tobacco excise tax policy to reduce smoking by focusing on the addictive component (nicotine) more than the tobacco weight. The New Zealand Medical Journal 125(1367): 35–48. O’Donoghue T, Rabin M. 2006. Optimal sin taxes. Journal of Public Economics 90(10–11): 1825–1849. Skeath SE, Trandel GA. 1994. A Pareto comparison of ad valorem and unit taxes in noncompetitive environments. Journal of Public Economics 53(1): 53–71. Copyright © 2015 John Wiley & Sons, Ltd.



859

Sobel RS, Garrett TA. 1997. Taxation and product quality: new evidence from generic cigarettes. The Journal of Political Economy 105(4): 880–887. Watson C, McCraw J, Polzin G, Ashley D. 2004. Development of a method to assess cigarette smoke intake. Environmental Science & Technology 38(1): 248–253. Wayne GF, Carpenter CM. 2009. Tobacco industry manipulation of nicotine dosing. In Nicotine Psychopharmacology, Henningfield JE (ed)., Handbook of Experimental Pharmacology, vol. 192. Springer-Verlag: Berlin; 457–485.

SUPPORTING INFORMATION Additional supporting information may be found in the online version of this article at the publisher’s website.



HOW DO SMOKERS RESPOND TO CIGARETTE TAXES? EVIDENCE FROM CHINA'S CIGARETTE INDUSTRY.

Cigarette Taxes and Older Adult Smoking: Evidence from the Health and Retirement Study.

Taxes and abortion.

Taxes and the N.H.S.

Cigarette Excise Taxes in Context: Cautionary Lessons from the U.S. Experience.

Exploring Impacts of Taxes and Hospitality Bans on Cigarette Prices and Smoking Prevalence Using a Large Dataset of Cigarette Prices at Stores 2001-2011, USA.

Taxes and the N.H.S.

Taxes and Bribes in Uganda.

Latency and accuracy characteristics of saccades and corrective saccades in children and adults.

Stuck in Neutral: Stalled Progress in Statewide Comprehensive Smoke-Free Laws and Cigarette Excise Taxes, United States, 2000-2014.

How smokers may react to cigarette taxes and price increases in Brazil: data from a national survey.

Death, taxes and advance directives.

Population characteristics and cigarette yield as determinants of smoke exposure.

Taxes and subsidies to improve diet--reply.

Using eye-tracking to examine how embedding risk corrective statements improves cigarette risk beliefs: Implications for tobacco regulatory policy.

Why fat taxes won't make us thin.

Prallethrin poisoning that taxes the brain.

Taxes and subsidies to improve diet.

[Corrective options for plagiocephaly].

Corrective measures for myopia.

Electronic cigarette use among patients with cancer: characteristics of electronic cigarette users and their smoking cessation outcomes.

Generalized Nutrient Taxes Can Increase Consumer Welfare.

[Taxes explanation: deductions for contract physicians].

Employment impact of sugar-sweetened beverage taxes.