Information and the provision of quality Differentiated products.

Brouhle, Keith ; Khanna, Madhu

I. INTRODUCTION

In the past 20 years, consumers have become increasingly conscious of the undesirable health and safety attributes of the products they consume, and surveys suggest that a growing percentage of consumers are willing to pay more for higher quality products, such as organic foods and household cleaners and detergents that contain less toxic ingredients (Guber 2003). Other high-quality products facing higher demand include energy-efficient products like extended-life lightbulbs and improved home insulation. Often, these high-quality products provide private benefits that are excludable to buyers as well as public benefits that are nonrival and nonexcludable. For example, reduced pesticide and chemical residue on food may lower the risk of cancer while also reducing contaminated run-off that degrades ground and surface water quality. Extended-life lightbulbs and improved home insulation may reduce an individual's utility bill while also reducing greenhouse gas emissions from lower energy consumption. Although interest in these types of high-quality products is growing, demand is often relatively small. Market shares of organic produce, for example, account for only 1%-2% of total sales (Baker et al. 2002).

One factor that may limit consumer demand for such products is uncertainty about the extent to which these products are indeed of higher quality (i.e., healthier and safer) compared to conventional products. For example, consumers are often unable to determine the amount of pesticide residue on a given piece of produce or the risks associated with its consumption. They may also be uncertain about the true benefits of switching to organic produce. Products whose quality characteristics cannot be determined before, during, or after use are known as credence goods (Darby and Karni 1973). While firms are increasingly advertising the health, safety, and environmental attributes of their products (Scientific Certification Systems 2002), private marketing claims are often vague (e.g., the term organic can refer to different things) or misleading (e.g., nontoxic cleaners may still be toxic when used in excess quantities). Surveys show that consumers are often uncertain about such marketing claims (Mater 1995; Morris et al. 1995), and this uncertainty may reduce consumer willingness to pay for such products (Ottman 1998).

The inability of the market to provide credible information has encouraged government agencies to enact several types of information provision programs. These include direct labeling programs such as the Environmental Protection Agency (EPA) EnergyStar eco-label or the recently approved U.S. Department of Agriculture organic food label. Government information provision may also include more indirect programs such as education and information campaigns as well as the development of guidelines for environmental marketing and labeling policies to improve the standardization and credibility of firms' advertising. (1)

Information provision programs enable consumers to differentiate among products and to express their preferences for product attributes in the market through their consumption choices. Firms may respond to these market signals by producing goods with higher levels of product quality. In an oligopolistic setting and when increasing quality is costly, a firm, however, must consider its rival's response when choosing the quality of its product. A firm producing a low-quality product, for example, must balance the incentive to increase product quality to capture higher consumer willingness to pay against the increase in competition that will result when the firm's product quality becomes closer to its rival. Our first objective in this article, then, is to examine the role that consumer beliefs and provision of information about the quality attributes of products play on the incentives for duopolistic firms to produce higher quality goods. Because information allows firms to more clearly transmit quality differences to consumers, information may allow firms to segment the market and exercise market power, which would allow them to charge higher prices. We therefore also ask how the new equilibrium levels of quality and degree of product differentiation in the market affect consumer surplus, firm profit, and social welfare.

Even if consumers have perfect information about product quality, the provision of quality by firms may be less than socially optimal if consumers are unwilling to internalize the external effects of their consumption decision. In this case, policy tools such as taxes on low-quality products or subsidies on high-quality products may increase the incentives of firms to raise product quality to socially optimal levels. Our second objective in this article is therefore to analyze the effects of information provision on the tax or subsidy rate needed to achieve given levels of environmental protection. The interaction between information and other policy instruments may vary across policies. For example, the effectiveness of an ad valorem subsidy depends on prices, which in turn depends on information. But an emissions tax on observable emissions (which are inversely related to product quality) creates incentives for increasing product quality regardless of the level of consumer awareness about product quality. After exploring the effects of implementing information provision alone and the effects of information on the effectiveness of other policies, our third and final objective is to compare the efficiency of information provision versus an emissions tax and output subsidy.

II. BACKGROUND LITERATURE

Early publications on eco-labeling by Mattoo and Singh (1994) and Sedjo and Swallow (2002) highlight the consequences of introducing an eco-label on both the equilibrium quality of a firm as well as the equilibrium quality that results in the market as a whole. They show that while eco-labeling can raise product quality of a firm, it can also raise the price of the product that could shift demand in favor of other goods produced in environmentally unfriendly methods. In net, the introduction of labeling and the separation of a market into quality differentiated goods could result in a decline in overall environmental quality. These studies assume that consumers have perfect information about product quality and that the quality level of each firm is determined exogenously.

Several studies--Mussa and Rosen (1978), Gabszewicz and Thisse (1979), Shaked and Sutton (1982), Ronnen (1991), and Lehmann-Grube (1997)--endogenize the quality provision decision of firms. These studies show that vertically differentiated firms in a duopoly have an incentive to differentiate their products to reduce price competition with their rival firm while responding to heterogeneous consumer tastes for product quality. Arora and Gangopadhyay (1995) and Crampes and Hollander (1995) apply this framework to a market for green goods and show that a minimum environmental quality standard leads to overcompliance by the high-quality firm. These studies assume that consumers fully internalize the environmental externality. Bansal and Gangopadhyay (2003) and Lutz et al. (2000) extend this framework to reexamine the efficiency of different types of government policies in a model where production of quality creates an externality: product quality affects the level of aggregate pollution in the environment. Bansal and Gangopadhyay (2003) focus on the effect of different types of tax regimes given the government's budget constraint, while Lutz et al. (2000) argue that the welfare properties of a minimum quality standard depend on the timing of the game between firms and a regulator. Eriksson (2004) also looks at the extent that "green" consumers affect product quality levels, although he frames the question within a horizontal rather than vertical differentiated product market. A common feature of these publications is the assumption that consumers have perfect information about the environmental or quality attributes of a good.

The effect of imperfect information on product quality and the role of information acquisition has a rich history in the IO literature. Work by Klein and Leffler (1981), Shapiro (1982, 1983), and Bagwell and Riordan (1991) shows that in spite of uncertain product quality, markets for quality differentiated products can arise. In such markets, information about product quality is signaled through market prices. These models are based on search or experience goods where product quality can be determined over time or assume that the market is characterized by some individuals who are initially informed of product quality. Goods with different levels of environmental attributes, though, are credence goods where quality cannot be ascertained by consumers on their own. Feddersen and Gilligan (2001) and Kirchhoff (2000) look at the provision of quality in a market for credence goods but assume there exists a third party or activist that is able to ascertain quality and impose reputational losses on firms that engage in greenwashing.

This article extends the literature by analyzing the role that consumer beliefs about the quality of credence goods play on the provision of high-quality products in the market. These beliefs depend on the extent to which consumers consider the information provided by firms or third parties about product quality to be credible. Even in the absence of any attempts at greenwashing by firms, consumers may not fully believe or incorporate all relevant information about product quality provided by firms into their decision making, and we therefore examine the impact of imperfect information on the incentives for duopolistic firms to produce vertically differentiated goods. We also examine the effect of information on the effectiveness and welfare gains from traditional policy instruments such as taxes and subsidies.

III. MODEL

Firm and Consumer Behavior

We consider a market with two firms that produce vertically differentiated products. All consumers derive the same intrinsic utility from consuming a unit of the product, but consumers are heterogeneous in the extent to which they value product quality. We assume consumers do not internalize the externality and thus only consider the private benefits in their decision making. (2) We let [theta] represent consumers' taste for quality and assume [theta] follows a uniform distribution with support [[theta].bar], [bar.[theta]]. To focus solely on the quality decision of firms, we fix aggregate quantity by assuming all consumers buy one unit of the good as is common in the literature (see, e.g., Cremer and Thisse 1994; Crampes and Hollander 1995).

The products considered here are credence goods. Unlike search or experience goods, consumers are unable to infer quality through market prices or experience consuming the product. (3) Because the quality of a good is difficult for consumers to determine on their own and because consumers may not understand, believe, or incorporate available information into their decision making, we assume quality is uncertain to consumers. Based on the current level of information, consumers form beliefs about the likelihood that the reported quality of each firm is accurate. We represent this likelihood by [alpha], where 0 [less than] [alpha] [less than] 1. (4) A higher value of [alpha] indicates a greater likelihood that one has information about product quality. Given this uncertainty about product quality, consumer j maximizes his/her expected utility: (5)

(1) [EU.sup.j.i] = y + k + [[theta].sup.j][[alpha]q.sub.i] - [P.sub.i],

where y is income, k is the intrinsic utility consumers receive from the functional aspects of the product, (6) and [q.sub.i] and [P.sub.i] represent the quality-enhancing aspects and price of the good produced by firm i.

The contribution of a firm's product quality [q.sub.i] to an individual's utility depends on both the individual's taste for quality ([[theta].sup.i]) and information or knowledge of that quality level ([alpha]) Furthermore, since [alpha] and [theta] enter in a multiplicative fashion in the utility expression and since 0 [less than] [alpha] [less than] 1, an increase in information is equivalent to an increase in the mean of consumer valuations for quality accompanied with an expansion in the range of consumer valuations for quality. As consumer valuations for quality become more diverse, this allows firms to produce products that are more differentiated from each other. When [alpha] equals zero, for example, firms are unable to transmit information about product quality to consumers, and profit maximizing firms are forced to produce identical products with no product quality. For [alpha] > 0, consumers receive different levels of utility from product quality depending on their individual taste for quality, and hence, some information about product quality allows consumers to demand products of different quality levels. An increase in information, then, expands the space of potential product qualities in which firms compete and allows firms to differentiate their products.

We assume a noncooperative duopoly market structure where each firm produces a single product quality; therefore, i = h (high quality) or 1 (low quality). Firms have an identical cost function C([x.sub.i], [q.sub.i]) = [x.sub.i]c([q.sub.i]), where [x.sub.i] is quantity and [q.sub.i] is quality. The cost of quality per unit of output is convex in quality, [c.sup.'](*) > 0 and [c.sup."](*) > 0. Later we assume a quadratic cost function for tractability as in Cremer and Thisse (1994), Crampes and Hollander (1995), and Lombardini-Riipinen (2001); in particular, we assume c([q.sub.i]) = (l/2)[q.sup.2.sub.i].

Product quality also generates public benefits in the form of reduced environmental degradation. We assume that production of the good degrades the environment by generating a given level of pollution, [rho] > 0, per unit of output. A higher quality product produces less pollution per unit of output such that net pollution is [rho] - [q.sub.i]. Aggregate pollution, then, is AP = [X.sub.h]([rho] - [q.sub.h]) + [x.sub.1]([rho] - [q.sub.l]), where [X.sub.h] and [x.sub.1] are the proportion of consumers of the highand low-quality good.

Key results in the article revolve around the incentives of firms to produce quality differentiated products. As a point of comparison, we define the preferred quality of each consumer as the quality level that maximizes their utility (fall potential variants are offered at marginal costs (Cremer and Thisse 1994). Formally,

(2) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

The preferred quality for each individual is the quality level that equates his or her marginal benefit of consumption ([[theta].sup.j[alpha]) to the marginal cost of producing that quality level ([c.sup.']([q.sub.j]). If we assume a quadratic cost function, ([c.sup.']([q.sub.j]) = (1/2)[q.sup.2.sub.j], the preferred quality for each individual is [q.sub.j] = [[theta].sup.j][alpha]. Note, the levels of quality are now also indexed by j because each individual would consume a different quality product. The set of preferred quality levels of all consumers follows a uniform distribution from [[[theta].bar][alpha], [bar.[theta]][alpha]] with a range [PHI]([alpha]) = [alpha]([bar.[theta] - [[theta].bar]).

Unregulated Market Equilibrium

With a noncompetitive duopoly market structure, the distribution of "preferred" qualities will not occur. Rather, firms solve a two-stage game; firms first make a quality decision and then compete in prices. (7) The model is solved by backward induction to ensure a subgame-perfect equilibrium.

To determine the demand for the low--nd high-quality products, define the critical parameter [??] by finding the consumer who is indifferent between the two qualities such that

[EU.sup.j.sub.h]([??]) = [EU.sup.j.sub.l]([??]) or

(3) y + k + [[??].sup.j] [alpha][q.sub.h] - [P.sub.h] = y + k + [[??].sup.j] [alpha][q.sub.l] - [P.sub.l]

(4) [??] = [[P.sub.h] - P.sub.l]]/[[alpha]([q.sub.h] - [q.sub.l]].

Those individuals with [theta] greater than [??] consume the high-quality product, while those individuals with [theta] less than [??] consume the low-quality product. (8) Demand for the high-quality product is

(5) [X.sub.h] = [[integral].sup.[bar.[theta]].sub.[??]] dF([theta]) = [[bar.[theta][alpha]]([q.sub.h] - [q.sub.l]) - ([P.sub.h] - [P.sub.l])] /[R[alpha]([q.sub.h] - [q.sub.l])],

where F([theta]) is the distribution function of [theta] and R = [[bar.[theta] - [[theta].bar]. Demand for the low-quality product is

(6) [X.sub.l] = [[integral].sup.[??].sub.[bar.[theta]] I dF([theta]) = [([P.sub.h] - [P.sub.l])- [[theta].bar][alpha]([q.sub.h] - [q.sub.l]) /[[R.sub.[alpha]([q.sub.h] - [q.sub.l])].

Because firms are identical and the distribution of consumers is uniformly distributed, firms split the market evenly in equilibrium. Note, holding prices and qualities constant, an increase in information decreases [??], which would increase demand for the high-quality product at the expense of the demand for the low-quality product.

With the demands of each product quality variant known, we solve the second-stage pricing game: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. Solving, the two equilibrium prices are

(7) [P.sub.h] = (1/3)[c([q.sub.l]) + 2c([q.sub.h]) + [alpha]([q.sub.h] - [q.sub.l])(2[[bar.[theta] - [[theta].bar]]

(8) [P.sub.l] = (l/3)[2c([q.sub.l]) + c([q.sub.h]) + [alpha]([q.sub.h] - [q.sub.l])([bar.[theta] - 2[[theta.bar]].

With second-stage prices known, firms choose product quality or abatement effort in the first stage that maximize profits: [[PHI].sub.i] = [[P.sub.i] - c([q.sub.i])][[x.sub.i]]. Maximization of profits yields the following first-order conditions,

(9) g + [alpha](2[bar.[theta]] - [[theta].sub.bar]) - 2[c.sup.'] ([q.sub.h]) = 0

(10) g - [alpha]([bar.[theta]] - 2[[theta].sub.bar]) - 2[c.sup.']([q.sub.l]) = 0,

where g is the additional per unit cost of increasing quality from [q.sub.l] to [q.sub.h] (g = [C([q.sub.h]) - c([q.sub.l])]/[[q.sub.h] - [q.sub.l]]). Because c([q.sub.i]) is a convex function, [c.sup.']([q.sub.l]) < g < [c.sup.']([q.sub.h]). The first-order conditions highlight that the quality choice of each firm depends on its costs (c(qi)), the quality choice of its opponent ([q.sub.-i]), consumer valuations of quality ([theta]), and information ([alpha]). The duopoly outcome arises when both firms produce positive output in equilibrium and earn nonnegative profits. From (5) and (6), output for both firms is positive if - [alpha]([bar.[theta]] - 2[[theta].bar]) < g < [alpha](2[bar.[theta]] - [[theta].bar]), which is satisfied by the first-order conditions. Firms also earn positive profits in equilibrium, which ensures both firms stay in the market (see Crampes and Hollander 1995).

Totally differentiating the first-order conditions, we can solve for the best response function:

(11) for the high-quality firm: d[q.sub.h]/d[q.sub.l] = [[c.sup.'] ([q.sub.l]) - g]/[[c.sup.'] ([q.sub.h]) - g - 2[c.sup."]([q.sub.h])([q.sub.h] - [q.sub.l])]

(12) and for the low-quality firm: d[q.sub.h]/d[q.sub.l] = [g - [c.sup.'] ([q.sub.l]) - 2[c.sup."] ([q.sub.l]) x ([q.sub.h] - [q.sub.l])]/[g - [c.sup.']([q.sub.h])].

The best response function [q.sub.h]([q.sub.l]) for the high-quality firm and [q.sub.l]([q.sub.h]) for the low-quality firm are represented in Figure 1. The convexity of the cost function and second-order conditions imply that both best response functions are positively sloped, which indicates the choice of quality is a strategic complement for each firm. Also, the best response function for the low-quality firm is steeper than the best response function for the high-quality firm. The intersection of the best response functions yields the Nash equilibrium qualities, [q.sup.*.sub.l] and [q.sup.*.sub.h]. Note, even absent government incentives, firms find it advantageous to produce quality differentiated products. This is because if both firms produce a product with the exact same level of quality, second-stage Bertrand price competition will ensure that profits are zero. Thus, price competition in the second stage coupled with heterogeneous consumer tastes encourage firms to produce differentiated products. We now explore how information, taxes, and subsidies provide different incentives for firms to produce quality differentiated products.

[FIGURE 1 OMITTED]

IV. GOVERNMENT INTERVENTION

In the unregulated market equilibrium, quality is underprovided for two reasons. First, a lack of information leads consumers to underconsume quality, and this underprovision may encourage governments to implement information provision programs to encourage the production of higher quality goods. Information provision programs encompass direct labeling programs as well as more indirect methods like educational campaigns and providing guidelines for nutritional and safety labeling. Second, even if consumers have perfect information, there will still exist an underprovision of quality if consumers do not internalize the public benefits generated from higher quality goods. Governments may therefore need to intervene with policies such as taxes, subsidies, or standards to provide incentives to firms to produce higher quality goods. In the next section we determine the effect of information provision on the quality choice of firms and the resulting market equilibrium. In the following section, we examine the effects of other policy instruments, and finally we compare these instruments and look at their effect on social welfare.

Information Provision

We consider information provision as a mechanism that gives consumers more trust in firms' reported product quality. We use the framework developed above to show the following:

PROPOSITION 1.

1. An increase in information will result in higher (lower) product quality for the highquality firm if {-[k.sub.l] [dg/[dq.sub.l]] + [c.sup."]([q.sub.l])} > (<) 0.

2. An increase in information will result in higher (lower) product quality for the low-quality firm if {[dg/[dq.sub.h]] - [k.sub.2[c.sup."] ([q.sub.h]) } > (<) O.

Proof The above conditions result from totally differentiating the first-order conditions (equations (9) and (10)) characterizing the market equilibrium (see A1-A9 in appendix). Note, dg/[dq.sub.i] is the change in the slope of the line between the costs of the two firms, [c.sup."]([q.sub.i]) is the change in the marginal cost of firm i, and [k.sub.1] and [k.sub.2] are constants (see appendix). Note, dg/[dq.sub.i], [c.supb."]([q.sub.i]), [k.sub.1]and [k.sub.2] are all positive. Q.E.D.

The fact that information may result in lower product quality is counter to the usual belief that information provision programs encourage firms to produce higher quality goods. To understand this counterintuitive result, it is helpful to recall that an increase in information is equivalent to an increase in consumer valuations for quality (both an increase in the mean and variance of consumer valuations). If only the mean valuation for quality increased, it would be straightforward to show that both firms would increase product quality (Arora and Gangopadhyay 1995; Eriksson 2004). An increase in the range of valuations, though, allows firms to produce products that are more differentiated from each other, and the proposition indicates that this greater product differentiation may be achieved by either raising or lowering levels of product quality by each firm. Examining the conditions of the proposition highlights the role that the anticipated reaction of a firm's rival plays in its quality choice.

Consider the quality decision for the high-quality firm. Proposition 1 indicates that the high quality firm is more likely to increase quality if (1) the change in the costs between the two firms is small and (2) the change in the marginal cost for the low-quality firm is large. Thus, information provision results in an increase in quality of the high-quality firm if the increase in quality does not put it at too much of a cost disadvantage compared to the low-quality firm and if the change in marginal cost of raising quality for the low-quality firm is increasing rapidly. The latter would reduce the likelihood that the low-quality firm would, ceteris paribus, match the increase in quality by the high-quality firm, thereby resulting in greater quality differentiation and lower price competition in the market. Note, the quality decision for the low-quality firm depends on a similar set of conditions. The fact that the quality choice of either firm in response to information can be positive or negative is an important result as information provision programs are promoted based on the presumption that they lead firms to produce goods with higher levels of quality. (9)

To look more closely at the effects of information on consumer surplus, firm profit, and aggregate pollution, it is helpful to assume a specific cost function, c([q.sub.i]) = (l/2)[q.sup.2.sub.i]. To support the duopoly outcome and to satisfy the nonnegativity conditions with this cost function, we also assume 2[[theta].bar] < [bar.[theta]] < 5[[theta.bar]. (10)We maintain these assumptions throughout the remainder of the article.

PROPOSITION 2. An increase in information results in the provision of a higher quality product by both the low- and high-quality firm, lower aggregate pollution, and higher profits for both the low- and high-quality firm.

Proof When c([q.sub.i])= (1/2)[q.sup.2.sub.i], we solve the first-order conditions (equations (9) and (10)) to determine [q.supb*.sub.h] = ([alpha]/4)(5[bar.[theta]] - [[theta].bar]) and q.sup.*.sub.l] = ([alpha]/4)(-[bar.[theta]] + 5[[theta].bar]). Differentiation with respect to [alpha] proves the first part of the proposition. The second result follows directly from the first result and the assumption that the market is fully covered.(11) To prove the third result, substitute the equilibrium quality and price levels into the profit expressions: [[PHI].sub.i] = [[P.sub.i] - c([q.sub.i])][x.sub.i] = (3[[alpha].sup.2]([theta] - [[theta].bar]))/8. This implies that d[[PHI].sub.i]/d[alpha] > 0. Q.E.D.

An examination of the best response functions provides the foundation for Proposition 2. Differentiating equations (9) and (10), the best response functions are:

(13) for the high-quality firm: [q.sub.h] = (2[alpha]/3)(2[bar.[theta]] - [[theta].bar]) + (1/3)[q.sub.1],

(14) and for the low-quality firm: [q.sub.h] = 2[alpha]([bar.[theta]] - 2[[theta.bar]) + 3[q.sub1].

[FIGURE 2 OMITTED]

The intersection of the best response function [q.sub.h]([q.sub.l]) for the high-quality firm and [q.sub.l]([q.sub.h]) for the low-quality firm determine the initial equilibrium values of quality, [q.sup.*.sub.h] and [q.sup.*.sub.l] (point A in Figure 2). From equations (13) and (14), an increase in information ([alpha]) shifts both best response functions up and shifts up the best response function for the high-quality firm ([q.sub.h]([q.sub.l]) to [q.sub.l.sub.h]([q.sub.l])) more than the best response function for the low-quality firm ([q.sub.l]([q.sub.h]) to [q.sup.1.sub.l]([q.sub.h])). The new intersection of the best response functions shows that information provision results in higher levels of quality by both firms ([q.sup.l.sub.l] > [q.sub.*.sub.l] and [q.sub.*.sub.h] > ; movement from A to A' in Figure 2).

To understand other results of Proposition 2, it is helpful to recall that information expands the space of potential quality levels and therefore lessens competition among firms in the market. With a quadratic cost function, we can now more clearly show this idea by defining the range of actual product qualities provided by the two firms: [lambda]([alpha]) = [q.sup.*.sub.h] [q.sup.*.sub.l] = (3[alpha]/2)([bar.[theta]] - [[theta].bar). Recall, [PHI]([alpha]) is the distribution of preferred qualities that would result if products were offered at their marginal costs and is equal to [alpha]([bar.[theta]] - [[theta].bar]). Figure 3 shows [lambda]([alpha]) and [PHI]([alpha]) and indicates that the duopoly market provides a wider range of qualities. Not only do firms in a duopoly provide "too much" differentiation, but by comparing [lambda]([alpha]) and [PHI]([alpha]) at different levels of information, we can see that the degree of excess product differentiation (i.e., the market power of firms) increases as information increases (see Figure 3).

[FIGURE 3 OMITTED]

As firms differentiate their products, they compete less vigorously in prices and prices rise (d[P.sub.i]/d[alpha] > 0). Of course, costs also rise as firms are producing a higher quality good. In the appendix (see A10-A12), we show that prices rise faster than costs (d[P.sub.i]/d[alpha] > dc([q.sub.i])/d[alpha]), which implies that an increase in information will result in higher profits for the two firms. An interesting result is that the new qualities and prices chosen in response to a change in information result in firms continuing to split the market evenly. (12) With the same market share, the increase in profits for the two firms is equal. The increase in firm profit implies that both firms would welcome an information-based policy. This result is in contrast to other government policies like taxes and standards that reduce the profit of the high-quality firm (Crampes and Hollander 1995). In these cases, the high-quality firm may expend socially wasteful effort to resist or lobby against a tax or standard (Lutz et al. 2000). Information provision, in contrast, will not face opposition from firms. This gives further insight into why firms may voluntarily agree to participate in information provision programs.

Since an increase in information results in higher product qualities but also higher prices of both goods, the effect on consumer surplus is ambiguous (see appendix A17-A18): (13)

(15) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Consumers must balance the gains from consuming a higher quality product, which depends on their individual valuation of quality [[theta].sup.j], against the loss due to the higher price, which depends on the degree of excess differentiation in the market. For consumers consuming a given product quality, consumers are more likely to benefit from an increase in information when they have high valuations of quality and when the increase in excess product differentiation is small (when [alpha] is small).

A final objective is to consider the welfare impact of information provision. We define social welfare as the sum of consumer surplus and firm profit, minus aggregate pollution as in Lutz et al. (2000) and Moraga-Gonzalez and Padron-Fumero (2002): W = [[integral].sub.j] [CS.sup.j] + [[summation].sub.i] [[PHI].sub.i] - AP. (14)

PROPOSITION 3. Information pro vision may not always be welfare enhancing. Information provision is welfare enhancing when the initial [alpha] is small, but may be welfare reducing when the initial [alpha] is large.

Proof.

(16) W = [integral] CS + [summation] [PHI] - AP

(17) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(18) dW / d[alpha] [??] 0,

after one substitutes equilibrium values of [q.sup.*.sub.h] and [q.sup.*.sub.l] (see appendix A19-A29). Q.E.D.

The fact that information is not always welfare enhancing reflects the different roles that information plays in the market equilibrium. From Figure 3, we saw that information results in higher quality products but also products that are more differentiated from each other. The increase in product quality is beneficial as it better matches consumer preferences and reduces aggregate pollution. The excess product differentiation, however, in the face of a convex cost function, is harmful as it results in higher costs than are socially optimal. In the appendix (see A19-A29), we show that dW/d[alpha] is positive when a is small (firms have little market power and the degree of excess product differentiation is small) but could be negative when [alpha] is large (firms have more market power and the degree of excess product differentiation is larger). Thus, we are able to conclude that an information-based program is welfare enhancing only if consumers start with low levels of information. (15)

Emissions Tax and Output Subsidy

An increase in information can correct the market failure of imperfect information and can increase product qualities. Product quality will still be underprovided, though, when there exists a public good aspect of quality such as pollution. There exist many instruments that governments may use to encourage higher level of quality provision, such as an ad valorem tax/subsidy on output, a per unit emissions tax/subsidy, a per unit output tax/ subsidy, technology subsidies, and minimum quality standards. We focus here on the first two types of policies and in particular on uniform taxes/subsidies because these instruments have been most frequently studied in the literature (Arora and Gangopadhyay 1995; Moraga-Gonzalez and Padron-Fumero 2002; Bansal and Gangopadhyay 2003) and one of the purposes of this article is to show the impact of consumer beliefs on the design and effectiveness of these instruments. For brevity, we do not analyze the effects of the other policies, but the framework developed here can be easily used to do so. (16) We first establish the effect of an emissions tax and output subsidy on equilibrium quality levels and the degree of product differentiation in the market and then determine if the effectiveness of these price instruments changes when consumers have different amounts of information.

Assume the government places a tax, t, on each unit of emissions. Firms face the following problem: Max [[PHI].sub.i] = [[P.sub.i] c([q.sub.i])- t([rho][q.sub.i])][[x.sub.i]]. Solving the two-stage game in the same fashion as in section III, the equilibrium levels of quality are [q.sup.t.sub.h] = ([alpha]/4)(5[bar.[theta]] - [[theta].bar])+ t and [q.sup.t.l] = ([alpha]/4)(- [bar.[theta]] + 5[[theta].bar]) + t (see point A in Figure 4). Regardless of the quality choice of its opponent, both firms will increase quality in response to a tax, and this results in a new equilibrium where the equilibrium quality level of each firm is higher (see point B in Figure 4). From the expressions of the equilibrium quality levels, we can see that both firms increase quality by the same amount, and the degree of product differentiation between the two products in the market does not change (d[lamba]/dt = 0). Because the degree of product differentiation does not change, price competition between the two firms is unaffected. With an inelastic market demand, then, firms are able to raise their price by an amount equal to the increased costs of producing the higher quality product plus the cost of the tax. Consumers face the entire burden of the increased costs of quality and cost of the tax, and therefore, firm profit is unaffected by a per unit emissions tax.

With an ad valorem subsidy s on output (where the per unit subsidy is proportional to the price level), the profit expressions are [[PHI].sub.i] = [[P.sub.i](l + s) - c([q.sub.i])][[x.sub.i]]. Solving the two-stage game yields the following equilibrium levels of quality: [q.sup.s.sub.h] = ([alpha]/4)(1 + s)(5[bar.[theta]] [[theta].bar]) and [q.sup.s.sub.l] = ([alpha]/4)(1 + s)(-[bar.[theta]] + 5[[theta].bar]) (see point A in Figure 5). An increase in the ad valorem subsidy rate will lead the high-quality firm to produce a higher quality good because it leads to a higher price (and hence higher subsidy payment) for two reasons. First, consumers are willing to pay more for a higher quality good, and second, a higher quality product by the high-quality firm results in less price competition in the market, and hence a higher price. The effect of an ad valorem subsidy on the low-quality firm is less obvious. If the low-quality firm increases quality, it would be able to get higher subsidy payments, but its product would be closer to the quality choice of the high-quality firm. Although the good has higher quality, it is possible that the resulting price competition would cause prices to fall and hence result in a lower subsidy payment. On the other hand, a reduction in quality by the low quality firm results in greater product differentiation, which may raise price (even through the good is of lower quality) and increase the subsidy payment. The equilibrium quality levels obtained from the best response functions (see point B in Figure 5) show that an ad valorem subsidy results in higher quality products by both firms. Because an ad valorem subsidy gives the high-quality firm a larger subsidy payment (because they have a higher price), the high-quality firm has a greater incentive to increase quality compared to the low-quality firm, and this results in a greater degree of product differentiation in the market (d[[lambda].sup.s/ds > 0). As expected, an ad valorem output subsidy increases the profit of both firms (see appendix A40).

[FIGURE 4 OMITTED]

Now that we have established the effect of a per unit emissions tax and an ad valorem output subsidy, we ask if the effectiveness of a tax or subsidy changes when consumers have different amounts of information. In Figures 4 and 5, we diagram a new equilibrium due to greater levels of information (see point A') and consider the effect of a tax or a subsidy on this new equilibrium (movement from point A' to point B').

PROPOSITION 4.

1. The increase in product quality due to a per unit tax is independent of the level of information.

2. The increase in product quality due to an ad valorem subsidy is greater when consumers have more information.

Proof See Figures 4 and 5 and the appendix (A30-A40). Q.E.D.

The different results with a per unit emissions tax and an ad valorem output subsidy arise because a tax and subsidy interact differently with information provision. Consider a per unit emissions tax. An emissions tax assumes there exists a knowledgeable government that can place a tax directly on emissions. In this case, the impact of a tax on a firm is independent of the level of information as the only thing that affects a firm's tax bill is its level of emissions. A subsidy on a firm's price, on the other hand, depends indirectly on the level of information as information affects firm quality and price, and hence the size of the subsidy a firm receives. At low levels of consumer understanding of product quality, firms have little incentive to respond to an ad valorem output subsidy as firms are unable to transmit their quality improvements to consumers. However, as information increases, a given increase in quality by a firm is more efficiently transmitted to consumers which results in a higher price, and hence a greater subsidy payment to the firm. This implies that a firm becomes more responsive to an ad valorem output subsidy as information increases. Previous literature (Arora and Gangopadhyay 1995; Bansal and Gangopadhyay 2003; Moraga-Gonzalez and Padron-Fumero 2002) that addresses the effectiveness of a subsidy has assumed that consumers have perfect knowledge of product quality ([alpha] = 1). We show here that imperfect consumer knowledge of product quality lessens the effectiveness of an ad valorem subsidy in changing firm behavior. With smaller changes in product qualities, firms are unable to differentiate their products as much. They face greater price competition, and therefore, the increase in firm profits due to an ad valorem output subsidy with imperfect information is smaller than the increase in firm profits when consumers have perfect information about product quality.

[FIGURE 5 OMITTED]

V. COMPARISON OF INSTRUMENTS

The final objective is to compare the efficiency properties of information provision, a per unit emissions tax, and an ad valorem output subsidy. As a basis of comparison, we design policy instruments that result in the same level of aggregate pollution. We show in the appendix (see A45-AS1) that information provision that raises consumer knowledge of product quality by [DELTA] results in a level of aggregate pollution equal to [rho]- (1/2)([alpha]+ [DELTA])([bar. [theta]] + [[theta].bar]). A per unit emissions tax of [DELTA]([theta] +[bar. [[theta])/2 or an ad valorem output subsidy of [DELTA]/[alpha] will achieve this same level of aggregate pollution.

[FIGURE 6 OMITTED]

The quality levels achieved by the low-and high-quality firms under information provision (I = [alpha] + [DELTA]), per unit emissions tax (t = [DELTA]([bar. [theta]] + [[theta].bar])/2), and ad valorem output subsidy (s = [DELTA]/[alpha]) are derived in the appendix (see A52-A54) and shown in Figure 6. Note, the quality levels are identical under information provision and an ad valorem output subsidy ([q.sup.I.sub.i] = [q.sup.s.sub.i] = [q.sup.I/s.sub.i] = h, I). Thus, any welfare considerations between these two programs will hinge on the relative costs of implementing these two programs. Second, the range of qualities under information provision or an output subsidy is greater than the range of qualities under an emissions tax. Third, note that although quality levels are functions of [alpha], s, and t, the degree of product differentiation is a function of only [alpha] and s. Hence, an increase in information ([alpha]) or the ad valorem subsidy (s) will increase quality levels as well as the degree of product differentiation, but an increase in the per unit tax (t) will only increase product quality.

With the quality levels determined, we can now turn to a calculation of social welfare. Because aggregate pollution is the same under each program, we can evaluate social welfare according to (19) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Social welfare depends on the distribution of qualities; in particular, it depends on how consumers value the quality distribution and how much it costs to produce the quality distribution. Because consumer valuations are linear in quality, consumers prefer the more disperse set of qualities under information provision (or an ad valorem output subsidy) compared to the more compact set of qualities under a per unit emissions tax. On the other hand, a convex cost function implies that costs are greater under the more disperse set of qualities compared to the more compact set of qualities. The question is which effect dominates: the gain in consumer valuations or the loss in costs. We show that the comparison depends on the absolute level of qualities of the two goods, which in turn depends on the level of consumer knowledge of product quality.

PROPOSITION 5. Social welfare under information provision or an ad valorem output subsidy is greater than social welfare under a per unit emissions tax if (2 - 3[DELTA])/6 > [alpha].

Proof.

(20) [[??].sup.I/s] [??] [[??].sup.t]

(21) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

Substituting in the equilibrium values of [q.sub.h] and [q.sub.t]

(22) (2 - 3[DELTA])/6 [??] [alpha].

Q.E.D.

When consumer knowledge of product quality is low, firms are unable to transmit quality to consumers and firms produce goods with relatively low levels of quality. In this case, costs of quality are relatively small, so gains in consumer surplus are more important than losses due to higher costs and information provision (or an output subsidy) is preferred to an emissions tax. When consumers are more informed of product quality, firms produce goods with higher levels of quality as well as goods that result in a greater degree of product differentiation in the market. With a convex cost function, this increased product differentiation results in costs rising relatively fast such that the losses due to the higher costs of quality now outweigh the gains in consumer surplus from the higher quality, and an emissions tax is preferred to information provision (or an output subsidy). (17)

VI. CONCLUSION

Proponents of information provision programs argue that increased consumer knowledge of product quality would enable better transmission of consumer preferences for quality to firms and provide incentives to firms to provide goods with higher levels of quality. Although these policies have been used more in practice, there has been little theoretical work exploring this topic. This article has addressed this shortcoming in the literature. First, we looked at how an information-based program works in isolation of other policies. Contrary to the commonly held belief that information provision will always result in higher levels of quality, we show that information expands the space of potential quality levels, which allows firms to increase or decrease product quality. We establish conditions when a firm will increase quality and find that this decision depends crucially on its costs and its rival's behavior.

Even if information provision results in a higher product quality offered by the two firms, the effect of information provision on social welfare is ambiguous. This result arises because information provision allows firms to engage in excess product differentiation. Although the higher quality goods more closely match consumer preferences and result in lower aggregate pollution, the excess product differentiation results in higher costs than are socially optimal. On the whole, social welfare can either increase or decrease depending on the initial levels of consumer knowledge of product quality and the cost of informing consumers. This is an important result because it shows how government policy can facilitate market power by subtly affecting the way that firms compete in a duopoly.

In addition to identifying the effects of an information-based policy in isolation, this article examines the effect of an information-based policy on other commonly used policy instruments. When consumers are more informed about the environmental attributes of a good, an ad valorem output subsidy becomes more effective at encouraging both firms to improve quality. Though it may be impossible to rely solely on information provision (due to the difficulty in educating all consumers) or on a subsidy (due to its large budgetary impacts), one may be able to achieve a given improvement in the environment by employing both programs simultaneously. In contrast, an information-based program and an emissions tax work independently of each other.

Finally, a comparison between information provision and different price instruments has shown that these programs differ in the incentives they provide for firms to differentiate their products. In particular, a per unit emissions tax does not affect how firms compete with each other and therefore does not change the distribution of product qualities in the market. Information provision or an ad valorem output subsidy, on the other hand, increase the incentives of firms to differentiate their products and result in a more dispersed quality distribution. The degree of product differentiation, then, affects which policy is preferred in reaching a target level of aggregate quality. We find the more disperse quality distribution under information provision or an ad valorem subsidy is preferred at low levels of information (because gains in consumer valuations outweigh losses in higher costs) while the more compact distribution under a per unit emissions tax is preferred at high levels of information (because costs eventually increase faster than consumer valuations).

APPENDIX

PROPOSITION 1.

Differentiating the first-order conditions in equations (9) and (10),

(A1) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(A2) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],

where

(A3) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Because the determinant of A is positive from the second-order conditions,

(A4) sign([dq.sub.h]/d[alpha] = sign[-3([bar.[theta]]-[[theta].bar]) (g - c'([q.sub.t])) + 2(2[bar.[[theta]-[[theta].bar])c"([q.sub.t])([q.sub.h] - [q.sub.t])]

(A5) sign([dq.sub.t]/d[alpha]]) = sign[3([bar.[[theta] - [[theta].bar])(c'([q.sub.h]) - g) - 2([bar.[theta]] - 2[[theta].bar])c"([q.sub.h])([q.sub.h] - [q.sub.t])].

One can see that the sign of d[q.sub.h]/[d[alpha] and d[q.sub.l]/d[alpha] depends on the cost function. These expressions can be simplified by rewriting them in terms of g. Because g = [c([q.sub.h]) - c([q.sub.l])/ [[q.sub.h] - [q.sub.t], define

(A6) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(A7) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Rewriting the expressions d[q.sub.h/d[alpha] and d[q.sub.l/d[alpha] by substituting in dg/d[q.sub.i], we get the following

(A8) sign([dq.sub.h/d[alpha]) = sign[-[k.sub.t], (dg/[dq.sub.l]) + c" ([q.sub.l])]

(A9) sign([dq.sub.l/d[alpha]) = sign[(dg/[dq.sub.h]) - [k.sub.2]c"([q.sub.h])],

where [k.sub.1 = 3([bar.[[theta] - [[theta].bar])/[2(2[bar.[theta]] - [[theta].bar.])] and [k.sub.2] = 2([bar.[[theta] - 2 [[theta].bar])/[3([bar.[[theta] - [[theta].bar])].

PROPOSITION 2.

Substituting the optimal choices of quality when c([q.sub.i]) (1/2)[q.sup.2.sub.i] into the equilibrium price expressions (equations (7) and (8)),

(A10) [P.sub.h] = ([[alpha].sup.2]/32)(49[[bar.[theta]].sup.2]] - 58 [[bar.[theta]][[theta].bar]+ 25[[[theta].bar].sup.2]) and

[P.sub.l] = ([[alpha].sup.2]/32)(25[[bar.[theta]].sup.2]] 58[bar.[theta]][[theta].bar] + 49[[[theta].bar]sup.2])

and into the cost expressions,

(A11) c([q.sub.h]) = ([[alpha].sup.2]/32)(25[bar.[[theta].sup.2] - 10[bar.[[theta][[theta].bar] [[theta].sup.2]) and c([q.sub.l]) = ([[alpha].sup.2]/32)([bar.[[theta].sup.2] - 10[bar.[[theta][[theta].bar] + 25[bar.[[theta].sup.2]).

Taking the derivative of each expression, it is easy to show

(A12) ([dP.sub.h/d[alpha]) > (dc([q.sub.h])/d[alpha]) and ([dP.sub.l]/d[alpha]) > (dc([q.sub.l])/d[alpha])

Alternatively, substitute the equilibrium values of [q.sub.h], and [q.sub.l] directly into the profit expressions,

(A13) [[PI].sub.i] = [[P.sub.i] = c([q.sub.i])][X.sub.i]

(A14) [[PI].sub.i] = 3[[alpha].sup.2]([bar.[theta]] - [[theta].bar].sup.2]/8.

Therefore,

(A15) d[[PI].sub.i/d[alpha] > 0.

For consumer j who buys from firm i,

(A16) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

For individuals that consume the high-quality product, the change in utility is

(A17) d[U.sup.j.sub.h]/d[alpha] = (1/16)[4[[theta].sup.j](5[bar.[theta]] - [[theta].bar.]) - [alpha](49[bar.[theta]].sup.2] - 58[bar.[theta]][[theta].bar] + 25[[[theta].bar].sup.2]

For individuals that consume the low-quality product, the change in utility is

(A18) d[U.sup.j.sub.l/d[alpha] = (1/16)[4[[theta].sup.j](-[bar.[theta]] + 5[[theta].bar]) -[alpha](25[[bar.[theta]].sup.2] - 58[bar.[theta]][[theta].bar] + 49[[[theta].bar].sup.2])].

It is clear that the sign of d[U.sup.j.sub.i]/d[alpha] depends crucially on the size of [[theta].sup.j] and [alpha]. All else equal, d[U.sup.j.sub.i]/d[alpha] is increasing in [theta] and decreasing in [alpha].

PROPOSITION 3.

Define the surplus from consumers and firms as

(A19) CS + [PI] = [[integral].sup.[??].[[theta].bar]] [[theta][q.sub.l - c([q.sub.l])dF([theta]) + [[integral].sup.[bar.[[theta].sub.[??]] [[theta][q.sub.h] - c([q.sub.h])]dF([theta])

(A20) = (1/(2R))[-[[??].sup.2]([q.sub.h] - [q.sub.l]) + [??]([q.sup.2.sub.h] - [q.sup.2.sub.l]) + ([[bar.[theta]].sup.2][q.sub.h] - [[[theta].bar].sup.2][q.sub.l]) + ([bar.[theta]][q.sup.2.sub.l] - [bar.[theta]][q.sup.2.sub.h])].

After one substitutes in the equilibrium values of [q.sub.h], [q.sub.l], and [??] and simplifies,

(A21) d(CS + [PI])/d[alpha] = (1/(32R))[(14[[bar.[theta].sup.3] - 10[[bar.[theta]].sup.2] [[theta].bar] + 10[bar.[theta]][[theta].bar].sup.2]] - 14[[bar.[theta].sup.3]) - 2[alpha](13[[bar.[theta].sup.3] - 23[[bar.[theta].sup.2][[theta].bar] + 23[bar.[theta]][[theta].bar].sup.2] - 13 [[theta].bar].sup.3])]

If [alpha] = 0

(A22) d(CS + [PI])/d[alpha] (1/32)[10([[bar.[theta]].sup.2] + [[theta].bar.sup.2]) +4([[bar.[theta]].sup.2] + [[bar.[theta]][[theta].bar] + [[[theta].bar.]].sup.2])] > 0.

If [alpha] = 1

(A23) d(CS+[PI])/[alpha] = -12([bar.[theta]] - [[[theta].bar].sup.2]/32<0.

Define aggregate pollution as

(A24) AP [x.sup.h]([rho] - [q.sup.h]) + [x.sub.l]([rho] - [q.sub.l]).

After one substitutes in the equilibrium values of [q.sub.h], [q.sub.l], [X.sub.h] and [x.sub.l] and simplifies,

(A25) AP = [rho] - ([alpha]/2)([bar.[theta]] + [[theta].bar])

(A26) d(AP)/d[alpha] = -(1/2)([bar.[theta]] + [[theta].bar]) < 0.

Now consider the combined effect on social welfare of a change in [alpha].

(A27) dW/d[alpha] = (d(CS + [PI])/d[alpha]) - (d(AP)/d[alpha].

If [alpha] = 0

(A28) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

If [alpha] = 1

(A29) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

PROPOSITION 4.

Per Unit Emissions Tax. Under a per unit emissions tax, firms maximize

(A30) [[PI].sub.h] = [[P.sub.h] - c([q.sub.h]) - t([rho] - [q.sub.h])][x.sub.h]

(A31) [[PI].sub.l] = [[P.sub.l] - c([q.sub.l]) - t([rho] - [q.sub.l)][x.sub.l].

Solving, equilibrium quality levels are

(A32) [q.sup.t.sub.h] = ([alpha]/4) (5[[bar.[theta]] - [[theta].bar]]) t and

[q.sup.t.sub.l] = ([alpha]/4)(- [[bar.[theta]] + 5 [[theta].bar]]) + t.

This implies

(A33) [dq.sup.t.sub.h]/dt = [dq.sup.t.sub.l]/dt = 1 and

d([dq.sup.t.sub.h]/dt)/d[alpha] = d([dq.sup.t.sub.l]/dt)/d[alpha] = 0.

Substitute in the equilibrium price and quality expressions under a per unit emissions tax,

(A34) [[PI].sub.h] = (3[[alpha].sup.2] / 8) [([bar.[theta]] - [[theta].bar]).sup.2] and [[PI].sub.l] = (3[[alpha].sup.2]/8) [([bar.[theta]] - [[theta].bar]).sup.2],

which is independent of t.

Ad Valorem Output Subsidy. Under an ad valorem output subsidy, firms maximize

(A35) [[PI].sub.h] = [[P.sub.h](1 + s) c([q.sub.h)][X.sub.h]

(A36) [[PI].sub.l] = [[P.sub.l] (1 + s) - c([q.sub.l])][x.sub.l].

Solving, equilibrium quality levels are

(A37) [q.sup.s.sub.h] = ([alpha]/4)(l + s)(5[bar.[theta]] - [[theta].bar]) and

[q.sup.s.sub.l] = ([alpha]/4) (1 + s)(-[bar.[theta]] + 5[[theta].bar]).

This implies

(A38) [dq.sup.s.sub.h/ds = ([alpha]//4)(5[[bar.[theta]] - [[theta].bar]]) and [dq.sup.s.sub.l/ds = ([alpha]/4)(-[bar.[theta]] + 5[[theta].bar].

(A39) d([dq.sup.s.sub.h/ds)/d[alpha] = (1/4) (5[bar.[theta]] - [[theta].bar]) > 0 and d([dq.sup.s.sub.l/ds)/d[alpha] = (1/4)(-[bar.[theta]] + 5[[theta].bar]

Substitute in the equilibrium price and quality expressions under an ad valorem output subsidy,

(A40) [[PI].sub.h] = 3[[alpha].sup.2]/8)(1 + [s).sup.2][([bar.[theta]] - [[theta].bar]).sup.2] and [[PI].sub.l] = (3[[alpha].sup.2]/8)[(1 + s).sup.2][([bar.[theta]] - [[theta].bar]).sup.2],

which depend positively on s.

To illustrate the results of Proposition 4, consider the best response functions under each scenario. The best response functions under a per unit emissions tax are,

(A41) for the high-quality firm:

[q.sub.h] = [2[alpha](2[bar.[theta]] - [[theta].bar]) + 2t]/3 + (l/3)[q.sub.l]

(A42) for the low-quality firm:

[q.sub.h] = [2[alpha]([bar.[theta]] - 2[[theta].bar]) - 2t] 3[q.sub.l].

Under an ad valorem output subsidy, the best response functions are,

(A43) for the high-quality firm:

[q.sub.h] = [2[alpha](1 + s)(2[bar.[theta]] - [[theta].bar)]/3 + (1/3)[q.sub.l]

(A44) for the tow-quality firm:

[q.sub.h] = [2[alpha](1 + s)([bar.[theta]] - 2[[theta].bar])] + 3[q.sub.l].

It is clear that an emissions tax (t), ad valorem subsidy (s), and information ([alpha]) only affect the intercept term of the best response functions. With an emissions tax, [alpha] and t enter the intercept term in a linear fashion while under an ad valorem subsidy [alpha] and s enter in a multipticative fashion. This implies that an emissions tax t shifts the intercept, but the size of this shift is independent of the level of [alpha] (see Figure 4; movement from A to B when [alpha] is small and from A' to B' when a is large). Thus, both the imposition of an emissions tax and information provision encourage firms to increase quality, but the effectiveness of each is independent of the other (distance between A to B = distance between A' to B'). On the other hand, the size of the shift in the intercept with a change in the ad valorem subsidy s depends on the level of [alpha] (see Figure 5). Therefore, a subsidy will increase quality more when information is higher (distance between A' to B' > distance between A to B). This implies that the government can achieve a certain improvement in the environment with a smaller subsidy when information is higher.

PROPOSITION 5.

Can we set a per unit emissions tax or an ad valorem output subsidy to replicate the level of aggregate pollution (AP = ([rho] - [q.sub.h])-[x.sub.h] + ([rho] - [q.sub.l])[x.sub.l]) achieved under an information provision that increases consumer knowledge of product quality A? Substitute in equilibrium values of [x.sub.h], [x.sub.l], [q/sib/h]. and [q.sub.l] under each scenario, aggregate pollution is

(A45) AP(with information) = [rho] - (1/2)([alpha] + [DELTA])([bar.[theta]] + [[theta].bar])

(A46) AP(with emissions tax) = [rho] t - ([alpha]/2)([bar.[theta]] + [[theta].bar])

(A47) AP(with output subsidy) = [rho] - ([alpha]/2 (1 + s)([bar.[theta]] + [[theta].bar]).

(A48) AP(with information) = AP(with emissions tax)

(A49) t = [DELTA]([[bar.[theta]] + [[theta].bar])/2

(A50) AP(with information) = AP(with output subsidy)

(A51) s = [DELTA]/[alpha],

which imply equilibrium quality levels of

(A52) [q.sup.l.sub.h] (([alpha] + [DELTA])/4)(5[bar.[theta]] - [[theta].bar]) and [q.sup.l.sub.l] = (([alpha] + [DELTA])/4)(-[bar.[theta]] + 5[[theta].bar])

(A53) [q.sup.t.sub.h] = ([alpha]/4)(5[bar.[theta]] - [[theta].bar]) + [DELTA]([bar.[theta]] + [[theta].bar] and [q.sup.t.sub.l] = (([alpha]/[DELTA])/4)(5[bar.[theta]] - [[theta].bar]) and

(A54) [q.sup.s.sub.h] = (([alpha] + [DELTA])/4)(5[bar.[theta]] - [[theta].bar]) and [q.sup.s.sub.l] = (([alpha] + [DELTA])/4)(-[bar.[theta]] + 5[[theta].bar]).

Substituting into social welfare when AP is equal in all three scenarios

(A55) [??] = [integral] CS + [summation] [PI]

(A56) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(A57) (1/2R))(-[[??].sup.2]([q.sub.h] - [q.sub.l]) + [??]([q.sup.2.sub.h] - [q.sup.2.sub.t]) -[[theta].barr]].sup.2] ql + [[bar.[theta]].sup.2] [q.sub.h] + [[theta].bar]][q.sup.2.sub.l] - [[bar.[theta]][q.sup.2.sub.h])

and solving

(A58) [??](I/s) > [??](t) if (2 - 3[DELTA])/6 > [alpha].

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(1.) For example, the Federal Trade Commission issued the "Green Guide" and the EPA issued the "Consumer Labeling Initiative." For a listing of government action in the environmental area, see U.S. EPA (1992, 1993, 1996).

(2.) If we allow consumers to internalize a part of the externality, the direction of the basic results of the model remain the same, but the algebraic expressions are less transparent.

(3.) An example of a group of products whose price does not necessarily signal quality is generic products.

(4.) Alternatively, [alpha] could represent the proportion of the population that believes the reported product quality of each firm is credible. In the aggregate, both interpretations of the model yield the same results.

(5.) When [alpha] equals one, the market is characterized by perfect information and the expected utility expression simplifies to [EU.sup.j.sub.i] = y + k + [[theta].sup.j][q.sub.i] - [P.sub.j], which is the represenration of utility commonly found in the literature (Bansal and Gangopadhyay 2003: Crampes and Hollander 1995: Lutz et al. 2000; Moraga-Gonzalez and Padron-Fumero 2002).

(6.) For example, consumer decisions to purchase a car will partly depend on the functional benefit they expect to derive from simply having a (any) car and partly on the benefits they obtain from specific features of the car, such as its safety. Though the former benefits are likely to be completely known to the consumer, the latter benefits will depend on the extent to which the consumer believes the manufacturer's claims or the safety ratings at the time of the purchase decision. Similarly in the case of lightbulbs, all lightbulbs with a given wattage provide the same amount of light per unit time, but a high-quality lightbulb may have a longer life and thus provide additional utility to the consumer.

(7.) The order of the price and quality stages does not affect the equilibrium outcome. We follow the tradition in the literature that price competition occurs after each firm makes their quality choice.

(8.) For the market to be fully covered, the consumer with the lowest taste parameter must get more utility from consuming the good than from not consuming. This will occur if k > [P.sub.l] - y - [[theta].bar][alpha][q.sub.l]].

(9.) The result in Proposition 1 depends on the assumption of lull market coverage. Several publications have developed vertically differentiated models to examine the provision of high-quality goods under the assumption that the cost of quality provision does not vary with output and that the market is only partially covered. In exploring the effects of partial market coverage using our framework. we find that information provision would lead both firms to increase product quality. Although different from the result obtained in Proposition 1, we find that this result is similar to that obtained in Proposition 2 with a quadratic cost function. However, the mechanism that leads to this outcome in the two models (with and without full market coverage) is very different. With incomplete market coverage, consumers are segmented into three groups: those with low [theta] who do not participate in the market, those with [theta] in the middle range who would purchase from the low-quality firm, and those with high [theta] who would purchase from the high-quality firm. The low-quality firm's choice of product quality is now affected by two considerations. On one hand, it could increase product differentiation by lowering quality and thus increasing monopoly profits, but on the other hand, lowering product quality could drive away consumers with very low [theta] (who may no longer purchase the good) and those with a high [theta] (who may switch to consumption of the high-quality good). We find that the potential loss of consumers overwhelms the potential gain in higher prices, and the low-quality firm prefers to always increase quality. This result is in contrast to that obtained with a fully covered market where the low-quality firm is less concerned about potentially losing consumers as everyone purchases the good. In this situation, the low-quality firm is more interested in increasing profits by exercising the market power that results from increased product differentiation.

(10.) To support the duopoly outcome, firm prices must exist within the following ranges: c([q.sub.h]) - [bar.[theta]][alpha]([q.sub.h] - [q.sub.l]) [less than or equal to] [P.sub.l] < c([q.sub.h]) + ([bar.[theta]] - 2[[theta].sub.bar])([q.sub.h] - [q.sub.1]) and c([q.sub.1]) + [[theta].bar][alpha]([q.sub.h] - [q.sub.1]) [less than or equal to] [P.sub.h] < c([q.sub.l]) + (2[bar.[theta]] - [[theta].bar])([q.sub.h] [q.sub.l]). If equilibrium prices are outside of these ranges, firms will find it more profitable to act as a monopolist than as duopolists (see Crampes and Hollander 1995). Given equilibrium levels of quality, the conditions are satisfied if 2[[theta].bar] < [bar.[theta]]. The second condition, [bar.[theta]] < 5[[theta].bar], ensures that the equilibrium quality level for the low-quality firm is positive.

(11.) This result is sensitive to the assumption one makes about the type of market coverage. Arora and Gangopadhyay (1995), for example, assume partial market coverage and find that more intense competition results in lower prices per unit of quality making the good more affordable. Thus, even though pollution per unit falls, aggregate pollution can increase if enough new consumers enter the market.

(12.) If quality levels were fixed as in Mattoo and Singh (1994) and Sedjo and Swallow (2002), it can be shown that [dx.sub.h]/d[alpha] > > 0 and [dx.sub.l]/d[alpha] < 0. Our model, however, allows firms to respond to changing market demands by altering their levels of quality. In response to a change in information and a change in market, demands, then, firms change their quality levels and maintain equal market shares.

(13.) We define consumer surplus of each individual as their surplus from quality minus price: [CS.sup.j] = [[theta].sup.j][q.sub.j] - [P.sub.i]. Note, this definition of consumer surplus is based on consumer's actual utility ([[theta].sup.j][q.sub.i] - [P.sub.i]). not their "expected" utility ([[theta].sup.j][alpha][q.sub.i] - [P.sub.i]). If one were to use expected utility, our welfare measure would confound the effects of a change in quality with the welfare effects of a change in information. Also, the definition of consumer surplus does not take into account aggregate pollution. We take aggregate pollution into account in our definition of social welfare.

(14.) We define [CS.sup.j] = [[theta].sup.j][q.sub.i] - [P.sub.i], [[PI].sub.i] = ([P.sub.i] - c ([q.sub.i]))[x.sub.i], and AP = [x.sub.h] ([rho] - [q.sub.h]) + [x.sub.l] ([rho] - [q.sub.l]).

(15.) As in Bansal and Gangopadhyay (2003), one may want to consider the cost or impact of implementing an information provision program on the government's budget constraint. Because the costs of informing consumers are in all likelihood also an increasing function of [alpha], the result that dW/d[alpha] is positive for small [alpha] and negative for large [alpha] will be further magnified if we consider the cost of providing information.

(16.) Other instruments commonly employed to increase product quality are a per unit output subsidy, technology subsidies, and minimum quality standards. It is straight-forward to show that the quality decision of each firm is independent of a per unit output subsidy. Because firms split the market in equilibrium and the market is fully covered, a per unit subsidy affects both firms equally and acts like a fixed subsidy, which increases profits but does not affect the quality decision of each firm. A technology subsidy lowers a firm's cost of producing quality, which will result in firms improving their product quality provided in the market. Since quality changes are more efficiently transmitted when consumers have more information, a technology subsidy encourages firms to increase quality more when information is higher. With a minimum quality standard, the low-quality firm will just meet the standard and high-quality firms will overcomply with the standard to differentiate its product from its rival. The effectiveness of a minimum quality standard is similar at different levels of information. Imposing minimum quality standards at different levels of information that achieve the same increase in quality by the low-quality firm also result in the same increase in quality by the high-quality firm. Proof of these results are available on request from the authors.

(17.) Note, a full comparison of these programs should alter the condition in Proposition 5 ((2 - 3[DELTA]/6 > [alpha]) to include the cost of implementing each program.

KEITH BROUHLE and MADHU KHANNA *

* We thank two anonymous referees who made useful suggestions.

Brouhle: Assistant Professor, Grinnell College, Grinnell, IA 50112. Phone 1-641-269-4843, Fax 1-641-2694985, E-mail brouhlek@grinnell.edu

Khanna: Professor, University of Illinois, Urbana-Champaign, Urbana, IL 61801. Phone 1-217-3335176, Fax 1-217-333-5538, E-mail khanna1@uiuc.edu