Demo or No Demo: Supplying Costly Signals to Improve Profits

Transcription

1 Demo or No Demo: Supplying Costly Signals to Improve Profits by Fan Li* University of Florida Department of Economics, P.O.Box Gainesville, FL Tel: Fax: Abstract Many software and video game firms offer a free demo with limited content to help buyers better assess the likely value of the services or goods that they may purchase. This paper examines fundamental issues concerning free demos, relating to the incentives and the risk to a monopoly seller of providing a demo. I find that a free demo enables the seller to segment the market and charge higher prices to high-value buyers, but can cause a decline in demand. Moreover, the seller risks losing part of the demand for her products because buyers may value a free demo enough to drive demand for the product to zero. Thus, the benefit of a free demo is offset by this cannibalization loss. In addition to the size and the content of a demo, the distribution of buyers prior beliefs affects a demo s ability to convey private information. In a variety of settings, these two tradeoffs are optimally balanced: either buyers are supplied with partial knowledge of their tastes, or no information is supplied by the seller. Keywords: signal, cannibalization, price discrimination, private information JEL Classification: D83, M31, L15 * I am grateful to Steven Slutsky, Jonathan Hamilton, David Sappington for helpful comments and suggestions.

2 1 1. Introduction Many companies offer free demos of their products as part of their marketing strategies. A free demo can help buyers get a feel for the product before deciding whether to buy the full version. There are two general types of free demos in the market a free, fully functional version with limited use time and a free unlimited time but with limited content (Cheng and Liu, 2011). In this paper, I will focus on analyzing the second type, of which many examples exist. One is Kinect Sports, a video game that contains simulations of six sports (Bowling, Boxing, Track & Field, Table Tennis, Beach Volleyball and Soccer) and eight mini-games. The free demo contains one of the mini-games. Another is Acrobat PDF Professional, where the PDF Reader is supplied freely, but customers must pay for the full package which includes the PDF Writer (Parker and VanAlstyne, 2000). A third is Wolfram Mathematica, computational software whose features include computer algebra, numerical computations, information visualization, statistics and user interface creation, of which simple numerical computations are freely offered by Wolfram Alpha. Offering free demos to help buyers get more informed about the product is common for items such as videos, games, music and software. Unlike search goods whose characteristics can be determined simply by inspection before purchase, these product categories are experience goods where product characteristics are difficult to observe in advance, but whose characteristics can be ascertained upon consumption (Nelson, 1970). Having uncertainty about the product characteristics can reduce buyers willingnesses to pay for the good. These products also share another property: they are digital goods. This means that, through the internet, there is a technology available to provide them at low cost. For example, Xbox 360 produced by Microsoft offers free downloads of available game demos. Hence, for digital experience goods, offering free demos is both possible and inexpensive. However, not all digital experience goods do supply such demos. For example, free demos are not available for iphoto and imovie, digital life management software applications developed by Apple Inc, or for Windows XP, Windows Vista and Windows 7, operating systems developed by Microsoft.

3 2 Given the increased importance of free demos in the market, there are a number of interesting questions about their use. What is the sellers motivation and risk in supplying free demos? Why are demos released for some products but nor for others? Under what conditions do sellers benefit from facilitating more informed purchase by offering free demos? How much and what kind of content should they release in free demos? Does releasing more content in demos raise or lower profits? Which factors determine the size and the content of demos? To better understand the fundamental role of demos, it is helpful to compare them with other product information channels. Traditionally, sellers may describe product attributes in informative advertisements (Nelson 1974, Milgrom and Roberts 1986), or may sponsor training seminars. As internet and information technology has developed, online customer reviews and expert reviews (Avery, Resnick and Zeckhauser 1999, Chen and Xie 2005) are new information channels that have become widely used to provide product information. However, for digital experience goods, by only offering overall information, these methods may ignore buyers idiosyncratic preferences for the products which can be realized only through personal consumption. Therefore, supplying free demos differs from the other formats that do not directly offer any of the content of the product. Analyzing free demos is related to the studies of information disclosure and signals. In deciding how extensive a demo to offer to potential buyers in advance of purchase, a monopoly seller faces a fundamental tradeoff between volume and profit margin. If a firm does not release a demo at all, then no information is provided and all buyers beliefs about the likely nature of the product would just be their initial priors. A seller would be able to extract some surplus from an average buyer, but this amount would be smaller than what could be gathered from some buyers if the product s true nature were partially or completely known. On the other hand, a seller can offer buyers more precise knowledge of her products by releasing a demo. This will change buyers beliefs about the likely nature of the product. As a result, buyers who like the demo will increase their willingness to buy the full product while buyers who dislike the demo will reduce their willingness. Through price discrimination, the seller can capture extra surplus from those typical buyers whose prior valuation is increased after using the demo.

4 3 Accordingly, by offering product information, the seller could extract more surplus from some buyers but lose the demand of the others who disliked the demo. There is a second possible effect on demand caused by a seller releasing a demo, which does not relate to information consideration. A demo might reduce demand for the full products because buyers get value from the demo without having to pay anything. In order to avoid this cannibalization effect, the seller can either reduce the price of the product or limit the content of the demo. Overall, by supplying demos that freely offer buyers a part of the full product, there is a signal effect that allows better matching between the products and a buyer s preference. However, this benefit may be offset to some extent by the opportunity cost from the signal providing value to buyers. In much of the marketing and economics literature, the signal itself is treated as having no cost and the accuracy of the signal is exogenous. Lewis and Sappington (1994) model signals in the form of on-site appraisals or product seminars that inform consumers of their match with the product. They examine how a seller chooses the precision of such signals and find that she often either chooses the most accurate signal possible or an uninformative one. Anderson and Renault (2006) show that a monopolist would reveal only partial information regarding how consumers match with her product, because by providing precise information on product characteristics, consumers would rationally expect the firm to charge such a high price that no consumer would incur the prior search cost. Chen and Xie (2008) show that a monopoly may change the initial information disclosure level in the presence of online customer reviews, because this new communication mode eliminates a seller's control over the content of product information accessible to consumers. Sun (2011) shows that when the product s quality is common knowledge, a monopolist with high quality is less likely to disclose the horizontal attribute because he is willing to hide an unfavorable horizontal attribute. A fundamental difference between my model and the existing signal literature is that I consider how the nature of the signal itself leads to partial release of product information. This paper applies the price discrimination analysis in Lewis and Sappington (1994), but it is quite distinct from their model. In that paper, the no cost signal is modeled by on-site appraisal or through a seminar, so the signal cannot

5 4 substitute for the full product. As a result, the tradeoff between profit margin and volume is the most important concern in deciding whether to disclose private product information. Here, the signal itself includes some of the content in the full product, so it can capture part of the demand. As more content is released in a free demo, the signal may become more informative, but it will cause higher cannibalization. Thus, in contrast to the case with a no cost signal, a signal in the form of a demo with limited content serves as a prototype that can compete with the product. If the benefit to buyers from the signal effect is less than the loss from the cannibalization effect, then supplying a demo fails to improve buyers willingness to purchase the full product. With a demo, the signal effect and the cannibalization effect are endogenously determined by how much and what kind of the content is offered in the demo, factors that can be controlled by the monopoly seller. Moreover, the signal effect is related to the ability of a demo to convey product information, which is exogenously affected by buyers prior beliefs about the nature of a full product. A simple example illustrates this key insight. I compare two cases with the different prior beliefs: (1) buyers initially believe that there is a 30% chance that the fraction of a specific type component in the full product is below 10%; (2) buyers initially believe that there is a 60% chance that the fraction of that type component is below 10%. If the seller releases just 10% of that type component from a full product into a demo under both cases, then the possibility of a full product including less than 10% of that specific type component is eliminated, because a demo already includes 10% of that type component. As a result, in case (1) the demo excludes that possibility by a 30% chance while in case (2) excluding by a 60% chance. Clearly, the function of a demo is to exclude certain possibilities about the nature of a full product. The more chances can a demo preclude certain possibilities, the more information can a demo convey. In the example, the same demo excludes certain possibilities of a full product by larger chances in case (2) than in case (1), so the demo in case (2) is able to convey more product information. After precluding certain possibilities about the nature of the full product, the buyers would build posterior beliefs based on the remaining possibilities. Thus, in addition to the size and the content of a demo, prior beliefs also affect the ability of a demo to convey product information. In this paper, buyers prior beliefs about the nature of a

6 5 full product are pre-determined and beyond the control of the monopoly seller. Given a demo s ability to convey information, the seller must decide whether it is desirable to choose a demo as her product information channel under the risk of cannibalization. The remainder of this paper is organized as follows. Section 2 presents the general model setup and derives analytical results about the conditions under which the seller should release free demos and about the optimal content and size of the demos. In Section3, I suppose one distribution of buyers prior beliefs second order stochastically dominates another one. Under these two different prior beliefs, comparative results about whether the seller should release demos, the signal effect of a given size and content demo and the optimal size are discussed to gain insight into how prior beliefs affect the signal effect. Finally, Section 4 concludes the paper and discusses some directions for future research. 2. Model 2.1 Buyers actual valuation for the product I model a monopoly seller whose product is a bundle of components, each of which either has attribute characteristic A or attribute characteristic B. For convenience, the mix of attributes is treated as a continuous variable and the size of product is normalized to 1. Given that characteristics A and B are mutually exclusive, let r denote the fraction of components that are type A and let be the fraction of components that are type B. To illustrate, the Kinect Sports is video game that contains six sports simulations, each of which is a component in this product. A key attribute in a video game is difficulty, how challenging is the game to play. Table Tennis in Kinect Sports is believed to have a high difficulty level, while the other components are easy games. Thus, Kinect Sports is a bundle of easy games and difficult games. Suppose buyers differ in their preferences toward the seller s product. For a given component, some buyers will find that the component matches their preferences, while others will find that the component does not match their preferences. A buyer whose taste is matched by attribute characteristic A is considered to be a type A buyer. A buyer whose taste is matched by attribute characteristic B is

7 6 considered to be a type B buyer. A buyer s actual valuation is either high ( ) for the component matching his taste or low for the component not matching his taste. I assume. To simplify, for any given buyer, suppose that there is an equal chance that a given component matches his preference, something that is known to both the seller and the buyers. A buyer s actual valuation for the product bundle is equal to the weighted average valuation of all components, More specifically, a type A buyer s valuation for the product is denoted by ( ) while a type B buyer s valuation for the product is denoted by. is linearly increasing in the fraction of component A, because there components match a type A s taste. In contrast, is linearly decreasing in the fraction of A components, because these do not match a type B s taste. Consider Kinect Sport. A potential buyer who is an expert in sports may prefer a difficult sports game while a potential buyer who is a novice may prefer an easy game. Consequently, given that Kinect Sports is a bundle of easy games and difficult game, the valuation for Kinect Sports of an expert is while the valuation of a novice is. 2.2 Buyers prior valuation for the product Without any additional information, each of the potential buyers has the same belief of the prior fraction of component A,. Assume is a random variable with a symmetric density function. Also denote the corresponding distribution function. Thus, each of the potential buyers has the identical expected prior fraction of component A,, and the fraction of component B,. A type A buyer s prior expected valuation for the product is denoted by and a type B buyer s valuation for the product is denoted by ( ). Accordingly, each of the potential buyers has the same expected prior valuation for the product. Assume that each buyer will purchase exactly one unit of the product if his expected valuation exceeds the price of the product. The seller can set price equal to this

8 7 expected prior valuation (i.e. ) and sell her products to the average buyers. Hence, without any additional information, the maximum profit of the firm would be (1) where is the marginal cost of producing and marketing each unit of the product. Notice the buyers are assumed to have the same distribution of the attribute fraction, but have different valuation (i.e. either or ) for an identical attribute. 2.3 Buyers posterior valuation for the product with a demo Before buyers decide whether to purchase the product, the seller can provide additional private information that may alter their expected valuation for the product. This additional information may arise from a free demo that includes some components which are in the product, but lists the titles of other components, which cannot be used unless a buyer purchases the full product. As a result, buyers not only gain value from using the demo, but also update their valuation for the products based on the product information the demo offers. Notice that the widely used channel to deliver the demo in the digital good market is to allow buyers to download demos over the internet for free. Thus, I assume that the demo can be provided at zero marginal cost and zero price to any user. However, the product is usually sold in a disk, so it is costly to produce and distribute. Demo is a subset of product, which discloses the amount of components A, (, and the amount of components B, exclude the case where. Here, because the seller releases components in a demo, I, which implies a seller releases no demo. To illustrate, assume Kinect Sports releases in a demo Bowling and Track & Field from the six simulations in the full product, so the demo has and, since it contains 2 of the 5 easy games and does not include the hard game. Demos serve as a prototype of the product, so I use the same assumption and setup of the product for the demo here. A buyer s actual valuation for a demo is equal to the weighted average valuation of all components in a demo,. More specifically, a type A buyer s valuation for

9 8 the demo is denoted by and a type B buyer s actual valuation for the demo is denoted by. Without loss of generality, I assume that Thus, I have. Accordingly, the demo gives type A buyers a high signal of the full product but gives type B buyers a low signal. In practice, the seller might have no information about the product attributes in advance of sales. For example, the developer of Kinect Sports might be uncertain about the challenge level of each component until she sells products and receives feedback from buyers. In that case, the seller would have to randomly choose components from the full product to release into a demo. Hence, a demo would be a random signal of the nature of the full product. Accordingly, the prior distribution of the full product would be updated according to the distribution of component A in the demo. This type of a demo is not considered in this paper. Indeed, I focus on the case where the seller has knowledge of the component attributes in the full product gained through such things as pre-sale consumer tests. This situation seems more realistic. Unlike a randomly released demo, the seller can control the mix of components included in a demo. For example, the developer of Kinect Sport can intentionally release more or fewer easy games. In updating their prior beliefs, buyer will recognize that the nature of the demo is chosen by the seller and may not reflect the true nature of the product. Accordingly, as a part of a full product, a demo ( ) excludes the possibility that a full product has less than or more than fraction of component A. Hence, after a demo is released, a buyer learns that the full product includes the component A by the fraction more than and up to but nothing else. Therefore, the information conveyed by a demo can eliminate some possibilities about the nature of a full product. To illustrate, assume buyers initially believe that the fraction of easy game in Kinect Sport is distributed as where. If Kinect Sports releases a demo with 2 easy games and 1 hard game from the 6 simulations in the full product, then buyers will change their initial beliefs. On one hand, buyers will realize that the full product of Kinect Sport should include 2 easy games at lease since a demo includes 2 easy games, but no more than 5 easy games since a

10 9 demo includes 1 hard game already. Those knowledge is achieved because a demo precludes other possibilities of the nature of a full product. On the other hand, because the seller can intentionally select components in a demo, buyers remain the conditional density as given. In one word, after a demo is released, the buyers believe that the fraction of easy games is distributed with the conditional density given but with conditional density 0 given and. The expected fraction of easy games should be calculated based on this updated belief. Formally, { and ), where is the posterior density function of the fraction of component A and is the expected fraction of components A after the demo is released. Clearly, is the conditional expected value of given that is distributed with conditional density function where. Given the assumptions that and that is symmetrically distributed, it follows that. Thus, after observing a demo ( ), a type A buyer realizes a high signal and revises upward his expected valuation of the full product to > ( ) and a type B buyer realizes a low signal and revises downward his expected valuation of the full product to ( ) Clearly, a type A buyer is a high value buyer and a type B is a low value buyer after utilizing the demo. Suppose each buyer purchases exactly one unit of the seller s product if his expected utility from buying the product exceeds his utility from just using the free demo. A buyer s utility from the demo equals his valuation for that demo,, where while the a buyer s utility from the full product equals his expected valuation for that product less the price, [ ] Therefore, the seller can set the highest price equal to a buyer s incremental valuation of consuming the product,. The seller can either set high price to only sell to the high-value buyers that are type A

11 10 or set low price to sell to the potential buyers that are either type A or type B. The proof that is in the appendix. Clearly, the profits from charging those two different prices would be different. Denote profits that the seller can secure by charging the higher price as, and those that can be secured by charging the lower price as. Moreover, buyers get value from a free demo without having to pay anything, so some buyers may just use that demo instead of purchasing a full product. In order to avoid this cannibalization effect, the seller must reduce the price by the amount of buyer s utility from that demo. In other word, after releasing a free demo, the seller only charges buyers for the contents remaining in the full product while forfeiting the value of contents in that demo. This cannibalization effect is measured by buyers utility for the demo, which equals to for type A buyers and equals to for type B buyers. The more content that is released in a demo, the larger is the cannibalization effect. Consequently, the seller s maximum expected profit as a function of the size and the content of a demo is where and. (2) Proposition 1. The profits from releasing a demo and then selling to everyone are less than the profits from not releasing a demo. Proposition 1 reveals that the seller can secure the most profits by (1) releasing no information and selling to all average buyers or by (2) releasing partial information and selling to high-value buyers. Therefore, the seller secures either or. Intuitively, after observing a low signal, the low-value buyers (type B buyers) revise downward their expected valuation for the products; while after observing a high signal, the high-value buyers (type A buyers) revise upward their expected valuation for the products. Consequently, if the seller prefers to sell to all buyers, the price under information release must be lower than the price under no information release. Therefore, the strategy of releasing a demo and

12 11 then selling to all buyers cannot be the most profitable strategy for the seller. Moreover, if the seller releases all components in the free demo, the cannibalization effect causes the seller to earn no profit, so the seller would not release full information. A seller either can release a demo containing only one type of component which I call a pure demo, or can release both types of components in a demo which I call a mixed demo. Thus, in deciding whether to release a demo, a seller must make 3 decisions: (1) whether to release a pure demo or a mixed demo; (2) whether releasing a demo is more profitable than not releasing a demo; (3) the optimal amount of each component to include in the demo. Proposition 2 answers the first question. Since I assume that buyers types and prior beliefs are symmetrically distributed, a seller is indifferent between releasing either component in a pure demo. Without loss of generality, I derive profits for a pure demo containing only component in what follows. 1 Denote profits that the seller can secure by releasing a mixed demo as and that can be secured by releasing a pure demo as, where >0. Proposition 2. Any mixed demo yields lower profits than a pure demo containing the same amount of component. ( ). Proposition 2 shows that the seller would rather release a pure demo than a mixed demo. According to Proposition 1, the purpose of releasing a demo is to segment the market and charge a higher price to the high-value buyers. Intuitively, to increase the high-value buyers expected valuation of a full product, the seller should increase buyers expected amount of component A in a full product by increasing the amount of component A and decreasing the amount of component B in a demo. Therefore, a mixed demo cannot be the optimal demo strategy. To simplify notation, let and, which denote the seller s profits and buyers expected amount of component A from a demo containing only of component A. Here, because a seller releases components in a demo, I assume that. 1 If either buyers types or prior beliefs are asymmetrically distributed, a seller must decide whether to release component A or B in a pure demo, which is not considered in this paper.

13 12 Next, I consider whether a seller should release a pure demo or not release a demo. As mentioned above, the incentive for a seller to release a demo is to improve some buyers posterior valuation for the product in order to increase their willingness to pay for the full product. Although the seller may successfully increase the prices by releasing a demo, the seller will suffer from a decline in demand because only high-value buyers will purchase the full product. Therefore, the seller faces a tradeoff between an increased profit margin and a reduced demand. Proposition 3 follows immediately. Proposition 3. A seller will release a pure demo of size where if it leads to nonnegative profit ( ), the signal effect is greater than the cannibalization effect ( ), and the margin advantage overweighs the demand disadvantage ( ). If, the seller makes negative profits with a demo, so the seller would not release that demo. As noted above, in deciding whether to release a demo in advance of sale, a monopoly seller faces a fundamental tradeoff between volume and profit margin. Because the seller sells only to half of the potential buyers after releasing a demo, she always loses demand. Hence, the incentive of improved private information through a demo is to enable the seller to charge higher prices to high-value buyers. To charge higher prices, the signal effect should be greater than the cannibalization effect. The signal effect is measured by, which is a high-value buyer s incremental valuation of a full product after using a pure demo with size. The cannibalization effect is measured by, which is a high-value buyer s utility from a demo. As mentioned earlier, after releasing a free demo, the seller forfeits the direct profit from that demo, which is equal to buyers valuation from a demo. Only if the signal effect is greater than the cannibalization effect ( ) can the seller take advantage of the higher profit margins. If the seller can raise prices after releasing a demo, whether this leads to higher profits depends on whether the higher price outweighs the loss in sales.

14 13 If, then the seller secures higher profits by releasing a demo and selling the full product to high-value buyers at a higher price. To ensure that offering a demo is more profitable than not offering one, there is an upper bound on the cost while to have a non-negative profit after releasing a demo, there is a lower bound on. For some values of to exist satisfying both conditions, the upper bound must exceed the lower bound. That is must hold. This inequality simplifies to be the condition that the signal effect is greater than the cannibalization effect ( ). To determine the optimal amount of each component to include in a demo, I need to find the optimal size of a pure demo first, and then evaluate if that size satisfies Proposition 3 to determine whether that demo leads to more profit than when no demo is released. Proposition 4 specifies some necessary conditions for the optimal size. Proposition 4. If a demo is to be released, there exists an optimal sized demo that is greater than 0 and less than. Necessary conditions for to be such an optimum are that and. Proposition 4 characterizes, the optimal size of a pure demo at a local profit maximum conditional on a demo being released. The optimal size increases as decreases locally. Intuitively, the seller is more likely to segment the market and sell products to high-value buyers if buyers preferences differ significantly, which is reflected in a smaller value of. There are two possible corner solution for either at or at. If a corner solution exists at, then the seller will not release a demo to secure higher profits. This follows since. Demand without a demo is twice the demand with an infinitesimally small demo, while the margins are almost the same under both cases. If a corner solution exists at, then the

15 14 seller would rather not release a demo either. Formally,. As mentioned before, the signal effect is less than the cannibalization effect at. Figure 1 illustrates that corner solutions for at either 0 or lead to lower profits than without a demo. When there is an interior solution for, the seller must compare with to decide whether she should release a pure demo with size or not release a demo (see Figure 2). Under any specific density function of prior beliefs, the global maximum for can be calculated based on comparing of profits at each local maximum. Figure 1. Corner solutions for Figure 2. Interior solutions for Interaction between the signal and the cannibalization effects can be partially controlled by the seller through the content and the size of a demo, but the ability of a demo to convey product information

16 15 is predetermined by the buyers prior beliefs about the nature of a full product, which are assumed to be beyond the seller s control. The main function of the information conveyed by a demo is to preclude some possibilities about the nature of a full product. As mentioned before, if Kinect Sports releases a demo with 2 easy games and 1 hard game from the 6 simulations in the full product, then buyers will realize that it is impossible that a full product includes less than 2 or more than 5 easy games. Hence, some possibilities about the nature of full product are precluded by buyers. Under different buyers prior beliefs, those possibilities will take account by different chances. To illustrate, the buyers could initially believe that the full product includes less than 2 easy games or more than 5 easy games by 5% chances, or could believe by 30% chances. A same size and content demo would preclude those possibilities by different chances, and then change buyers posterior beliefs differently. The more chances can a demo eliminates certain possibilities about the nature of the full product, the more information can that demo convey. Therefore, I use the chances by which certain possibilities are excluded from the nature of the full product to measure the amount of information a demo could convey. Definition 1. A demo with size can convey the amount of information by under buyers prior beliefs. Definition 1 shows the amount of information a demo could convey is predetermined by the buyers prior beliefs. Figure 3 illustrates how the information changes buyers posterior beliefs if the size of a demo is equal to 0.2. After a demo with size is released, the posterior density function will shift up proportionally where and shrink to 0 where. Formally, {. The information the demo conveyed shows as the shaded area. The larger the shaded area, the more chances certain possibilities about the nature of the full product are eliminated. Hence, the posterior valuation of the full produce is determined by the updated beliefs.

17 16 Figure 3 An example of the change in density function To simplify the density function about buyers prior beliefs, I only discuss the type of density functions which are continuous and either single-peaked or single-troughed. Proposition 5 specifies the type of density function under which a demo is not able to convey a large amount of information. Proposition 5. If buyers prior beliefs about have a symmetric single-peaked density function, then a seller would never release a demo. Figure 4 shows one example of a single-peaked and a single-troughed distribution function, where for an, the shaded area under the single-troughed density function is greater than that under the single-peaked density function. That implies a demo with size is able to provide more information under the former distribution than the latter one. To raise the price through releasing a demo, the signal effect should be greater than the cannibalization effect. The greater signal effect requires more information conveyed by a demo. When buyers prior beliefs are more likely to distribute at the tail and are less likely to distribute at the middle, a demo with size is able to convey more information. Proposition 5 shows that the opposite type, a symmetric single-peaked density function limits a deme s ability to convey enough information, because here buyers prior beliefs are less likely to distributed at the tail and are more likely to distribute at the middle. Therefore, it is undesirable to choose a demo as

18 17 the product information channel under the risk of cannibalization when buyers prior beliefs have a symmetric single-peaked distribution. Figure 4. An example of the single-troughed and single-peaked density function 3. Comparative Results under Different Distributions of Prior beliefs. Proposition 5 precludes the single-peaked density function under which a demo would release no demo. This section will discuss the single-troughed density function under which a demo may release a demo. Buyers prior beliefs affect the seller s demo strategy through determining the amount of information a demo could convey. To capture this effect, the following assumption characterizes the two single-troughed distributions underlying the buyers prior beliefs in the symmetric setting. Assumption 1.The fraction of component A under the buyers prior beliefs is continuous random variable with a symmetric density function either or at, whose distribution functions are such that,and. Assumption 1 implies that second order stochastically dominates. Figure 5 shows one example of those two distributions, where prior beliefs is more likely to distribute at the tail under than under. Accordingly, a demo of size is able to convey a larger amount of information under than under. Formally,. I now generally compare the demo strategy under those two distributions of prior beliefs.

19 18 4 ; g r F ; G r Figure 5. An example of two distributions Proposition 6. Suppose Assumption 1 holds. Then if a pure demo of size is to be released, the signal effect under distribution is greater than that under distribution (i.e. ). Proposition 6 shows how the signal effect raises under different distributions of prior beliefs. Intuitively, the more information can a given sized and content demo convey, the bigger the signal effect it shows, which is measured by. The prior beliefs affect the signal effect through the updated beliefs, since. If a demo can eliminate certain possibilities about the nature of the full product by a larger chances ( ), then a demo could change the expected fraction of the component A in the full product to a larger extent. Proposition 6 compares the signal effect under different prior beliefs, but it is more important to compares the average signal effect which captures the impact of every single unit of a demo. The average signal effect is measured by the signal effect divided by the size of a demo,, and the average cannibalization effect is. Given the prior beliefs, the average signal effect varies with the size of a demo, while the average cannibalization effect is fixed. Denote ( ) as under distribution and as under distribution.the following assumption characterizes the demo size which maximizes the average signal effects under the different prior beliefs.

20 19 Assumption 2. The size maximizes the average signal effect under distribution, and the size maximizes the average signal effect under distribution. From Assumption 2 the maximum average signal effects under distribution and are and respectively. I now compare those two maximum average signal effects and then derive how they affect the seller s demo strategy. Proportion 3 shows that one of necessary conditions of releasing a demo is that the total signal effect is greater than the total cannibalization effect (i.e. ), which can be rewritten as the average signal effect is greater than the average cannibalization effect. It is obviously that if this condition is violated under prior beliefs, the seller would not release a demo. Now I consider whether the seller releases a demo or not under another distribution which second order stochastically dominates the former one. Clearly, if the maximum average signal effect is less than the average cannibalization effect under distribution, then the condition will be violated for a demo of any size. Proposition 7 follows immediately to answer if a seller should release a demo under distribution. Proposition 7. Suppose Assumption 1 and 2 hold. Then if the maximum average signal effect is less than the average cannibalization effect under distribution, than the seller should not release a demo under distribution or under distributions. ( i.e. If, then.) Proposition 7 shows that when the maximum average signal effect is less than the average cannibalization effect, then the seller should not release a demo of any size. If that is true under

21 20 distribution, then the seller should not release a demo of any size under distribution either where a given sized pure demo includes less information. From assumption 1, if a demo fails to convey enough information under prior beliefs, then that demo is not able to convey enough information under prior beliefs. Compared with under distribution, under distribution buyers prior beliefs are more likely to distribute at the tail and are less likely to distribute at the middle. Proposition 6 and 7 shows that more information can be contained in a given sized pure demo under prior beliefs. It is reasonable to expect that the seller can use a smaller sized demo to disclose a given amount of product information under prior beliefs. Can this imply that the optimal size of a pure demo is smaller under prior beliefs than under? Proposition 8 shows this is not true. Proposition 8. Suppose Assumption 1 holds. Then if it is profitable to release a demo, the optimal size of a pure demo under distribution can be greater or smaller than under distribution. Proposition 8 shows how the optimal size of a demo varies with the dispersion of the distribution. One thing should keep in mind is that the size of a pure demo that maximizes the average signal effect is not the size that maximizes profits if a demo is to be released, because a seller should balance both the signal effect and the cannibalization effect to maximize her profits. Therefore, the fact that more information can be conveyed in a demo under a particular prior belief does not necessarily imply that the optimal size of a demo will be smaller under that belief. 4. Conclusion and Extension In addition to such channels as advertisings, product reports, consumer reviews and expert reviews, a demo serves as an important marketing channel to help buyers identify digital experience goods best match their idiosyncratic tastes. Unlike the other channels of product information, a free demo supplies partial contents of a full product to offer information about the likely value of the full product and serves as a prototype that can compete with the full product. This latter cannibalization effect can significantly change the seller s optimal demo strategy.

22 21 In this paper, I model the case where a monopoly seller whose full products include multiple components reveals certain components in a demo and buyers differ in their tastes for the product. To improve profits through releasing a demo, the seller will segment the market and only sell products to the buyers who like the demo. I showed that differences in buyers prior beliefs about the full product affect a demo s ability to convey product information. If buyers initially believe that the mix of attributes is more likely to distribute in the tail and is less likely to distribute in the middle, then a given sized and content demo is able to exclude certain possibilities about the nature of the full product by a larger chance. Thus, a demo can convey a larger amount of product information, which leads to the greater signal effect. If the signal effect can be greater than the cannibalization effect, a seller could raise prices after releasing a demo. Hence, whether charging higher prices but reducing volumes leads to higher profits depends on whether the profit margin overweighs the loss in demand. That is true if the marginal cost is sufficiently large. As a result, the seller should release a demo and sell products to high-value buyers at higher prices. Moreover, because the incentive of releasing a demo is to improve some buyers valuation for full products, the seller should only release the components that match those buyers taste in a demo. Accordingly, the seller always releases a pure demo rather than a mixed demo. The results of this paper show two factors that lead the seller to release a demo: (1) moderate marginal cost of producing and marketing one more unit of the product; (2) buyer s initial beliefs about the nature of the full product which concentrate in the tail. Here, since the marginal cost of producing for digital goods is almost zero, I focus on discussing the marginal cost of marketing when applying my theoretical model to explain how the total marginal cost affects the demo strategy of digital products. In practice, the operating systems developed by Microsoft, such as Windows XP, Windows Vista and Windows 7, rarely release a demo. This is consistent with the model when the marginal marketing cost is very low due to the popularity of Windows operating system, Microsoft is willing to sell products to more consumers rather than charging higher prices. However, there is a lot competition in the video game market, so advertising and marketing is comparatively costly. Through releasing a demo those firms are more willing to raise prices and sell products to consumers who like the demo instead of selling to more

23 22 consumers. When analyzing the effect of prior beliefs, I apply two symmetric distributions and where second order stochastically dominates. Apple Inc. offers a good example to interpret the effect of prior beliefs. As one of the most creative companies in the world, Apple Inc. rarely releases a demo for her products, such as iphoto, imovie and digital life management. Before Apple really publishes her products, most consumers have no clear idea of what to expect about the nature of the product, so the every potential attribute mix in the full product would be possible and with the same chances, which implies that a demo is not able to convey enough information (i.e. a demo under in my theoretical result), so the seller should not use a demo as her marketing channel. Some of the more important extensions of my analysis should be discussed. First, I assume that buyers tastes are symmetrically distributed, so a seller is indifferent between releasing either type of components in a demo. If the buyers tastes are asymmetrical, will the seller prefer to release a demo with the type of components that matches the most buyers? Second, the seller in my analysis is a monopoly. It is of interest to examine the impact of competition on a seller s demo strategy in a duopoly market, where both firms offer the exactly same products. Intuitively, the sellers may compete to release more product information to attract the buyers whose tastes match the product or release no product information to divide the whole market. It is also possible that one seller targets the buyers who observe the high signal, while the other seller serves the remaining buyers. Thirdly, this paper only discusses the case where the seller intentionally releases a demo. Future research should extend to the case where the seller has no information about the product attributes in advance of sales. In that case, the seller randomly chooses components from a full product to release into a demo, so the nature of that demo should reflect the nature of that full product. Hence, buyers prior distribution function of the full product should be updated according to the component mix of that demo. As a result, not only the range of but also the initial distribution function itself should change after a demo is released. Fourth, this paper does not discuss the other type of demos which are free, fully functional but only could be used for limited time.

24 23 Signal and the cannibalization effects will also exit there. The approach in this paper could be applied to that type of demos, which are also widely used in practice.

25 24 APPENDIX Proof of From assumption that, I know.if supplying demo is more profitable, the inequality must hold, so I have. To ensure that, I require and non-negative profit constraint. Hence, the following inequality must hold to find a solution for :, which is simplified as. Hence,. Thus,, which is consistent with the condition that. Proof of Proposition 1.. Proof of Proposition 2. [ ] Thus,. follows from this inequality:

26 25 Proof of Proposition 3. To compare and, note that. If, then, which yields. Since profits from a demo are, then follows immediately. For and to hold both, it must be true that. This simplifies to, which is the condition in. Since for any, if the size of the demo is greater than or equal to, then the signal effect is less than the cannibalization effect ( ). Hence, if the seller releases a demo, the optimal size of a demo should be less than. Proof of Proposition 4. First, the seller s profit maximization problem is for which the first-order condition is: ( (3) A necessary condition for to be the optimal size of a pure demo is that satisfying (3) which can be written as.

27 26 Second, such an is a local maximum if the second order condition is also satisfied:. (4) Hence, (4) holds if. Third, it is not trivial to determine when this will hold. To consider the condition for this, an expression for can be determined. By definition: [ ] or [ ] [ ] which simplifies to [ ]. (5) Then {[ ] } [ ] [ ] [ ] (6) Substituting (5) into (6), yields [ ] Since.Using the facts that,, and (given ), the necessary condition that the inequality holds is. Proof of Proposition 5. It shows in the proof of Proposition 4.

28 27 Proof of Proposition 6. As mentioned before, the signal effect under distribution is measured by and the signal effect under distribution is measured by. First, to compare the former signal effect with the latter signal effect, it is equivalent to compare with. By definition, and. Second, integration by parts yields. Substituting this into, I have. Analogously, I have. Thus, it is equivalent to compare with to determine under which distribution a given sized demo leads to higher signal effect. Since if a demo is to be released, the size must be between 0 and, I only derive my result at. The following three steps show how I derive I. First, yields. (7) II. Second, to compare and 1, I rewrite. (8)

29 28 Define as the distance from to a particular value of, where. Then define a function as the distance from to, and analogously define a function as the distance from to. Because is symmetrically distributed at, and then I can rewrite { ( ], and { ( ]. which is rearranged to { ( ], and { ( ]. (9) Substituting (9) into (8), yields [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ] Collecting terms yields [ ] [ ] [ ] [ ] [ ] [ ] [ ] [ ]. (10) Using the fact that and, I have. Accordingly,. Hence, from (10): (11) From (7) and (11):. (12) Rearranging (12),yields:

30 29. Therefore,. (13) Proof of Proposition 7. Suppose maximizes and maximizes. From (13):. (14) Since maximizes, it must be true that. (15) From (14) and (15): (16) If, then Proof of Proposition 8. First, by definition: [ ] [ ]. (17) Analogously,. (18)

31 30 Second, from (17):. (19) From (13) and (7):. (20) Third, using properties of second order stochastic dominance, I have and. Therefore, it is ambiguous to compare with. Fourth, I need to compare with given. According to Proposition 4, one of necessary conditions for to be an optimum size is. Hence, it is equivalent to comparing with given. The above result of comparing with suggests that the comparison between with is ambiguous.