A feedback e ect from stock market trading to innovations in a Bertrand duopoly

Transcription

1 A feedback e ect from stock market trading to innovations in a Bertrand duopoly Haina Ding* Abstract Knowledge spillover often in uences rms innovation decisions and consequently the technological advance of an industry. Spillover may be caused by involuntary or strategic disclosures of rms intermediate R&D progress. It can also occur due to the feedback from stock prices to decisions about innovation investment. In this paper, I endogenize the probability of knowledge spillover, which is no longer the consequence of disclosure strategies. I show that changes in stock price can amount to information leakage about the success probability of an innovation, which induces the interdependence between the fundamentals and the amount of information produced in the stock market. When providing additional information to competing rms in a Bertrand duopoly, this feedback e ect may also result in fewer innovations and decreased consumer welfare, provided that the innovation requires low investment and has a low success rate. Once the participation of stock market traders is also endogenized, the trading incentive of speculators no longer monotonically increases in the e ectiveness of the innovation, and the probability of knowledge spillover becomes dependent on the industrial characteristics. Keywords: Knowledge spillover; Feedback; Information e ciency *Toulouse University 1 - Capitole, Graduate School of Management, CRM, Rue du Doyen Gabriel Marty 3104 TOULOUSE CEDEX 9, France. I am grateful for helpful comments from Alexander Guembel, Bruno Biais, Sophie Moinas and other participants in the PhD workshop at Toulouse School of Economics. 1

2 1 Introduction Understanding how the product market and information structure interact and a ect rms innovation decisions helps regulators to design policies that encourage technology advances and maximize social welfare. Private knowledge about a certain innovation may be transferred from one rm to another in the industry, attributed to voluntary disclosure or involuntary leakage. Such information transmission can also occur due to speculator s participation in stock market trading. Firms may consequently alter their ex-ante decisions in innovation investment, knowing that their private information can be partially revealed in share price. This occurs via the trading process in stock market that transmits into prices the information produced by speculators trading activities (Grossman and Stiglitz, 1980; Kyle, 1985, and others). This process then leads to a non-trivial feedback from stock prices to corporate decisions, which internalizes the expected cash ows of an investment. While such an e ect can in uence the real economy in many di erent ways, this study aims to initiate an analysis of its impact on rms innovating activities in a duopoly industry. I present a simple model where two rms compete in a Bertrand duopoly market with di erentiated products. They need to decide whether to invest in a risky innovation that may reduce rms marginal production cost with a positive probability. When the uncertainty about the e ectiveness of this innovation is solved at the intermediate stage, it is privately learned by the rm that has invested in the innovation. Given that rms are listed in a stock market, speculators may also acquire this private information and pro t from share trading. The informed trading will then partially reveal to the public the e cacy of the innovation technology via share price as in Kyle (1985). The whole process generates a knowledge spillover, that is, a transmission of useful knowledge from the rm that innovates rst to the follower rm. Knowledge spillover bene ts the receiver by allowing it to adopt a more e cient technology at the intermediate stage. It may, however, discourage up-front investment, because it reduces the rent an innovating rm can capture. The possibility that this spillover will occur is taken into account by both rms in their ex-ante innovation decisions, which indeed a ects rm value ex post. Moreover, rms in this model do not choose to manage their rivals belief by revealing and concealing intermediate information. The amount of information being revealed about their innovation progress is more a consequence attributed to their innovation strategies and traders incentives in the stock market, both interdependent with the fundamentals. More speci cally, I show that if the innovation has a very high success rate, informed trading in stock market does not a ect rms innovation strategy. If the success rate is

3 however too low to encourage up-front innovations, the feedback e ect can decrease rms innovating activities and the consumer surplus, because it provides rms with an option to wait for additional information before making decisions. The timing of innovation is thus delayed. If the innovation has a relatively high probability to succeed but demands large investment, the possibility of learning better information at an intermediate stage induces more investment in innovation and improves consumer welfare. The impact of share trading on innovation strategies further depends on the information environment if the participation of stock market agents and thus trading volume are endogenized. I show that, for instance, if noise traders gain a low private bene t from having a position in the stock, an increase in the success rate and e cacy of the innovation can actually reduce the trading incentive of speculators. This then lowers the probability of information leakage and feeds back to the ex ante innovation strategies. The occurrence of the spillover is thus endogenized via the link between information e ciency in the stock market and product market activities. This paper relates to the literature that studies the interaction between product market competition and rms nancing decision, and how di erent sources of nancing, private debt or equity, a ect rms innovation strategies 1, and the intensity of product market competition. Another strand of literature show that IPO decisions are a ected by product market characteristics such as productivity and competitive interactions 3, which in uence the trade-o between a cheaper capital raised from the equity market and intensive competition caused by a probable increase in information disclosure after IPO. 4 One assumption frequently seen in these studies is that the probability of the information leakage is imposed exogenously. It is, however, important to understand that the fundamental values in the economy and information e ciency promoted by informed trading in the stock market a ect each other more than a one-way causality. This paper demonstrates that when information revelation via the stock market can induce knowledge spillover about technological innovations, the magnitude of such an impact is taken into account in both rms innovation strategies and the trading strategies of stock market agents, which determines the probability of the information spillover. Although this paper stays away from rms nancing problem, such an endogeneity adds additional concerns to rms nancing decisions in the context of innovations and production market competition. 1 See Brander & Lewis, 1986; Maksimovic, 1988, among others. See Bolton & Scharfstein, 1990; Lyandres, 006; Khanna and Schroder, See Chemmanur & Fulghieri, 1999; Clementi, 00; Chod and Lyandres, See Bhattacharya and Ritter, 1983; Maksimovic & Pichler, 001; Spiegel & Tookes,

4 Most of existing literatures (e.g. Stenbacka and Tombak, 1994, Hoppe, 000, and Schmidt-Dengler, 006) investigate the information spillover that shows in the descending innovation cost over time due to general advances in knowledge and technology. Rather di erently, this study analyzes a spillover that is not manifested in the cost parameter but in the knowledge about whether a risky innovation will succeed, i.e., the follower rm may have the chance to invest after learning of the innovation progress of the leading rm in innovation. Thijssen and Huisman (001) analyze a sequential game, in which a Stackelberg leader in the investment of a risky project has the rst-mover advantage and the follower can get signals of the success probability that arrive in a Poisson process. These authors do not consider speci cally product market interactions in either price or output. A speci c model of product market competition, as in this paper, captures more precisely the return to the innovation investment under di erent realizations of production cost, and hence rms innovating strategies. This paper also di ers in having a simultaneous game in which an innovation succeeds is determined by nature with an exogenous probability. I consider a cost reducing innovation in this paper. According to the classical view that technological advances take place as a succession of incremental changes with rare discontinuities that may destroy or enhance the competence of existing rms, most industries can be characterized by long periods of incremental product and process changes (Tushman and Anderson, 1986). The general features of a process innovation are thus contained in this simple model. Also, it is of interest to choose the setup with a duopoly industry where rms possess market power. One rm s activity strategically responds to the other s, such that the information in share price can be naturally incorporated in rms innovation decisions. Moreover, a duopoly model may well present the features of industries with similar products and manufacturing processes. For instance, the knowledge spillover may indeed have signi cant impacts in the industries of aeronautics, automobiles and computers. This paper speci es that rms can invest in an innovation at the same cost and the risks in doing so are perfectly correlated across rms. Consequently, good news about one rm s innovation investment makes its rival more optimistic about their own opportunity and thus more incentivized to invest. A good illustration of this e ect can be found in Choi (1991), who uses an example of the break-through of cold super-conductivity in 1986 by IBM. IBM s intermediate success made other rms more optimistic about this technology and increase their investment intensity. Similarly, Austen (1993) observes in the biotech industry that an intermediate success of one rm leads to an increase in valuation of its competitors. On the other hand, R&D projects that improve one rm s competitiveness 4

5 can meanwhile reduce the pro t of its rivals even if a transfer of information occurs from the former (De Bondt and Veugelers, 1991). The externality from rms innovations to their competitors makes the timing of investment strategic. A number of studies have investigated the value of delaying an irreversible investment in an risky innovation. Jensen (198) is the rst to introduce uncertainty in a technology adoption model. Hoppe (000) extends it to a model where the second mover advantages can arise in equilibrium due to information spillover. In the papers by Huisman (001), Pawlina and Kort (001), and Weeds (00), strategic interactions between duopolists in the product market prompt rms to trade o between the rst-mover advantage and the value of the delay option. Last but not least, it is important to note that even though rms are under mandatory requirements for R&D related disclosures, the extent of such disclosure is limited to R&D expenses, R&D acquisition and contracting 5. Meanwhile, voluntary R&D disclosure that is potentially valuable to competitors may hurt the future product market performance of the rm. Gal-Or (1986) proves that voluntary disclosure is not optimal to the duopolists in Bertrand competition when there exists an ex-ante uncertainty in the production cost. As a result, a model where information is revealed via the stock market may thus better capture information transmission and innovation adoption in an industry where rms compete in price, compared to a setup relying on rms disclosure to shareholders. Having a similar model setup in the product market as in Gal-Or (1986), I neglect the discussion of rms voluntary and strategic disclosures of innovation progress. 6 The paper proceeds as follows. Section presents the setup of the model. Firms equilibrium strategies are computed in Section 3, and participation of stock market agents is discussed in Section 4. Section 5 concludes. Part of the calculations are relegated to Appendix. The Model.1 The timeline The model is concerned with an imperfectly competitive sector consisting of two rms that engage in a non-cooperative game. There are four dates in this model. Both rms have an 5 See Statement of Financial Accounting Standards (SFAS), 68, 141 and See Jansen (006 and 008), Magazzini, Pammolli, Riccaboni and Rossi (009), among others, who investigate rms disclosure strategies regarding their innovations given the presence of product market competition. 5

6 opportunity to invest in a risky innovation at either date 0 or date 1. If one rm invests in this innovation at date 0, it will know privately at the next date whether this innovation succeeds. If the other rm decides not to innovate at date 0, it can choose either to invest in the innovation at date 1 or forgo the investment opportunity. If at least one rm is publicly listed, its private information about innovation progress can be acquired by speculators in stock market at date 1. At the same date, informed trading occurs in the stock market subsequently, which will partially reveal private information to the public. Firms compete in the product market at both date and date 3, and they liquidate at the end of date 3. Next, I explain in detail the assumptions about the product market and the innovation.. The product market The duopolists in this industry produce di erentiated products without capacity constraints. They start at date 0 with the same marginal production cost, c, and they produce and sell at two dates ( and 3). To make the computation more tractable, I follow most literature of industrial organization by assuming that the duopolists in this economy share the information about production cost before setting prices. 7 Following Singh and Vives (1984), I assume that there exists a representative consumer P in the economy, who maximizes at both date and 3 his utility function U(q i ; q i ) p i q i, when consuming quantity q i of goods from rm i at price p i, i = 1;. U(q i ; q i ) is quadratic and strictly concave, formally written as, i=1 U(q i ; q i ) = (q i + q i ) 1 q i + q i q i + q i ; 0 < < 1; (1) where q i is the output of rm i, and q i of the other rm. The parameter measures the substitutability between the goods produced by two rms. The higher is, the closer substitutes rms products are and thus the stronger their competition is. The following demand functions for the goods of rm i maximizes the utility of the representative 7 More drastic restrictions on the communication about production cost may not only lead to a convolution in results due to the e ects from di erent sources, but also yield additional welfare losses since communication between competing rms enables more e cient decision making in product market (Kuhn and Vives, 1995). By simplifying the information structure that is less relevant to rms innovation decisions, I can draw clearer inferences about the impact when having the feedback e ect regarding the innovation progress. 6

7 consumer, Consequently, rm i sets price p i to maximize its pro t i, q i = ( p i) ( p i ) 1 () i = (p i c i ) ( p i) ( p i ) 1. (3) At date 0, two rms possess the same production technology and they face a process innovation that requires an investment I. This innovation will either decrease a rm s marginal production cost by with probability or make no change with probability 1, (0; 1) and 0 < < c. For simplicity, I assume that the investment cost, I, remains unchanged from date 0 to date 1. I also assume that it takes two dates for the investment in this innovation to exert in uence on cost reduction. More speci cally, if one rm invests at date 0, and the innovation succeeds, production costs at date and 3 are c. If the rm invests at date 1 instead, its production cost at date stays at c, and if the innovation succeeds, the cost changes to c at date 3 only. A rm innovating at date 1, i.e., the follower, may thus be disadvantaged in the rst-stage product market competition at date, if the innovation of the leading rm is found to be e ective. This opportunity to invest in this innovation is no longer available after the end of date 1. 8 In addition, the realization of the innovation is assumed to be perfectly correlated across rms regardless of the timing of innovation, and this is common knowledge. This assumption is plausible for the innovations that concern rms with only technological risk. 9 also assumed to be publicly observable. 10 Firms decision to invest in innovation is.3 The stock market Three types of agents exist in the stock market. A competitive market maker earns zero pro t in expectation by setting share price based on his rational expectation of a rm s pro t when observing the submitted orders. There also exists a noise trader who either buys or sells 1 unit of each listed rm for liquidity reason. Finally, there are two speculators 8 The presumed nal liquidation of rms makes it not optimal for rms to invest in innovation later than date 1, even if such an option is still available then. 9 We can relax this assumption by having an exogenuous correlation between cash ows of the competing rms when they both invest in the innovation. It would not change the qualitative result, however. 10 This may be obligatory for the rms due to disclosure requirement, particularly when the innovation investment is nanced by the issuance of equity. This assumption also allows me to focus on the pure equilibrium strategy. 7

8 in the stock market, who can acquire at date 1 the private knowledge regarding rms innovation progress and trade on this information if pro table. Share trading is assumed to occur at date 1 after innovating rms acquire their own private knowledge. Order ows in the stock market are publicly observable. When only one rm innovates at date 0, this information can be used by their competitor to decide whether to innovate at date 1. Speculators reap their trading pro ts at date when the e ectiveness of the innovation is observed and rms produce and sell. Note that I assume no other information leakage or spillover in this economy. Consequently no private knowledge about innovation progress will be revealed without informed trading in stock market. Also, if no investment is made at date 0, speculators cannot know whether this innovation will be successful, and hence they will not trade. 3 Firms Equilibrium Strategies 3.1 A benchmark model with no feedback I consider rst a case where there is no stock market. As previously speci ed, rms know their rivals marginal production cost just before they enter price competition. The representative consumer chooses quantities of goods (q i ; q i ) to maximize the utility function given in equation (1), and each rm maximizes its pro t given in equation (3). By deriving the rst order condition of the pro t function with respect to p i, the best response functions of price can be obtained as below, p i = 1 [ (1 ) + p i + c i ]. (4) Solving the system of the response price functions of rm i, we can obtain the optimal price p i for rm i, i = 1;, p i = (1 ) + c i + c i 4 (5) Using the optimal price p i and the demand function q i established in formula (), I can then state the equilibrium pro ts of rms as functions of c i and c i, ci ;c i = ( c i ) + (c i c i ) (6) ( + ) (1 ) Formula (6) shows that rm i s pro t increases in its competitor s pro t c i. If rm 8

9 i has invested in an innovation that shows e ectiveness in reducing its cost, rm i would prefer that its competitor does not invest in the same innovation, i.e., the strategic e ect of technology adoption is negative under Bertrand competition. Consequently, there exists no incentive for rm i to reveal a good progress of the innovation. The revelation of bad news would not be expected to occur either, because otherwise it could be perfectly inferred when the innovation is learned to be successful. As a result, the information about the innovation progress will not be revealed before the product market competition. Due to the absence of knowledge spillover in the benchmark case, it is never optimal to invest at date 1 if no rm invests at date 0. This therefore leaves two pure strategies to each rm, either to "invest in innovation at date 0", denoted by L, or not to innovate at all, denoted by N. Strategy L and N complete rms action space in the benchmark case, = fl; Ng. The action space provide four possible combinations of strategies (A i ; A i ) chosen by rm i and its competitor, and each combination leads to a di erent expected pro t for both rms at either date or 3. To facilitate the presentation hereafter, I rst compute rms pro t under each realization of their production cost, denoted by ci ;c i, c i fc; c i = 1;. From the following expressions of ci ;c i, we can observe that c ;c > c ;c > c;c > c;c. c ;c = c ;c = 1 1 c;c = ( c) + ( ) ( + ) (1 ) 1 g, (7) ( c + ) (8) c;c = 1 1 ( 1 c) (9) ( c) ( + ) (1 ) (10) Given the success rate of the innovation, we can then compute the ex ante expectation of rm i s pro t, denoted by i, under each strategy pair (A i ; A i ) chosen from. i (A i ; A i ) consists of rm i s pro t at both date and 3 as well as the cost of innovation if the investment has taken place. As a result, if both rms choose the same strategy, i (L; L) = c ;c + (1 ) c;c I and i (N; N) = c;c. If, however, only rm i invests in the innovation, i (L; N) = c ;c + (1 ) c;c I and i (N; L) = c;c + (1 ) c;c. I derive the Nash equilibria and present the equilibrium conditions in Proposition 1. 9

10 Proposition 1 If I I, (N, N) is the unique Nash equilibrium; if I I, (L, L) is the unique Nash equilibrium; and the equilibria are (N, L) & (L, N), if I > I > I, where I = ( c ;c c;c ), and I = ( c ;c c;c ) Proof. See Appendix. From the equilibrium conditions stated in this proposition, we observe that there exist two thresholds in the scale of required investment, I and I. Both rms innovate at date 0 when the investment cost I is lower than the lower threshold I 11, while neither of them innovate if I is higher than the upper threshold I. When I falls in between I and I, there exist two equilibria where only one of the rms invests in the innovation. Since rms have the same action space and the related payo s are symmetric, the discussion of mixed strategies does not render additional insights and is therefore skipped. Notice also that these thresholds increase in both the success rate of the innovation (), and the magnitude of the cost reduction (). Intuitively, the investment in an innovation technology is more likely to be taken when it has a high probability to succeed and brings a bigger advantage in product market competition Equilibrium in a model with feedback I now assume that there exists a stock market in the economy and both rms are publicly listed. All other assumptions regarding the competition in product market remain as previously stated. Compared to the benchmark case where the innovation progress is known only to the rm that makes the investment, speculators can also acquire this private information for trading purpose. As a consequence, the innovation progress may now be partially revealed via informed trading in the stock market. With this additional ingredient, the model becomes a three-stage game. At the rst stage (date 0), rms choose to invest or to wait, and at the second stage (date 1), the non-leading rm decides whether to invest in the innovation after observing the total order ows or share prices in the stock market. Product market competition takes place at the last stage (date and 3). If no rm invests 11 The lower threshold I is zero when the degree of substitution is very close to 1 (i.e., the perfect substitution). 1 Note that when I < (1 ) (1+)( ) [ + ( c)], (N, N) becomes an ine cient Nash equilibrium and rms fall into a Prisoner s dilemma. This inequality however contradicts to the equilibrium conditions in Proposition 1, given that goods are substitutes in this model. Therefore we do not nd an equilibrium with ine cient investment strategies. 10

11 in the innovation at date 0, there will be no private information for the speculator to acquire and trade on, and consequently submitted orders will contain no private information. Each speculator is assumed to trade only one rm s shares (i.e., speculator i only trades rm i s shares, i = 1; ), even if they may have access to the private information about both rms. This assumption simpli es the discussion of the trading part of the game. It, however, preserves the situation where both rms shares are traded while private information is not to be fully revealed by share price. Although speculators are allowed to choose any order size to submit, speculators will follow nevertheless the optimal strategy de ned by the lemma below. Lemma 1 The optimal strategy of the speculators is to submit an order with a xed size 1 for the rms that they trade exclusively. Proof. Since the noise trader always submits an order of one unit for each rm, the expected order ow for a listed rm is zero. The market maker will then quote higher based on a total order ow greater than zero, or lower otherwise. The speculators would thus either easily expose their identities by submitting an order with a size larger than one, or make lower pro t by trading a fractional order. The optimal way to hide his identity and obtain a favorable quote is to submit an order of the same size as the one from the noise trader, regardless of the trading direction. To analyze the situation where at least one rm innovates at date 0, it helps to understand rst the probability distribution of order ows. Consider that rm i will invest in the innovation at date 0, and the other rm decides to wait. Suppose rm i learns at date 1 that its innovation will succeed, this information is then acquired by speculators. Speculator i interprets it as good news to rm i and thus submits a buy order of rm i s share. Meanwhile, the other speculator sees it as bad news to rm i who will be disadvantaged in price competition for at least one stage, and thus submits a sell order of rm i. Recall that the noise trader buys or sells 1 unit of both rms s shares with equal probability and there is no correlation in their orders across rms. Evidently, the total order ow of rm i s shares can be either + if the noise trader also submit a buy order, or 0 if the noise trader submits a sell order. Under the same reasoning, the total order ow of rm i will result in either or 0. Let x i denote the total orders submitted for rm i, x i f0; g and x i f ; 0g, i = 1;. We observe immediately that there are four possible combinations of x i and x i, each attached with the same probability 1 on condition that the innovation succeeds. Given that 4 11

12 rms innovating activities are publicly observable, the good news of rm i can be inferred by the other agents except when the order ows of both rms are zero. More speci cally, when (x 1 ; x ) belongs to the set f(; ) ; (; 0) ; (0; )g, the private information of the innovation being successful is fully revealed by informed trading. Order ows thus reveal the private information with probability 3 conditional on that the innovation succeeds, 4 thus a total probability 3. Similarly, the probability of revealing the information that 4 the innovation fails is 3 (1 ), and 1 (1 ) otherwise. Using the same algorithm, we 4 4 conclude that the probability of information revelation is the same for the case where both rms invests at date 0. It is now clear that agents expect ex ante that share prices will be informative with probability 3 4. When observing x i = x i = 0, the rm that chooses not to invest up-front has to decide whether to invest based on its prior belief. If, however, the private information is revealed in stock market, this rm can update his belief about the success probability of the innovation and compare its expected pro t from investing in the innovation at date 1 with otherwise. Given that the pro t functions of both rms are publicly known, the market maker is able to anticipate the best response in innovation strategy of the follower rm, and set the share prices accordingly. I continue to use the notation "L" and "N" as in the benchmark case, and add two others for the purpose of illustration. The rst one "F " denotes the strategy "to invest in the innovation at date 1 only when order ows reveal good news about the innovation". The second notation is " e F ", denoting the strategy "to invest in the innovation at date 1 when order ows reveal good news or no private information". The action space for each rm now consists of four pure strategies, i = fl; F; ~ F ; Ng, i = 1;. Given that rm i leads in the innovation investment at date 0, the expected payo to the other rm with the new strategies F and F ~ are, respectively, 5 4 c;c c ;c + (1 ) 3 c;c I and 4 1 ( c;c + c ;c ) + (1 ) c;c + 3 I. 4 4 In order to decide whether F e can be an optimal strategy, a rm needs to compare its expected pro t under e F versus the other strategies, when considering possible deviations of its competitor. The next lemma excludes e F from the Nash equilibria. Lemma The strategy pairs (L, e F ) and ( e F, L) are not Nash equilibria. Proof. First, when rm i leads in innovation investment and x i = x i = 0, the expected payo of the other rm is ( c;c + c ;c ) + (1 ) c;c I if it chooses to follow at date 1, and c;c + (1 ) c;c otherwise. Comparing these two payo s, we know that 1

13 only when I < ( c ;c c;c ), i.e., I < 1 I, the follower rm would prefer to invest at t = 1, conditional on zero order ows. I is as de ned in Proposition 1. Next, given rm i chooses L, for e F to be optimal to rm i there needs to be a pro table deviation from the strategy L, i.e., i (L; L) i ~F ; L < 0. This inequality requires I > I. 3(1 ) These two conditions, I < 1 I and I > I cannot be both satis ed at the same 3(1 ) time, 8 (0; 1). (L, F e ) and ( F e, L) thus cannot be Nash equilibria. The other strategies fl; F; N g nevertheless survive in equilibrium. I now summarize in the following proposition the equilibrium conditions where the stock market trading induces a feedback e ect to rms innovation strategies. Proposition There is a unique equilibrium (N; N) if I I, 8. When < 1, (L, L) is the unique Nash equilibrium if 0 < I < 5 I and < I (4 3) I the 5 equilibria are (L, F ) & (F, L) if I < I < I, while (N, L) & (L, N) cannot be (4 3) equilibria; and if I I ; 1 the equilibria are (L, F ) & (F, L) if 5 I < I < 1 I, and (4 3) (L, N) & (N, L) if 1I < I < I. When 1, (L, L) is the unique equilibrium if I < I, and (N, L) & (L, N) if I < I < I, while (L, F ) & (F, L) cannot be equilibria. I and I are de ned as in Proposition 1. Proof. The proof is relegated to Appendix. There are a few observations when comparing Proposition and Proposition 1 that is established in the benchmark case. First, both propositions give the same condition for the equilibrium where both rms nd it optimal not to invest, i.e., I is higher than the upper threshold I. It is due to the assumption that if no rm innovates at date 0, no knowledge spillover occurs and thus rms do not innovate at date 1 either, the equilibrium condition for the strategy pair (N, N) is not a ected by having feedback. Also note that when the success probability of the innovation is relatively high, i.e., > 1, Choosing F is no longer optimal for the non-leading rm regardless of the magnitude of the required investment, and equilibrium strategies go back to the ones in the benchmark case. This result adheres to the intuition that if the innovation requires a low investment but will succeed with a higher probability, a rm would choose to innovate at the beginning in order to avoid the disadvantage in the rst-stage price competition. Or the non-leading rm will simply forgo the innovation opportunity when it is too costly to invest. 13

14 Example 1 More interesting situations occur when < 1 and at least one rm invests in the innovation at date 0, of which the equilibrium conditions are di erent from the benchmark case. To explain the di erences more clearly, I present the graphs of equilibrium strategies for a numerical example, in which = 3, c = 3, = and the utility parameter = 5. 4 The required investment I for the innovation is scaled on the vertical axis and the success rate is on the horizontal axis. Comparing the graph of the equilibrium with and without feedback, we observe that the feedback e ect causes two changes. First of all, the graph on 5 the right shows that the upper threshold for (L, L) becomes I, drawn by the dark (4 3) curve. This curve lies below the dashed line representing I, the threshold in the original case without feedback. In the region between these two lines, rms that would choose to both invest at date 0 in the benchmark case no longer nd it optimal to do so. Instead, one of them now wait to see whether share prices will reveal the innovation progress of the leading rm. As a result, the total amount of innovation investment decreases, and the overall timing of innovation adoption is delayed. We also observe an opposite in uence on rms ex-ante innovation strategies in the region where the required investment is above the dashed line. As previously illustrated, if one rm leads at date 0, the other one has the option to wait and make use of the possible information spillover at date 1. In consequence, when < I and the required investment is 5 relatively high, I < I < I, (L, N) and (N, L) are no longer the equilibria, and the (4 3) amount of innovation investment increases when the non-leading rm chooses to innovate if the total order ows convey good news. The impact of this information spillover on the innovation activities depends on the the size of I and. When approaches 1 from below, there is more uncertainty to the outcome of the innovation but also a relatively higher probability to succeed in the innovation. We observe that the region with one leader and I 14

15 one follower shrinks, since it is more likely that rms nd it optimal to both invest up-front. The general impact from the feedback becomes smaller. Moreover, the impact of this information spillover on the innovation activities increases in the e ectiveness of the innovation, as the lower boundary of (N; N), I, increases in 5 more signi cantly than the lower boundary of (L, F ) and (F, L), I. In other (4 3) words, an increase in the reduction of marginal cost makes the innovation investment more pro table especially when the rm is the only investor. The pro t to the follower rm also increases, and thus the strategy F becomes more desirable. From Example shown below in the graph on the left, where the value of increases from (in Example 1) to :5 while values of all the other parameters remain unchanged, we see that a bigger part of the region where without feedback (L, N) and (N, L) would be the equilibria is now replaced by (L, F ) and (F, L). The opposite result is shown by Example 3 where takes the value 1:4. Example ( = :5) & Example 3 ( = 1:4) The overall message conveyed by the above analysis is the following. If the innovation demands a relatively low investment, it is less optimal for rms to both invest in the innovation up-front. Instead, they are inclined to make use of the spillover at the cost of a potential disadvantage in the price competition for one period. When the required investment is high, however, rms increase their innovations compared with the benchmark case, due to the possible access to the private information revealed in stock market. The impact of feedback increases in the size of cost reduction and decreases when the success rate of innovation get closer to 1. 15

16 3.3 Consumer surplus In this subsection, I investigate how consumer s welfare may be a ected in the presence of the feedback from informed trading, by comparing the ex-ante expectation of consumer surplus in di erent equilibria. From the previous section, we already know that the threshold in the investment scale for the equilibrium (N, N) is the same in the benchmark case. Therefore, my main interest in the welfare analysis is for the equilibrium where at least one rm invests at date 0. Let CS denote the consumer surplus in this market. Using the P formula CS = U (q 1 ; q ) p i q i with U(q 1 ; q ) as the utility function given in formula (1), i=1 it is then easy to compute the consumer surplus for each equilibrium. Let CSA t i ;A i denotes the sum of consumer surplus at date t in the equilibrium where rms choose the action (A i ; A i ), and let c t i, p t i, and qi t denote the production cost, price and the output for rm i at date t, where i = 1;, and t = ; 3. The innovating rm will have the production cost c with probability, or c otherwise. For example, when (A i ; A i ) = (L; L) and the innovation is successful, the prices and demands can be computed and simpli ed to be: p i = p 3 (1 ) + c i =, (11) qi = qi 3 = c + ( ) (1 + ). The total consumer surplus over two stages is, conditional on that the innovation succeeds, the sum of CSL;Lj and CS3 ( c+) L;Lj, which equals. This expression can be simpli ed ( ) (1+) to 1 c ;c, using the notation de ned in (8). Similarly, if the innovation fails, the consumer surplus over date and 3 is ( c) ( ) (1+), expressed by 1 c;c by the notation in (9). The ex-ante expected consumer surplus is therefore 1 c ;c + (1 ) c;c ) if both rms innovate at date 0, and 1 c;c if no rm invests. Using the same algorithm, I compute the expected consumer surplus in the equilibrium where one rm chooses L and the other chooses N. CS L;N equals CS L;Nj + (1 ) CSL;Nj1, as the surplus will have the same value at both dates. Similarly, let denote the ex-ante expected consumer surplus for the equilibrium where one rm CS L;F chooses L and the other rm chooses F. We know already from Lemma that the nonleading rm will follow at date 1 only when learning good news from order ows. The surplus CS L;F thus consists of two parts; the expected consumer surplus at date, which is equivalent to 1 CS L;N, and the surplus CS 3 L;F (at date 3). CS3 L;F includes 3 4 CS L;Lj when 16

17 good news being revealed, 3 4 (1 ) CS L;Nj1 when bad news being revealed, and 1 4 CS L;N when order ows reveal no private information. We know CS L;Nj1 = CS L;Lj1 since the production cost of both rms remains unchanged if the innovation fails. The expression for CS L;F can then be simpli ed to 5 8 CS L;N CS L;L. By comparing the ex-ante expectation of consumer surplus in di erent equilibria, I obtain the proposition below. Proposition 3 The ex-ante consumer surplus is highest when both rms invest at date 0. The ex-ante consumer surplus is higher when one rm invests at date 0 and the other one follows at the next date, than when only one rm innovates. Proof. See Appendix. Naturally, the impact of having a feedback e ect on consumer surplus is consistent as its impact on the amount of innovation. When is lower than 1, the consumer bene t from the non-leading rm choosing F instead of N compared to the benchmark case, but his surplus declines when the equilibrium strategy (L, L) in benchmark case is replaced by (L, F ). The impact on consumer welfare therefore depends on the scale of required investment. If I is relatively low, consumer surplus is negatively a ected by having more information available in product market, as rms optimal strategy may change from both investing at an early stage to having only a leading rm in innovation. If the required investment is relatively high, however, consumers will bene t from the increased amount of innovation when the non-leading rm chooses to innovate at date. The corollary below compares the amount of gain and loss to the representative consumer due to the feedback. Corollary 1 When one rm invests in innovation at date 0, the consumer s bene t increases more when the other rm s equilibrium strategy changes from F to L, than its strategy changes from N to F. Proof. See Appendix. To see the total impact of stock market trading on consumer surplus, it is useful to compute the di erence in the regions on the investment scale for each equilibrium strategy between the benchmark and the case with feedback. First, when the informed share trading exists in the economy with < 1, the region of (L, L) being the equilibrium shrinks by a 5 length of I, and the region of (L, N) and (N, L) being the equilibria shrinks by 1 a length of I. Comparing these two expressions, we can see that the region where the strategy F replaces N is larger than the one where it replaces L. Based on Corollary 17

18 1, we see that the total impact on consumer welfare is ambiguous, even though the overall amount of innovation increases. 4 Participation of stock market agents 4.1 Speculator s pro t I rst investigate trading incentive of speculators, since the signi cance of the feedback e ect eventually depends on how much private information can be produced by informed trading in the stock market. As assumed previously. each of the two speculators trade only one rm s shares. I compute speculators expected pro t and show how the pro tability of their information acquisition can be a ected. Recall that if no rm innovates at date 0, no informed trading will occur at the next date as no private information is there for acquiring. On the other hand, if both rms invest at date 0, speculators still make trading pro t, even though the revealed private information is no longer used for rms decision making. Assuming rm i innovates at date 0, the probability of the innovation success being revealed is 3, and the probability of bad news being revealed is 3 (1 ). Thus, the 4 4 speculator earns zero trading pro t with probability 3. It is already proven that the nonleading rm will not innovate at date 1 if order ows are not informative. The 4 market maker thus quotes the price P i and P i for the share of rm i and belief of the success possibility. i, based on his prior P i = c ;c + (1 ) c;c I (1) P i = c;c + (1 ) c;c With probability, speculator i learns goods news about the innovation progress of rm i, and his trading pro t from buying one share of rm i is ( c ;c I) P i. Similarly, he earns P i ( c;c I) when getting bad news about rm i 0 s innovation, which occurs with probability 1. Given the probability of zero order ows being 1 4, speculator i0 s ex-ante expected pro t is (1 ) ( c ;c c;c ), denoted by S i jl; N. The di erence in notation is to indicate that N is the ex post action taken by rm i upon observing zero order ows. By the same algorithm, the expected pro t of speculator i, S ijn; L, is 4 [P i c;c ] + (1 ) 4 [ c;c P i ], which can be simpli ed to (1 ) ( c;c c;c ). When both rms invest at date 0 and zero order ows are observed, the market maker will set the same price 18

19 for both rms, P i = P i = c ;c + (1 ) c;c I. The speculators thus have the same ex-ante expected pro ts (1 ) ( c ;c c;c ), because the expected pro t of both speculators is (1 ) ( c ;c c;c ) if the innovation succeeds, and ( c ;c c;c ) otherwise. Despite the di erent magnitudes of speculator s pro ts in each case, the rst order derivatives of their expected pro ts with respect to are of the same sign. Also, due to the assumption that rms investment actions can be observed by all agents, the speculator s pro t is not related to the cost of the innovation investment I. 13 proposition summarizes how speculators expected pro t depends on and. The next Proposition 4 The ex-ante expected pro t of the speculators decreases in the success rate of innovation,, when > 1, but increases in when < 1. It monotonically increases in the scale of cost reduction,. Proof. See Appendix. Relating to the equilibrium conditions in the case with feedback, we observe that when the required investment is low, both rms are inclined to innovate at date 0, the information produced by the speculators is thus less useful to rms in the product market. When only one rm innovates at date 0 and the innovation has a larger impact on the production cost (a higher ), all the thresholds in the equilibrium conditions stated in Proposition increase. This then yields a higher incentive for speculative trading since it becomes less likely that no rm invests. Also, a higher makes the leading rm more advantaged in competition if the innovation succeeds, and the speculative trading becomes more pro table as a result. Proposition 4 also states that if the investment in the innovation is more risky, i.e., closer to 1, speculators have a higher incentive to acquire and trade on the privation information, which enable rms to ride on better information set and thus improve investment decision. It is clear so far that if an industry is facing innovations that require relatively large investment but promises success probability lower than one half, additional information produced by stock market trading encourages process innovations and improves consumer welfare. Speculators also have stronger trading incentive when this innovation can bring a larger cost reduction in this case. This may be seen in an industry in its earlier stage with relatively immature technologies. Its innovations may less likely succeed but can be very e ective once it does. They often require large investments either because innovations are more drastic or because the average capital level in the industry is still low. If policy makers 13 Note that this is no longer true under the assumption that rms investment activities become private information. 19

20 are more concerned with the advance in technology, they should endeavour to encourage this feedback e ect from the stock market. The opposite can be said for industries in the later stage of their life cycles, when the prevailing technology is maturer and hence the relevant innovations carries lower risks, have lower impact on production cost, and require lower investment. Thus for a young innovative industry, policy makers may nd it bene cial to facilitate informed trading, since rms would want to conceal their innovation success in order to maintain their advantages in competition, particularly when the leader sends spillover but receives none as modelled here Monopoly speculator Before characterizing the equilibria when the participation of stock market traders is fully endogenized, I rst introduce rms equilibrium strategies when there exists a monopoly speculator in the market. This may arise when noise traders quit from trading one rm, which leads no incentive for the speculator to trade the same rm. With the information structure and timeline under the same assumptions as in Section 3, we look at two possibilities separately; either both rms invest at date 0 or only one rm invests at date 0. With the rst possibility, rms could both succeed with probability or fail with 1. The speculator thus has two options when submitting orders. Either he can submit orders with the same sign for both rms and hence x i f ; 0; g, i = 1;. With probability 1 4, the speculator can conceal his orders from the market maker, that is, when x i = x i = 0, and he will earn zero pro t otherwise. If however the speculator intends to disguise the true information that he acquires privately, he may choose to submit orders with opposite signs. In the case when both rms innovate up-front and hence no investment decision needs to be made in future, the orders submitted by speculator will not change the innovating activities. It however leads to zero pro t due to the opposite orders for two rms that will liquidate with the same value. Therefore the speculator will always submit the orders with the same sign if he trades on both rms. With the second possibility, when rm i chooses not to innovate at date 0 and to take advantage of information spillover, the speculator may submit an order for only one rm, and then compare their expected pro t to the strategy of trading both rms. Assuming 14 Milliou (009) employs a model where rms both receive and send spillovers and nd that with a su ciently low degree of substitution rms have incentives to let their R&D information unprotected in order to enhance their rivals investments that they can free-ride in turn. 0

21 that the speculator only trades on the leading rm i, the feasible set of order ows is f for rm i, and f ; 0; g for rm i. So the possible combinations, when the innovation is successful, are f; 1g, f; 1g, f0; 1g, and f0; 1g. Evidently the probability of full revelation is 1. So is the probability of order ows revealing that the innovation is unsuccessful. Using the same algorithm as in the previous section, we can obtain the expected pro t for the speculator, that is, (1 ) ( c ;c c;c ). We can also compute the expected pro t if the speculator decides to trade only rm i s shares, that is, (1 ) ( c;c c;c ), lower than trading only rm i s share. Similarly, we can show that trading only rm i is also more pro table than trading both rms that reveals private information with probability 3. It is therefore optimal for a monopoly speculator to trade the leading rm in innovation. Knowing the optimal strategy of the speculator, rms can choose optimal 4 innovation strategies as summarized in the proposition below. Proposition 5 When a monopoly speculator participates in the informed trading, rms innovation strategy pro les in Nash equilibria are: a unique equilibrium (L, L), if 0 < I < (L, F ) & (F, L) if 3 I I < 1I, 8 I ( ) I ; 1 (L, N) & (N, L) if 1 I I < I, 8 I I ; 1 ; a unique equilibrium (N, N), if I > I, 8. Proof. See Appendix. 1; 1g 3 I, 8 (0; 1], and if I < I, 8 ( 1; 1]; ( ), and if 3 I < I < I, 8 < I ( ) I ; It is worth mentioning the di erence between the equilibrium conditions stated in Proposition 3 and in this proposition. For the equilibrium with the strategy pro le (L; L), notice that if 0 < < 1, the upper bound for the size of required investment increases from 5 I to 3 I. Meanwhile the lower bound for the strategy pro les (L; F ) and (F; L) (4 3) ( ) to be in equilibrium increases by the same amount for 0 < < 1. We do not observe any di erence in the conditions for the strategy (L; N), (N; L) and (N; N), however. The intuition is that having a monopoly speculator lowers the probability of revealing private information in the stock market, which then makes rms less prone to wait for knowledge spillover from their competitor in the product market. When the required investment is relatively small, it becomes optimal for both rms to invest early in the innovation The above analysis is analogically similar to assume that only one of the duopolists are listed in the stock market, where one speculator can trade on her private information and the other speculator exits the market. The probability of concealing the order from the speculator then increases to 1. 1