Endogenous Market Transparency and Price Competition

Transcription

1 ömföäflsäafaäsflassflassflas ffffffffffffffffffffffffffffffffffff Discussion Paers Endogenous Market Transarency and Price Coetition Klaus Kultti University of Helsinki and Mikko Leääki Helsinki School of Econoics and GSF and Eeva Mauring University of Helsinki Discussion Paer No. 78 October 009 ISSN HECER Helsinki Center of Econoic Research, P.O. Box 7 (Arkadiankatu 7), FI-0004 University of Helsinki, FINLAND, Tel , Fax , E-ail info-hecer@helsinki.fi, Internet

2 HECER Discussion Paer No. 78 Endogenous Market Transarency and Price Coetition* Abstract We introduce a odel of rice coetition with endogenous arket transarency, where it is costly for consuers to get infored about the announced rices. We show that there is syetric ixed strategy euilibriu with a onotonic relationshi between the degree of transarency and intensity of coetition. Interestingly, we find that there exist ultile euilibria with zero, low and high levels of arket transarency with the high level of arket transarency being the stable euilibriu. Once coaring the stable euilibriu with the welfare axiizing one we find that the rivate arket solution entails excessive investents in inforation acuisition. That is, at high levels of transarency the gain of consuers fro increased transarency is saller than the loss in the firs rofits leading to decrease in total welfare. JEL Classification: D4, L, L5 Keywords: Endogenous arket transarency, rice coetition, ixed strategy, ultile euilibria, welfare. Klaus Kultti and Eeva Mauring Mikko Leääki Deartent of Econoics, Graduate School of Finance, University of Helsinki Helsinki School of Econoics P.O. Box 7 (Arkadiankatu 7) P.O. Box 0 FI-0004 University of Helsinki FI-000 Helsinki FINLAND FINLAND e-ail: klaus.kultti@helsinki.fi e-ail: eeva.auring@helsinki.fi e-ail: ikko.leaaki@hse.fi * We are grateful for Zhang Shilei and Natalia Nikola for research assistance.

3 Introduction It is often argued that a high arket transarency is desirable for society as it fosters coetition. How exactly a certain level of arket transarency is achieved reains tyically soewhat unclear. In this aer, we roose a odel where the level of arket transarency is endogenously deterined. Moreover, an ilication of tyical arguentation, of course, is that the higher the arket transarency, the higher the social welfare is. Interestingly, we conclude the oosite; in our set u the socially otiu would reuire lower arket transarency than the rivate arket solution entails. We ut forward a standard odel of rice coetition, where the consuers behaviour is not catured by the deand curve. They can also decide to acuire inforation on announced rices. They get to know the revailing rices only if they acuire the rice inforation. Our odel relicates the standard Bertrand coetition case when transarency, i.e., the roortion of consuers who are infored, is at the highest level. With both infored and uninfored consuers the rs ricing is in ixed strategies. The novelty with resect to rior literature is that the degree of arket transarency is endogenous as also consuers are allowed to behave strategically. In our set u rs coete in rices, roduce a hoogeneous good, and have the sae arginal costs of roduction. It is costly for consuers to becoe infored about rices. A consuer who acuires rice inforation can, of course, choose the lowest rice o er. The higher the roortions of infored consuers the lower the rices are in euilibriu. Thus, those consuers who do not get infored also bene t, but only on average. We show that there exists syetric ixed strategy euilibriu in rices with a onotonic relationshi between the degree of arket transarency and intensity of coetition. Most interestingly, we nd nuerically ultile euilibria with zero, low and high levels of arket transarency with the high level of arket transarency being the stable euilibriu. When coaring the stable euilibriu with the social otiu, it turns out soewhat surrisingly that the social otiu would reuire less transarency than there is in euilibriu. That is, there is too uch rivate investents in inforation acuisition.

4 Of course, we are not the rst ones to address arket transarency. Varian (980) is robably the ioneering study. In his odel the consuers are identical, while we allow for heterogeneous valuations. There is also an old research agenda of increased arket transarency leading to intensi ed arket coetition (see Stigler (96)) as increased transarency iroves the consuers ossibilities to choose goods with lowest rices. However, on the downside of increased transarency is the rs iroved ossibility for collusion in a reeated relationshi as increased transarency akes it easier to detect any deviations fro collusive ricing. For recent contributions, see for instance Møllgaard and Overgaard (00) and (00), Nilsson (999) and Schultz (005). While the rior literature has exained the e ects of transarency on ricing, intensity of coetition and welfare we fully endogenize the level of arket transarency by introducing the consuers strategic behavior in an otherwise standard odel of rice coetition. Moreover, our nding of ultile euilibria of arket transarency is new in the literature. In search theoretic fraework Lester (009) nds that while rs are caacityconstrained the relationshi between transarency and rices is not as clear as rior theoretical literature has argued. In articular, higher transarency can lead to either higher or lower rices. Schultz (004) analyzes the e ects of arket transarency in a Hotelling odel where a fraction of consuers are infored about the rices and locations of rs. He shows that increased transarency leads to unabiguous iroveent in consuers and total welfare. Our welfare results with resect to transarency and consuers welfare are in line with those of Schultz (004) while we deonstrate that the e ect of increased transarency on total welfare is abiguous. Naely, at high levels of transarency the gain of consuers fro increased transarency is saller than the loss in the rs ro ts leading to decrease in total welfare. 4

5 The Basic Setu Consider a ass of consuers noralized to unity. Assue that their valuations of a hoogenous coodity are indeendent draws fro the unifor distribution on unit interval. Once the valuations are realized there is a linear deand curve =. Notice that other distributions would, of course, generate different deand curves. Assue further that there are two rs which roduce a hoogenous good with constant arginal cost noralized to zero. Let us call these rs A and A. Below we denote the roortion of those consuers who have observed the rs announceents by ; and this is intended to be a easure of arket transarency. That is, roortion of consuers have observed nothing, and will visit the rs randoly. To construct an euilibriu we assue that consuers use a syetric ixed strategy. The rs behaviour is then necessarily syetric. De nition An euilibriu is a roortion [0; ] of observing consuers and rices and s.t. no consuer wants to deviate and the rices axiize the rs ro ts. Price Coetition: Syetric Euilibriu Consider the rice coetition where the rs A and A announce their rices and siultaneously, and assue further that roortion of consuers observe the announced rices. In a syetric euilibriu both rs then get consuers to start with, and they coete for the consuers. If the rs coete in rices in a Bertrand-fashion it is clear that for > 0 there does not exist a syetric ure strategy euilibriu for exactly the sae reason as in the standard Bertrand-coetition case. There, however, exists a syetric euilibriu in ixed strategies and that is what we construct next. The suort of the ixed strategy F is a closed interval ; and it has no ass oints (see Kultti and Virrankoski, 00 for the reasoning and roof in an analogous case). It is clear that the highest rice is never higher than the onooly rice. Also, it cannot be lower since when 5

6 a r chooses the highest rice it only gets the non-observing consuers and ight as well charge the the onooly rice. Assue that A uses F and that A chooses rice fro the suort of the ixed strategy. A s ro t is then F () ( ) + ( F ()) + ( ): () This agnitude ust be constant for all in the suort of the ixed strategy. In articular, it ust eual the ro t at the onooly rice =. Notice that at this rice F ( ) =. Euating () and the ro t of A at the onooly rice yields the following forula for the ixed strategy F () = To deterine notice that F the ro t at yields the following condition The sensible root is 4( + )( ) ( ) : () 8( ) = 0. Now euating the onooly ro t and + = 0: () 4( + ) = + as the other root is greater than the onooly rice. To suarize we have the following result: Proosition There exists an euilibriu where rices are on the interval + ; ;and where = and = : That is, when = the lower liit is at the coetitive level with two rs, and at = 0 the lower liit is at the onooly level of a single r. Thus, we have a nice and sooth transition fro the onooly rice to the coetitive rice in a duooly when the roortion of the infored consuers goes fro zero to unity. The intensity of arket coetition is thus increasing in arket transarency and uite naturally consuers are then also better o due to the lower rices. Let us next exaine consuers incentives to becoe infored about announced rices in the rst lace. (4) 6

7 4 Transarency in Euilibriu Assue that consuers have to ay a xed cost of to becoe infored about the rs osted rices. We want to nd the euilibriu roortion of consuers who decide to becoe infored. In euilibriu the consuers ust be indi erent between observing the rices and not observing the. First we deterine the exected utility of a consuer who does not incur the cost of becoing infored. He chooses one of the rs at rando and the exression for his utility is Z v Z (v )f()ddv + (v )f()ddv: (5) The above exression gives the consuer s exected utility when the r has set rice which haens with robability f(): In (5) the rst art is the exected utility of the consuer whose valuation v is on the interval [; ], and when the rice set by the r lies in the interval [; v]: Notice that in the consuer s valuation the lower liit of integral starts fro instead of zero, since all those consuers whose valuation is lower than will not buy the good and thus receive zero. The second art of (5) gives the consuer s exected utility when his valuation is at least the onooly rice. integral the uer liit hits the axiu valuation of v = : Thus, in the rst After soe routine algebra (executed in Aendix ) exression (5) can be develoed into for = ln( r + ) 5 : (6) Consider next the case when consuers can learn the announced rices. By aying a consuer observes the rices announced by A and A, and then gets to choose the lower rice, i.e., he gets to choose the lower of two identically distributed rando variables. The robability g() that the lower of the two rices is is g() = f() ( F ()) = ( )( ) 4( ) ( ) 8( ) : (7) 7

8 Now the exected utility of a consuer who observes the rices can be exressed as follows Z v Z (v )g()ddv + (v )g()ddv : (8) By aying a consuer becoes infored about the rices and chooses the lowest one, i.e., rice : Otherwise the exression of the exected utility reains the sae as in (5). After soe rather involved but routine algebra (see Aendix ) euation (8) turns out to eual ( ) 4 4( + ) r + 6 ln( ( + ) + 4 ln + ) : In euilibriu a consuer ust be indi erent between observing and not observing the rices which condition deterines the euilibriu value of. That is, by euating (6) and (9) one should in rincile be able to solve. It should not coe as a surrise that it is iossible to solve such in a closed for. We solve the odel nuerically, and resent grahics for the exected utilities. Assuing that the cost of getting infored,, takes values in the set f0; 0:0; 0:05g we can lot (6) and (9) in the sae icture. (9) 8

9 Figure : Observer s (dashed) and unobserver s (solid) exected utilities at =0:05: 9

10 Figure : Observer s (dashed) and unobserver s (solid) exected utilities at =0:0: Figure : Observer s (dashed) and unobserver s (solid) exected utilities at =0: 0

11 We can suarize the results with di erent levels of cost of getting infored,, as follows: Proosition There is always an euilibriu where no-one observes. When > there is a uniue euilibriu where no-one observes. When (0; ] there are ultile (three) euilibria with zero, low and high levels of arket transarency i.e. where [0; ). If = 0 there exists two euilibria with either = 0 or = : Soewhat surrisingly it turns out that there are ultile euilibria. On re ection this is easy to understand; what atters to a consuer is the arginal utility fro observing the rices. When very few consuers observe the rice it does not ay to observe the rice since the suort of the rs ixed strategy is not very large, and thus getting the lower of the two rices results in not-so-big reduction in the rice. When any consuers observe the rice the suort of the ixed strategy is large and getting the lower rice results in a big reduction in the rice. Of the two euilibria where > 0; the one of higher transarency is the stable euilibriu. Notice that there is also a third euilibriu where no one invests in getting infored, and then = 0: Quite naturally when the cost of getting infored increases it does not ay to becoe infored any longer, and thus the curve reresenting the exected utility of an observing consuer oves downwards. 5 Welfare To deterine how the arket euilibriu fares coared to the social otiu we ostulate that the social welfare easure is the su of ro ts and consuer surlus. This is easy to calculate as roortion of consuers gets the exected utility in exression (9) and roortion gets the exected utility in exression (6). There are also two rs both of which ake the sae exected ro t which is the sae as the ro t at the onooly rice (since it belongs to the suort of the ixed strategy). Forally, the social welfare easure is

12 4 ( ) 6 +( ) 4( 4 6 ( + ) + ln( + ) + + ln( r + ) + 4 ln + A r + ) A5 + ( ): (0) 4 Which can be consolidated into the following for ( ) ln ( ): () 4 The grah of the social welfare easure () shows that welfare is a concave function, increasing in transarency till a uniue axiu is reached and decreasing thereafter (the latter with ositive cost of getting infored) as seen in gure 4. Increase in the cost of obtaining inforation shifts the tail of the curve downwards, here lotted at values 0, 0:0, 0:0 and 0:0. Taking the rst order condition of the welfare function with resect to yields the following condition for the social otiu ( + ) + ( + ) ln = 0 () It is of soe interest to coare the rivately chosen stable euilibriu with high level of arket transarency with that of the welfare axiizing s chosen by the social lanner. Since fro () it is iossible to solve in a closed for we use instead nuerical analysis and solve both the rivate and social otiu and coare those. Assuing the cost of getting infored will take values 0, 0:0, 0:0 and 0:0; we can solve the rivate euilibriu value of transarency, by euating (6)

13 Figure 4: Total utilities at values 0 (solid); 0:0 (dashed); 0:0 (dot-dashed); 0:0 (dotted). and (9). Siilarly by lugging in () di erent values of we can derive the socially otial level of transarency, s : These values are reorted below in table. Table : Coarison of rivately chosen euilibriu and welfare axiizing s = 0 = s = = 0:0 = 0:97 s = 0:9 = 0:0 = 0:90 s = 0:8 = 0:0 = 0:74 s = 0:7 We nd that for all ositive values of (u to after which no one observes) there is too uch arket transarency in the otial rivate arket solution coared to social otiu. The intuition behind this result is that for low levels of transarency the gain of consuers fro increased transarency exceeds the loss in the rs ro ts, as shown in gure 5. However, at higher

14 Figure 5: Growing consuers surlus at f0; 0:0; 0:0; 0:0g and declining ro ts. values of transarency the loss in the rs ro ts outweighs the increase in consuers welfare. The gure shows that if at low levels of the sloe of the curves reresenting the consuers welfare is bigger in absolute ters than of rs ro ts, then the situation is the oosite at higher values of transarency. Thus, if the social lanner assigns eual weight to the well-being of both rs and consuers, then socially otial level of arket transarency is lower than that of rivately otial. Note also that if rs ro ts decreased non-linearly in transarency, then the result would change deending on the relative decrease of the rs utility coared to that of consuers. Proosition 4 The rivate and socially otial levels of arket transarency coincide only when the cost of getting infored is zero. For all other values of the otial rivate arket solution involves too uch transarency. 4

15 6 Conclusion We have develoed a odel of endogenous transarency where it is costly for consuers to get infored about the rices announced by the rs. We show that there is a syetric ixed strategy euilibriu that we derive exlicitly. We deonstrate that there is a onotonic relationshi between the degree of transarency and intensity of coetition; the rices and ro ts decrease fro onooly level to coetitive level as transarency increases fro zero to erfect transarency. It is clear that there always exists an euilibriu, if nothing else then an euilibriu where no-one acuires inforation. Nuerical analysis reveal that there exist ultile euilibria (exactly three) with zero, low and high levels of arket transarency. Zero and high levels of transarency are stable euilibria whereas the low level is unstable. Quite surrisingly, it turns out that the stable euilibriu with strictly ositive transarency entails higher than socially otial level of inforation acuisition. The arket solution features too uch transarency. This nding is contrary to the results in the aers entioned in the introduction. It also runs counter to the often entioned reuireents to increase transarency in various arkets, the nancial arkets being the leading exale. There are two reasons for too high transarency in euilibriu. One is that the agents decision to acuire inforation akes rice coetition ore erce, and lowers the ro ts of the rs. As ro ts are art of the welfare it ay well go down. The other reason eanates fro the fact that the analysis is of artial euilibriu tye. In a general euilibriu odel the consuers would also be the owners of the rs and the rs ro ts would be distributed to the consuers. Taking into account these general euilibriu e ects ight well change the result. References [] Kultti, K. and J. Virrankoski 00: Price Distribution in a Syetric Econoy.Toics in Macroeconoics. htt:// 5

16 [] Lester, B. 009: Inforation and Prices with Caacity Constraints: ieo. University of Western Ontario. [] Møllgaard, H.P. and P.B. Overgaard 00: Market Transarency and Coetition Policy. Rivista di Politica Econoica [4] Møllgaard, H.P. and P.B. Overgaard 00: Market Transarency: A Mixed Blessing? University of Coenhagen. ieo. [5] Nilsson, A. 999: Transarency and Coetition. Stockhol School of Econoics. Working Paer Series in Econoics and Finance No. 98. [6] Schultz, C. 004: Market Transarency and Product Di erentiation. Econoics Letters [7] Schultz, C. 005: Transarency on the Consuer Side and Tacit Collusion. Euroean Econoic Review [8] Stigler, G.J. 96: The Econoics of Inforation. The Journal of Political Econoy [9] Varian, H. 980: A Model of Sales. Aerican Econoic Review

17 Aendix : Derivation of exected utility of uninfored consuer. Z v Z (v )f()ddv + (v )f()ddv It is useful to change the order or integration as follows = Z (v )dvf()d + (v )dvf()d =. ( v v) +. ( v v) f()d = f()d = ( ) f()d: Now we can substitute in f() = F 0 () = ( ) ( )( ) 8( ) d: = Z ( ) 8 ( ) d = ( ) 6 ( )d = ( ) 6. ( ln ) after substituting = and = + we have 7

18 ( ) = ln( r + ) 5 Aendix : Derivation of exected utility of infored consuer Z v Z (v )g()ddv + (v )g()ddv : Again it is useful to change the order or integration as follows Z (v )dvg()d + (v )dvg()d We forget for a oent and develo the the rst two exressions. As in the case of the unifored consuer we get the following exression = ( ) g()d: recalling that g() = f()( F ()) we get ( ) ( )( ) 4( ) ( ) 8( ) d = ( ) ( ) 8 4( ) d Now we can develo ( ) 4( ) d 8

19 further on in the following for ( ) 4( ) d 4( ) d = 4 d d Z 4 ( ) d + d = ln ln + ln( ) + ln 4 Plug in above = = + and then solve the exression, and one gets the following exression for the ayer s exected utility where the ultilier reintroduced ( ) 6 and the cost of getting infored, are ( ) 6 4 4( ( + ) + ln( + ) r + ) + 4 ln : 9