The University of Adelaide School of Economics
Research Paper No. 2006-06
Intertemporal Price Discrimination and Competition Ralph-C Bayer
Intertemporal Price Discrimination and Competition
Ralph-C Bayer School of Economics, University of Adelaide†
Abstract In this study we investigate the impact of competition on markets for non-durable goods where intertemporal price discrimination is possible. We develop a simple model of di#erent potential scenarios for intertemporal price discrimination and implement it in a laboratory experiment. We compare the outcomes in monopolies and duopolies. Surprisingly, we %nd that competition does not necessarily prevent intertemporal price discrimination, as our model predicts. However, competition generally reduces sales prices, but by far less than theory predicts. As expected, competition increases e'ciency. Keywords: Price Disrcrimination, Oligopoly, Market Experiments JEL Codes: L12; L13; C91
Introduction Some econometric evidence suggests that the extent of price dispersion in markets for non-durable goods - such as airline tickets and perishable commodities - does not negatively depend on the competitiveness of the market, as basic intuition would suggest. Stavins (2001) and Borenstein & Rose (1994) even %nd that competition increases price dispersion. School of Economics, University of Adelaide; Tel.: ++61-8 8303.4666; fax: ++61-8 8323.1460. E-mail address:
[email protected] † I wish to thank the Facilty of Professions at the University of Adelaide for funding under the Faculty Research Grant scheme. I am also grateful for helpful comments from John Hatch, Ludevic Renou and seminar participants at various instituions. I am indebted to Nick Robinson for great IT support, to Yang Shen for very valuable research assistance, and to Timothy Bridgeman from Vigin Blue Australia for providing me with some insight into the pricing strategies of Virgin Blue.
1
There are a variety of possible reasons for the persistence of intertemporal price dispersion in competitive markets. Candidates o#ered in the literature are repeated interaction, demand uncertainty, capacity constraints or costly buyer search. Price dispersion can be discriminatory, i.e. customers with di#erent preferences pay di#erent prices, or the consequence of real cost di#erences. These two cases are hard to disentangle, as anti-trust cases have repeatedly shown. For example airline tickets that are purchased well in advance are usually cheaper than tickets that are bought close to the departure date. This can be interpreted as intertemporal price discrimination, as holiday makers with low reservation prices purchase in advance, while business travellers with high reservation prices buy close to the time of departure. However, it can also be argued that the di#erent ticket prices just reBect real cost di#erences. Lott & Roberts (1991) argue that the higher price for late bookers includes the opportunity costs of the airline’s risk of having empty seats. They also argue that price dispersion cannot be discriminatory, since competition and low search cost prevent pricing above marginal cost. So can we conclude that all intertemporal price dispersion in markets for nondurables with more than one %rm, can only be due to cost di#erences? An increasing body of theoretical literature suggests that this conclusion is not valid, as it shows that under certain circumstances intertemporal price discrimination is possible even in competitive non-durables markets.1 Some kind of uncertainty, capacity constraints and/or repeated interaction are the necessary ingredients for models where intertemporal price discrimination for non-durables prevails under competition.2 Gale (1993) shows in a model, where consumers ex ante do not know which variety of a good they prefer, that the price dispersion between advance-purchase prices and spot prices is higher in a duopoly than in a monopoly. The results are driven by the uncertainty, which implies that goods are ex ante homogeneous, but become di#erentiated once the consumers have learned their preferences. So ex post there is some scope for price discrimination. Dana (1998) shows that market segregation of low and high-valuation customers can be achieved by competitive %rms if capacity is costly and there is some correlation between individual valuations and demand uncertainty. In a model with durable goods Sobel (1984) shows that price cycles (high prices with periodical discounts) are an equilibrium even when there are multiple %rms selling an homogenous 1
Elmaghraby & Keskinocak (2003) provide a comprehensive overview over current dynamic pricing practices. Both cost and discrimination are shown to be reasons for %rms changing prices over time. 2 The potential existence of static inter%rm equilibrium price-discrimination was %rst outlined in Prescott (1975) and formalised by Eden (1990).
2
good. The discounts are used to get low-valuation customers to buy and %rms make supernormal pro%ts. The main reason why the Bertrand logic of undercutting does not necessarily apply in durable goods markets is that repeated interaction gives rise to trigger strategies which support an equilibrium with price cycles. This logic can easily be extended to %rms who compete repeatedly in subsequent non-durable goods markets. Burdett & Judd (1983) and Stahl II (1989) show that price dispersion can prevail under competition if consumers’ costly search creates some demand uncertaincy. In this paper we test experimentally whether intertemporal price discrimination really disappears with competition if we use a very simple framework that does not exhibit any of the characteristics that were used to theoretically explain price di#erntiation. Put di#erently: are there any behavioural reasons why we might observe intertemporal price discrimination even when the competitive environment appears to favour the law of one price? Alternatively, are there potential reasons why we should not observe price discrimination even when is a monopolist seller? A potential behavioural factor that mitigates the pressure of competition towards a stable sales price is the limited depth of iteration exhibited by consumers. To see this, put yourself in the shoes of a consumer who wants to purchase an airline ticket. Assume for instance that you know that there are more seats than potential travellers. You check the ticket prices of the di#erent operators continuously on the web. For the Bertrand logic to work, i.e. price undercutting down to marginal cost without any sales at prices above marginal cost, consumers have to anticipate and to be sure that %rms will eventually undercut each other. Consumers also have to be sure that the other customers also know this and will act accordingly. For certain conjectures about the behaviour of the other market participants it becomes optimal for a customer to buy in advance and at a price above marginal cost. On the other hand, fairness considerations could explain why a monopolist loses some of his price-discrimination power. Suppose your plan to By develops at short notice. From experience you know that the price will be quite high and would have been much lower if you booked earlier. If you are spiteful about the unfairness of the monopolist trying to extract a very high proportion of the surplus just because you decided spontaneously to By, then your reservation price given the pricing policy of the airline might be lower than your valuation of the Bight. You %nd the pricing of the monopolist unfair and are willing to forgo the bene%t of travelling rather than be exploited by the airline. So you might call the price "ridiculous" and abstain from travel even though the price is below your valuation. Preferences like these limit the price-discrimination 3
power of a %rm regardless of market power. We experimentally implemented two typical market environments where theory predicts that in equilibrium a monopolist can price discriminate, while duopolists cannot and compared the outcomes for monopolies and duopolies. We call these environments last-minute discounting and early-bird discounting. In both cases the typical Bertrand logic applies for markets with more than one %rm and price discrimination should not be observed in equilibrium. In the last-minute discounting scenario the intuition as to why a monopolist can price discriminate is similar to that in Dudey (1996). A market where posted prices can be revised many times before the nondurable good is delivered (or perishes) allows a monopolist to sell at (or just below) the monopoly price initially, in order to revise the price downwards later on. Consumers, which are heterogenous in there valuation, anticipate that the price will never fall below the monopoly price, if nobody buys early. So at least one consumer with a high valuation is willing to accept early.3 Then once the %rst high-valuation customers are out of the market the monopolist can charge the now decreased pro%t maximising price to the remaining low valuation customers. Such a pricing strategy is pro%table, since consumers with valuations below the static monopoly price now generate revenue, while the consumers with higher valuations self-select and buy at the static monopoly price. Our experiments reveal that in the last-minute scenario duopolists do not achieve any intertemporal price discrimination. Surprisingly, the monopolists have severe problems, too. Monopolists are only sometimes able to price discriminate and hardly do any better in terms of pro%ts than the duopolists. The second scenario is the commonly observed early-bird discounting situation. When customers with lower valuations for the good start searching earlier for cheap prices than consumers with higher valuations then it is possible to sell to these customers at early-bird discount prices, while the high valuation customers who enter later can be charged higher prices. The main objective of the monopolist is to get the low-valuation customers out of the market before the high-valuation customers arrive. The low-valuation customers accept early, as they anticipate that the prices will go up over time. We observed that the experimental monopolists were able to price discriminate quite regularly. Surprisingly, the 3
In our case where a consumer only wants to buy one unit the high valuation customers are indi#erent between buying early at the monopoly price or waiting. The monopolist can break the tie by lowering the price slightly. In Dudey’s model high-valuation customers prefer buying early, as that will guarantee lower prices for addtional units in the future.
4
duopolists were able to do so, too. Comparing the frequency of successful price discrimination even suggests that duopolists were more successful; but monopolists achieved higher prices than duopolists, whenever they were able to price discriminate. Over all, the monopolists did not make higher pro%ts though, as they quite often were confronted with spiteful consumers who did not buy at all. The refusal of some customers to accept prices, which were high but still below the valuation, hurt the monopolists pro%ts. The reminder of the paper is organised as follows. Sections 1 and 2 lay out the two market environments and characterise the equilibria for monopolies and duopolies. Section 3 brieBy discusses the crucial behavioural assumptions necessary for the polarly di#erent equilibrium predictions for duopolies and monopolies, while section 4 describes the experiment. In section 4 the experimental results are presented. Section 6 concludes.
1
Last-minute discounting
One well known phenomenon in dynamic pricing is discounting such as last-minute pricing in travel industries. Discounting can be used by monopolists as an instrument for intertemporal price discrimination. We use a simple example in order to demonstrate how such discounting works. Suppose we have two consumers - denoted by 1 and 2 - with di#erent valuations (v1 v2 ) for one unit of an homogeneous good. The valuations, but not the identities of the consumers, are common knowledge. There are N %rms which sell the good. For simplicity assume that %rms are identical and have zero marginal cost. The set of %rms is denoted by K. The consumers enter the market at period t0 = 1 and the market has a %nal date T. After period T the good is worthless, just like an airplane ticket once the plane has left. In each period t {1, 2, ..., T } the %rms simultaneously set their prices pk (t). Consumers observe the prices and decide to buy from a speci%c %rm or to wait. Denote the decision to buy or not from %rm k in period t as ai (t, k), with ai (t, k) = 1 indicating a purchase and ai (t, k) = 0 indicating a non-purchase. Ex post payo#s for the consumers are given by:4 T
N
Vi =
ai (k, t) (vi
pk (t))
(1)
i = 1, 2
t=1 k=1
The %rm’s ex post pro%t is given by: T k
2
=
(2)
ai (k, t)pk (t) i = 1, 2. t=1 i=1
4
Note that a consumer only wants to buy one unit of the good (
5
t
k
at,k = 1).
Suppose that %rm’s only observe their own sales and the past prices of their competitors. Consumers only observe their own purchases. First observe that for N > 1 intertemporal price discrimination is never an equilibrium. The usual Bertrand logic of undercutting applies. Proposition 1 For N > 1 in the last-minute setting we have 2
ai (k, t)pk (t) = 0 t i=1
{1, 2, ..., T }, k
K.
Proof. For each period and history a %rm has to have beliefs about which customer is still interested. Suppose that in period T at least two %rms believe that there is a positive probability that there is at least one remaining consumer. Then pk (T ) = 0 for at least two %rms. Otherwise there is a pro%table deviation. Note that the remaining customer will accept the lowest price in T. If pmin (T ) = mink [pk (T )] > 0 then at least one %rm j has a pro%table deviation by posting pj (T ) = pmin (T ) . Suppose that pmin (T ) = 0 for only one %rm j with pk (T ) > 0 for all k = j, then %rm j has a pro%table deviation by posting a price pmin (T ) + . Beliefs have to be consistent in equilibrium, which implies that if there is still an interested customer all %rms must assign a positive probability to this. Therefore mink [pk (T )] = 0 if there is still a customer in the market. Anticipating this, consumers will never buy for prices above 0 in earlier periods. So either ai (k, t) = 0 or pk (t) = 0. The proposition above shows that there is no scope for pro%table intertemporal price discrimination in a dynamic Bertrand Oligopoly. We now turn to the monopoly case. A monopolist who cannot price discriminate will be able to achieve a monopoly pro%t. As the game is a kind of ultimatum game the monopolist has all the power. So he can always charge and implement the unitary monopoly price pM :5 pM = arg max p
M
=
M,
with
0 if p > v2 p if v2 p > v1 2p if p v1
Therefore the monopoly price depends on the valuations. Sometimes it pays to charge a price which leads to both consumers buying the good. Sometimes the monopolist only wants to sell to the high-value customer: pM = 5
v2 if v2 v1 else
2v1
We implicitly assume that an indi#erent consumer accepts.
6
We now ask if the monopolist can do better than the monopoly pro%t if he has the option to charge di#erent prices over time. This is possible if v2 2v1 . Then the monopolist can force the high-valuation customer into early acceptance at price p = v2 (or v2 ), while he can charge the low-valuation customer p = v1 later. Denote the point in time when the high valuation customer accepts as t and the period when the lowvaluation customer accepts as t, respectively. Then we can state the following proposition. Proposition 2 If v2 2v1 then t < t, pM (t) = v2 , pM (t) = v1 , pM (t) v2 for t t, and pM (t) v1 for t < t t describe equilibrium price paths in the last-minute discounting case. Proof. For the high-value customer any price above v1 clearly indicates that the low-valuation customer will not accept. A high-valuation customer not accepting in the penultimate period will induce the monopolist to charge pM (T ) = v2 . Not accepting in earlier periods t will trigger prices pM (t) v2 in t where t < t < T. Therefore the high-valuation customer will accept if pM (t) v2 . The low-valuation customer will always - independent of beliefs - accept a price pM (t) = v1 , as she anticipates that it is never optimal for the %rm to charge a lower price. Given this strategy of the consumers a price path characterized above is optimal for the monopolist, as he extracts the maximum surplus v1 + v2. Note that if v2 < 2v1 intertemporal price discrimination is not feasible if consumers make no mistakes. A high-valuation customer will never accept a price above pM = v1 , as she knows that this will be the price charged if both consumers stay in the market until the last period. The low-valuation customer will never accept a price above v1 , since this is a dominated strategy. Both units will be sold at the static monopoly price.6 Typical examples of pricing following a pattern described in the proposition above are last minute-pricing (for airline tickets, products sold at fruitmarkets just before closing, or during end of season fashion sales),or high introductory prices for books (hardbacks vs. paperbacks), movies (cinemas vs. DVD rentals) or electronic gadgets. The keen, impatient consumers buy early at a high price, while the less keen and more patient consumers purchase later at a lower price.
2
Early-bird discounting
In some other instances we see that the prices in dynamic markets do not decrease but increase over time. There might be many reasons for 6
If consumers have a downward-sloping demand for more than one unit price discrimination is possible for less extreme valuations.
7
such a pricing policy. Early bookings for example reduce uncertainty for airlines, who might be willing to forgo some pro%t in order to reduce this uncertainty. Introductory pricing in markets with network externalities might be another reason. Here we want to investigate intertemporal price discrimination between di#erent customer groups, who enter the market at di#erent points in time. One might think of holiday makers versus business travellers in the market for airline tickets.7 Holiday makers usually plan ahead and enter the market for a particular Bight quite early, while business travellers often cannot plan well in advance. Additionally, the reservation price of business travellers is much higher than that of holiday makers. A monopolist airline will try to persuade as many lowvaluation customers as possible to book early, such that it can charge higher prices later when the high-valuation customers have entered the market.8 We can use our simple framework from above to investigate earlybird discounting. We again have two consumers with di#erent valuations, v2 > v1 . Now assume that only the low-valuation customer enters the market at t0 = 1, while the high-valuation customer only starts looking for a ticket at tˆ, with 1 < tˆ T. Again, the distribution of the privately known valuations and the timing are common knowledge. As in our previous setting, there is obviously no scope for price discrimination if there is more than one %rm. Proposition 3 For N > 1 in the early-bird setting we have 2
ai (k, t)pk (t) = 0 t i=1
{1, 2, ..., T }, k
K.
Proof. The proof is analogous to that of proposition 1. In a monopoly price discrimination is certainly possible. Denote the point in time when the low valuation customer accepts as t and the period when the high-valuation customer accepts as t, respectively. Then, assuming that an indi#erent consumer accepts, we can state the following proposition.9 7
Another example are early-bird rates for parking space, blocks of discounted tickets for sports and other events issued well in advance of the event. 8 Technically, airlines divide the seats on a Bight in contingents with di#erent prices. Holiday makers buy the cheaper tickets, while these are sold out when the business travellers book. Airlines also use other discrimination devices, such as conditions and restrictions on tickets which are only acceptable for non-business travellers. 9 This is just to break a tie. The alterntive assumption would result in equilibriumpurchase prices to be marginally lower. Allowing consumers to randomise if they are indi#erent complicates the analysis, but does not lead to additional insights.
8
Proposition 4 For N = 1 in the early-bird setting, t < t˜, pM (t) v1 for t < t˜, pM (t) = v1 , and t t˜, pM (t) v2 for t t˜, pM (t) = v2 characterise the equilibrium paths. Proof. At any point in time the monopolist knows how many consumers there are in the market, as he is the only seller. Given that there is at least one consumer in the market in the last stage posting a price below v1 is never sequentially rational since posting v1 will lead to all consumers in the market accepting and raising the price to v1 therefore increases the pro%t. This logic extends to period T 1, T 2, and so on. Therefore a low-valuation consumer, given the assumption that indi#erence leads to a purchase, will always accept a price of v1 . So charging pM (t) v1 and pM (T ) = v1 at least once in the periods t < t˜ results in the low valuation customer buying. Then with customer 1 out of the market the monopolist can, independently of customer 2’s beliefs about the presence of customer 1 in the market, force customer 2 to accept a price of pM (t) = v2 , as the game becomes an ultimatum game (i.e. consumer 2 will always accept pM (t) = v2 in t = T ). A monopolist can never improve on a pro%t of M = v1 +v2 , which extracts all the surplus. So the pricing strategies guaranteeing this payo# are the equilibria of the game.
3
Price discrimination and crucial assumptions
Our simple model gives very stark predictions. In both settings, a monopolist can perfectly price discriminate and earn the maximum pro%t of v1 + v2 , while under competition the %rms have no scope for price discrimination at all and earn zero pro%ts. Two commonly employed assumptions are absolutely crucial for these stark predictions: 1. Players behave sequentially rational over all periods and know that the other players also do so. 2. Fairness motives are absent. Various (experimental studies) have shown that these assumptions are often violated by individuals. Individuals seem to have problems with sequential rationality already under perfect information (see for example Brandts & Figueras (2003) or Selten (1978)). Furthermore, studies have shown that individuals often believe that other individuals are not clever enough to behave rationally(e.g. documented by Fehr & Tyran (2001)) and therefore best-respond to some anticipated non-optimal behaviour. Moreover, the result of perfect inter-temporal price discrimination is
9
based on the ultimatum game logic. The failure of simple backwardinduction logic was %rst shown by (Guth, Schmittberger & Schwarze 1982). There responders are not content with pittances o#ered by the proposers and frequently reject low o#ers, even if rejection means a payo# of zero. Fehr & Schmidt (1999) explain this behaviour with inequality aversion, where rejections are a means of reducing inequality, as they enforce equality by destroying all surplus, leading to zero payo#s for both the proposer and the responder. If we relax the two assumptions a wide variety of behaviour in our two dynamic pricing scenarios can be rationalised. If e.g. consumers in the case of N > 1 believe that %rms will not undercut each other until they arrive at a price of zero, acceptances of relatively high prices (maybe even early in a market) become possible. Given that a consumer with a high valuation is more prone to accept early (or that %rms believe that) some price discrimination becomes possible in the last-minute scenario with N > 1. On the other hand, if the high valuation consumer does not foresee that a monopolist might charge a price close to his valuations as long as both consumers are in the market then in the last-minute scenario a monopolist might lose his price discrimination ability. A further limiting factor for price discrimination by a monopolist might work through inequality aversion. If the monopolist foresees that a customer is willing to reject "unfair" %nal-round o#ers even if a purchase would lead to a positive surplus then he may decrease the price in order to ensure a sale. On the other hand, if consumers are willing to accept equal splits of surplus immediately with positive probability, as suggetsed by many ultimatum-game experiments, then there might be the chance of price discrimination in markets with competition.10 Given that we believe that the behavioural assumptions above are not necessarily valid we cannot predict whether competition really eliminates (or at least reduces) inter-temporal price discrimination. To investigate this question further we implement the two scenarios from sections 1 and 2 in the laboratory and compare actual behaviour in markets with one %rm to that in markets with two %rms.
4
Experimental implementation
We used z-tree by Fischbacher (1999) to run nine sessions with a maximum of 24 participants each. Overall we had 190 participants. The subjects were assigned to di#erent treatments (monopoly - early bird, duopoly - early bird, monopoly - last minute or duopoly last minute). 10
Note that Fehr-Schmidt preferences alone are not su'cient for such behaviour. Their formulation of inequality aversion would predict that proposer competition rules out price discrimination.
10
Table 1 shows the treatments with the parameters, predicted purchase prices (pi ) and acceptance periods (t, t). Recall that ti denotes the period when a consumer with valuation vi enters the market, T gives the last trading period, and N is the number of %rms.
Early Bird t1 = 1, t2 = 6, v1 = 75, v2 = 100 Last Minute t1 = 1, t2 = 1, v1 = 45, v2 = 100
Monopoly T = 10, N = 1 p1 = 75, p2 = 100 t 5 0.37). The di#erences in the two last-minute treatments come from the fact that the duopolists were not able to start with prices both high enough to deter the low-valuation customers from buying early and at the same time low enough to lure the high-valuation customers into early acceptance. Figure 6 reveals that the acceptance pattern under a duopoly does not di#er between low and high-valuation customers. To the contrary, the monopolist can charge initial prices high enough for the low-valuation customers not to accept. Consequently, many high-valuation customers accept early, while more than 55% of the accepting low-valuation customers only do this in stage 10. 16
Median Trading Prices (Last-Minute Duopoly)
45
p1-duopoly
40
p2-duopoly
Price
35 30 25 20 15 1
2
3
4
5
6
7
8
9
10
Period
Figure 5: Development of the median trading prices (duopoly) over the 10 markets
5.2
Inter-temporal price discrimination dynamics
The tests above are only valid under some rather strict assumptions: the absence of serial correlation within a group and the absence of treatment speci%c time trends. In this section we use panel estimation to allow for serial correlation and treatment-speci%c time trends. However, this comes at a cost. We have to make assumptions on the distribution of the error terms, which might be problematic with our small sample. We estimate %xed-e#ect panel Probits for the two scenarios allowing for a general time and a treatment-speci%c time trend.13 The dependent variable is successful price discrimination as de%ned above. The Probit estimation shows that our preliminary understanding needs some correction when we control for serial correlation and treatmentspeci%c trends. In the early-bird scenario our observation that intertemporal price discrimination is observed slightly more often in the duopoly treatment becomes weakly signi%cant. The reason for this is that the downward trend in successful price discrimination in a duopoly is absorbed by the interaction competition×period. So we can say that the duopolists are initially better able to price discriminate, while this e#ect is eroded over time, as the monopolists learn how price discrimi13 Omitting the treatment-speci%c time trend yields very similar results as the nonparametric analysis. The treatment e#ects are very week and generally not signi%cant.
17
Duopoly
40 20 0
Pe rcen t
60
Monop ol y
0
5
10
0
5
10
a cce ptance sta ge for lo w-v alu ation cu sto me r (last m inu te) Graphs by t reat
Duopoly
40 20 0
Percent
60
Monop ol y
0
5
10
0
5
10
a cce ptance sta ge for hi gh- valuation cu stom er (last m inute ) Graphs by t reat
Figure 6: Acceptance stages in the last-minute scenario nation can be achieved.14 We can con%rm that in the early-bird scenario competition does not reduce the ability of %rms to price discriminate it rather enhances it. For the last minute treatment the results from the panel analysis con%rm the results we obtained from the non-parametric tests. Competition reduces the ability to price discriminate considerably. However, the gap between the two treatments is reduced over time.
5.3
Welfare
In our very simple setting in equilibrium all four situations should be e'cient. Ine'ciencies only arise if customers do not buy the good. Why should a customer reject an o#er in the last stage, when acceptance guarantees a positive payo#? In games with similar structure (like ultimatum games e.g.) responders readily reject pro%table o#ers in order to punish the proposer for making an unfair o#er. Rejection reduces not only the own payo# to 0 but also wipes out any surplus for the proposer. So if an individual wants to avoid disadvantageous inequality then rejection becomes an option. We would expect - if there are rejections at all that most of them come from low-valuation customers in the monopoly 14
This interpretation comes from a positive trend for price discrimination in both treatments, while the treatment-speci%c trend for the duopolist is negative.
18
discrim
early bird
last minute
N Log pseudo-likelihood P rob > 2
260 158.59 (< 0.01)
260 139.31 (< 0.01)
competition
0.73 (0.059)
1.34 (0.011)
competition×period
0.10 (0.083)
0.18 (0.007)
period
0.15 (< 0.001)
0.19 (< 0.001)
constant
1.08 (< 0.001)
0.53 (0.128)
0.11 (0.023)
0.41 (< 0.001)
Wald test (H0 :
u
= 0)
p-values in parentheses; ** sign. on 5%-level; * sign. on 10%-level
Table 4: Panel probit estimations of successful price discrimination treatments. Low-valuation customers may perceive the same o#er as much less fair than a high-valuation customer, as the relative surplus distribution is much more skewed in favour of the seller if viewed from the standpoint of the low-valuation customer. Additionally, we expect competition to lead to downward pressure on the prices and therefore to lower o#er prices, which are perceived as fairer and therefore result in less rejections in the duopoly treatments.
Monopoly Duopoly Total
Early Bird 175 75 0 117 10 13 114 1 5 231 11 18
Last Minute 145 100 45 85 44 2 115 5 0 200 49 2
0 9 0 9
Total 280 240 260
Table 5: Welfare by treatment and scenario
Table 5 shows the experimental frequencies of di#erent levels of surplus by treatment and scenario. Surprisingly, we observe that in the early-bird scenario rejections are more common among high-valuation 19
customers than among low-valuation customers (23 versus 13 in the monopoly and 6 versus 5 in the duopoly treatment). This can be explained by the shorter amount of time the high-valuation customer has to accept. In the last-minute setting we observe the expected pattern. Low-valuation customers reject more often (53 versus 11 in the monopoly and 5 versus 0 in the duopoly). This is easily explainable, as it becomes optimal for the monopolist (where the lion’s share of rejections happen) to price the low-valuation customer out of the market, whenever he cannot lure the high-valuation customer into early acceptance. Clearly, competition increases welfare in our experiment, even though that the underlying model does not predict this. Using the (pooled) frequencies from above and conducting chi-squared tests con%rms this suspicion: in both scenarios welfare is greater in the duopoly treatments (p < 0.01 in both cases). We also ran random e#ect ordered Probits in order to allow for correlation within markets. The non-parametric results are con%rmed by the panel analysis.
5.4
Distributional analysis
We have seen that competition enhances welfare, even though it does not perfectly eliminate price discrimination. Additionally, we neither observe marginal-cost pricing in the duopolies nor monopoly pricing in the monopolies. However, the analysis above has revealed that prices in the duopolies are lower. Here we investigate the impact of competition on distribution. Theoretically, the introduction of competition should shift the surplus entirely from the sellers to the consumers. We do not observe this extreme shift. However, there is a shift. We ran random e#ect Tobit regressions for the joint consumer surplus of the customers. The results are summarized in Table 6. In both scenarios competition increases consumer surplus only with experience. The treatment-period interaction is highly signi%cant. So consumers bene%t from competition only in later periods. We now turn to the sellers. There we would expect that competition decreases the producer surplus (pro%t). We compare the pro%ts of the monopolists with the joint pro%t the two duopolists achieve. The results are surprising. In the early-bird scenario competition has no inBuence on pro%ts. Even repetition does not bring the proftis closer to the predicted zero-pro%t outcome. In the last-minute scenario competition even tends to increase pro%ts initially, while this e#ect is %rst eroded and then overturned in later markets. The appropriate question is the following. Why don’t monopolists make signi%cantly higher profits than duopolists, even though they achieve higher sales prices? The reason is quite simple. The higher prices charged by monopolists lead 20
consumer surplus
early bird
last minute
N Log pseudo-likelihood P rob > 2
260 1197.56 (< 0.01)
260 1126.93 (< 0.01)
competition
11.43 (0.326)
1.49 (0.821)
competition×period
2.84 (0.017)
4.76 (< 0.001)
period
0.09 (0.915)
0.76 (0.177)
73.08 (< 0.001)
66.59 (< 0.001)
0.43 (< 0.001)
0.22 (< 0.001)
constant
Wald test (H0 :
u
= 0)
p-values in parentheses; ** sign. on 5%-level; * sign. on 10%-level
Table 6: Panel probit estimations of successful price discrimination to more rejections. The pro%t enhancing e#ect of higher sales prices is counteracted by the greater number of consumers not buying. However, as consumers learn that the monopolists will not really react to rejections with lower prices in later periods, rejections become less frequent and monopolists pro%ts increase.
6
Conclusion
In this paper we investigated the e#ect of the introduction of competition on market dynamics in settings where theory predicts that monopolists can price discriminate by changing posted prices over time, while duopolists cannot. We experimentally implemented two scenarios. In the early-bird scenario, the customer with the lower valuation for the good enters before the high-valuation customer. Price discrimination occurs when the low-valuation customer buys before the high-valuation customer enters. In the last-minute scenario both customer enter at the same time, while the valuations are so di#erent that price discrimination may occur when the high-valuation customer is lured into accepting early. We found that at least some price discrimination occurs in all but the duopoly treatment of the last-minute scenario, even though theory predicts no price discrimination in both duopoly treatments. In the 21
producer surplus
early bird
last minute
N Log pseudo-likelihood P rob > 2
260 1211.06 (0.209)
260 1125.22 (< 0.01)
competition
0.13 (0.326)
12.35 (0.079)
competition×period
1.90 (0.144)
2.95 (< 0.001)
period
0.50 (0.575)
0.53 (0.344)
73.33 (< 0.001)
59.83 (< 0.001)
0.23 (< 0.001)
0.30 (< 0.001)
constant
Wald test (H0 :
u
= 0)
p-values in parentheses; ** sign. on 5%-level; * sign. on 10%-level
Table 7: Panel probit estimations of successful price discrimination monopoly treatments we %nd less price discrimination than expected. Comparing the monopolists’ and the duopolists’ ability to price discriminate it is not clear that competition is actually harmful for the sellers. In the early-bird scenario competition even seems to enhance the ability to price discriminate initially, while with increasing experience this advantage is eroded. In the last-minute scenario we observe the opposite e#ect. Competition per se eradicates price discrimination opportunities. However, the monopolists loose their advantage with repetition. Competition enhances e'ciency in the experimental markets. Welfare is lower than predicted in all four treatments, as buyers sometimes deviate from the theoretical prediction by rejecting pro%table o#ers in the %nal stage of a market. However, the e'ciency loss is much smaller in the competitive treatments. The additional surplus created in the competitve treatments is appropriated by the consumers. Lower sales prices lead to increased consumer surplus in the duopoly treatments. In contrast, the producer surplus (equal to the pro%ts) is roughly the same in monopolies and duopolies. The higher sales prices in monopolies are counteracted by more consumers refusing to buy. In conclusion we %nd that the promotion of competition is bene%cial in markets where inter-temporal price discrimination is possible. It substantially increases consumer surplus, without strongly reducing pro22
ducer surplus; but the bene%cial e#ect on consumer surplus is by far not as strong as theory predicts. The monopolists had much less pricing power than predicted by standard theory, while the duopolists - also contrary to the prediction - were able to retain at least some pricing power. The most striking advantage of competition is the increase in total welfare. In a situation where demand is perfectly inelastic, we would not expect competition to have any positive inBuence on welfare; but it does. Somewhat lower prices signi%cantly reduce the number of disgruntled customers, who boycott the sellers for reasons of inequaltiy aversion. This (unexpected) welfare bonus renders competition a valuable force for achieving better market outcomes, despite of the fact that competition does not necessarily erradicate discriminatory price dispersion.
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