Consumer poaching, brand switching, and price transparency

Economics Letters 123 (2014) 266–269

Contents lists available at ScienceDirect

Economics Letters journal homepage: www.elsevier.com/locate/ecolet

Consumer poaching, brand switching, and price transparency Christian Schultz Department of Economics, University of Copenhagen, Denmark

highlights • • • • •

I model price transparency in markets with behavioral price discrimination. I examine effects of changes in price transparency. Increasing transparency reduces price discrimination and benefits consumers. Increasing transparency increases competition, lowers prices and profits. Brand switching and welfare effects depend on availability of long-term contracts.

article

info

Article history: Received 26 July 2013 Received in revised form 17 February 2014 Accepted 28 February 2014 Available online 12 March 2014 JEL classification: L 13 L 41

abstract This paper addresses price transparency on the consumer side in markets with behavioral price discrimination which feature welfare reducing brand switching. When long-term contracts are not available, an increase in transparency intensifies competition, lowers prices and profits, reduces brand switching and benefits consumers and welfare. With long-term contracts, an increase in transparency reduces the use of long-term contracts, leading to more brand switching and a welfare loss. Otherwise, the results are the same as without long-term contracts. © 2014 Elsevier B.V. All rights reserved.

Keywords: Behavioral price discrimination Oligopoly Price transparency Competition policy

1. Introduction In many markets firms know their customers’ identity. This enables them to poach potential new customers with an introductory discount. Such behavioral price discrimination is observed e.g., in mobile phone markets, insurance markets, and in newspaper subscriptions. In these markets it is not always easy to compare prices. This begs the question: what is the effect of behavioral price discrimination when some consumers are not well-informed about prices, i.e., where transparency on the consumer side is not perfect? Is an increase in transparency pro-competitive, as it usually is in markets without behavioral price discrimination? Many countries prohibit long-term contracts. In Denmark, for instance, it is illegal to tie consumers for more than half a year in mobile telephony market. Is that wise?

E-mail address: [email protected]. URL: http://www.econ.ku.dk/Cschultz. http://dx.doi.org/10.1016/j.econlet.2014.02.024 0165-1765/© 2014 Elsevier B.V. All rights reserved.

This paper addresses these questions. Building on Fudenberg and Tirole (2000) it introduces market transparency through a fraction of consumers who do not observe prices but have price expectations. I first consider the case where firms cannot offer long-term contracts. Forward-looking consumers realize that buying from a firm in the first period implies that it will not poach them with a low price in the second period. This lowers the elasticity of demand in the first period and lead to higher first period prices and less brand switching and lower prices in the second period as shown by Fudenberg and Tirole. I show that this effect is intensified when the transparency of the market is low since it makes the first period elasticity of demand even lower. In the second period more switching to a less preferred brand induces a further welfare loss. Hence, prices, price discrimination and brand switching are reduced and welfare improved if the market becomes more transparent. Long-term contracts make the firms compete over the larger long-term market; this intensifies competition, and thus the contracts are bad for firms as shown by Fudenberg and Tirole. Longterm contracts improve welfare, fewer consumers switch brand

C. Schultz / Economics Letters 123 (2014) 266–269

and prices in both periods fall. I show that the use of long-term contracts is larger when transparency is low, since the market then is even more profitable. Hence, when transparency increases, profitability decreases and firms offer fewer long-term contracts. This increases the contestable share of the market in the second period and induces more brand switching and a welfare loss. It hurts firms and benefits consumers: first period prices and second period poaching prices fall, while second period prices to old customers are not affected. The long-term contract price falls. Behavioral price discrimination has been studied extensively, see the surveys by Armstrong (2006) and Fudenberg and VillasBoas (2007). Market transparency has been analyzed for instance in Varian (1980), Stahl (1989), Schultz (2004, 2009), Sinitsyn (2009) and Gu and Wenzel (2011). To my knowledge, no papers consider the effect of market transparency under behavioral price discrimination. 2. Basics Consider a differentiated Hotelling market over two periods. Consumer x is located in x ∈ [0, 1], firm A in 0 and firm B in 1. Consumers know firms’ locations. Marginal costs are constant, normalized to zero. In each period, a consumer buys at most one unit. If she buys at price p from a firm located d away, her utility is V = u − p − td, where u > 0 and t > 0. Firms and consumers both have the discount factor δ ∈]0, 1]. A consumer can only visit one firm per period and only a fraction, φ , of consumers is informed about prices before deciding which firm to visit as in Varian (1980); φ is our measure of transparency. The uninformed consumers have rationally expected prices equal to the actual prices in equilibrium. Both information types are uniformly distributed on [0, 1]. We assume that 1 3



4

φ

−

1−φ

(φ + 2)2

 +

1 2

<

u t

2 + φ 3 − 2φ − φ 2



<

2φ 2 − φ − φ





 . 2

(1)

The first inequality ensures that the market is covered in equilibrium and the second a firm will not deviate to a high price and only serve the uninformed consumers. This ensures that a pure strategy equilibrium exists.1 Fulfilling both restrictions requires φ > φ ≈ 0.69. The firms know that a fraction φ of consumers are uninformed but not who they are. Firms do not know the consumers’ locations but in the second period they recall who were old customers so they can price discriminate: firm A offers pˆ A to repeat customers and pA to newcomers. We focus on a symmetric equilibrium, the uninformed consumers expect symmetric prices and those with x ≤ 1/2 buy from firm A and the rest from B. We solve the model backward (for a perfect Bayesian equilibrium).

267

First, consider firm A′ s turf, its old customers: informed consumers with x ≤ 12 + γ , where γ ≷ 0, and uninformed consumers with x ≤ 1/2. Here firm A offers pˆ A while firm B offers pB . As usual, we need to solve second period subgames on and off the equilibrium path. We therefore consider subgames in period two, where one firm, B, has set the equilibrium price in the first period and the other firm, A, has possibly deviated so the first period market shares may be non-symmetric. Since the firms are initially in a symmetric situation, this suffices for our purposes. The indifferent, informed consumer is located at 1

x pˆ A , pB =





2

+

pB − pˆ A 2t

,

while the indifferent, uninformed consumer is at x = α . Firm A′ s demand from its home turf is DAA = φ x pˆ A , pB + (1 − φ) α.





The uniformed consumers on A′ s turf have observed A′ s period one price. If A did not deviate in period one, γ = 0, and rational price expectations entail that pˆ eA = pˆ A (0) and peB = pB (0), where pˆ A (γ ) and pB (γ ) are second period equilibrium prices given γ . A deviation by firm A in period one is an out-of-equilibrium event and accordingly Bayes’ rule does not determine expectations. I assume that consumers understand that the non-symmetric market shares in period one, γ ̸= 0, imply, pˆ eA = pˆ A (γ ) and   e pB = pB (γ ), so α = x pˆ A (γ ) , pB (γ ) . One may alternatively assume that consumers have passive beliefs, which do not change after an out-of-equilibrium price has been observed in period 1. As it turns out the qualitative results reported here do not change.2 Firm A maximizes profit pˆ A DAA taking as given α . Taking the first-order condition and then inserting for α gives A′ s best reply pˆ A =

1 1+φ

(t + pB ) .

Firm B′ s demand on A′ s turf is



DBA = φ

1 2

     1 + γ − x pˆ A , pB + (1 − φ) −α . 2

(2)

Maximizing profit, pB DBA , and then inserting for α gives B′ s best reply pB =

pˆ A + 2t γ φ 1+φ

.

(3)

Solving for the equilibrium prices pˆ A (γ ) = pB (γ ) =

1+φ



2γ

φ (2 + φ) 

+

φ (2 + φ)

+

1



2+φ

t

and

2γ (1 + φ) 2+φ



(4) t.

Therefore 3. Behavioral price discrimination

α = α(γ ) =

1+φ 2 (2 + φ)

+

γφ 2+φ

.

In the second period, the timeline is: firms set prices, which are observed by the informed consumers only. Uninformed consumers form expectations depending on their observations in the previous period. Then consumers decide on purchases.

In the first period informed consumers x ≥ 1/2 + γ and uninformed consumers x ≥ 1/2 bought from B. The latter did not see A′ s first period price pA1 . In a symmetric equilibrium, they

1 The analysis of mixed strategies is bound to be very complicated. See Sinitsyn (2009) for an analysis in a differentiated Hotelling market with no behavioral price discrimination.

2 Due to the space constraint these results are not reported here but are available on request. I am grateful to a referee for pointing out that passive beliefs may be a realistic alternative to the belief formation assumed in the main text.

268

C. Schultz / Economics Letters 123 (2014) 266–269

believe that both firms set the same price in first period and shared the market equally. Hence, in period two they expect pˆ B (0) and pA (0). The location of the indifferent informed consumer on B′ s turf is x pA , pˆ B , and the indifferent uninformed consumer is located in

5. Equilibrium

β = x pA (0), pˆ B (0) . Hence, A′ s demand on B′ s turf is        1 1 DAB = φ x pA , pˆ B − +γ + (1 − φ) β − .

solving for the symmetric equilibrium gives the first period price:





2

 (5)

2

DBB = φ 1 − x pA , pˆ B





+ (1 − φ) (1 − β) .

The equilibrium prices are

(1 − 4γ ) φ + 2β (1 − φ) t and 3φ 3 − (1 + 2γ ) φ − 2β (1 − φ) t. pˆ B (γ ) = 3φ pA (γ ) =

pˆ A = pˆ B =



3+φ



γ

+

2 (2 + φ)

3

and

β=

3+φ 2 (2 + φ)

.

The equilibrium prices on B′ s turf are pA (γ ) =



4γ

1

 (6)

Firm A′ s second period profits are

2

+ (1 − φ) β −

1 2

.

(7)

4. First period demand Consumers will not receive a second period poaching offer from a firm they buy from it in period one. Consumers in the middle therefore switch brand in the second period. Forward-looking consumers understand this. The indifferent informed consumer is located in x = 12 + γ ; she switches brand and foresees second period prices, and hence



1





+ δ pB (γ ) + t 1 −   1 = pB1 + t 1 − +γ

pA1 + t

2

+γ 





1 2

+γ



+ δ pA (γ ) + t



1 2

3



1

φ

−

1−φ



(φ + 2)2

t,

(11)

(12)



1 2φ

−

(1 + φ) (2 + φ)2 φ



t,

are lowered when φ increases as a result of the more intense price competition.

6. Long-term contracts A long-term contract provides a consumer with a unit of good in both periods. When a firm sells long-term contracts at a price PA and also offers two consecutive short-term contracts to repeat customers, it has to be that PA = pA1 +δ pˆ A ; otherwise all customers would prefer one of the options. As Fudenberg and Tirole (2000), I assume that long-term contracts are taken by consumers who are most fond of the firm’s good.4 Hence, there is a cut off ψA , so that consumers with x ≤ ψA buy the long-term contract from A, consumers with ψA < x ≤ α buy two consecutive short-term contracts from A, and consumers with α < x ≤ 1/2 + γ buy from A and then B. The demand for firm A′ s second period short-term contract on its home turf becomes DAA = φ x pˆ A , pB − ψA + (1 − φ) (α − ψA ) .

 

2



δ

Proposition 1. Suppose long-term contracts are not available. An increase in transparency, φ , lowers first and second period prices, profits, and brand switching in the second period. It benefits consumers and total welfare and hurts firms.

πA2 (γ ) = pˆ A (γ )α(γ ) + pA (γ )     1 × φ x(pA (γ ), pˆ B (γ )) − +γ 

φ

+

1 1+φ t and pA = pB = t. (2 + φ) φ (2 + φ) φ

πA2 = πB2 =

t and − φ (2 + φ) 3   1+φ 2 pˆ B (γ ) = − γ t. φ (2 + φ) 3



1

Both are lowered when transparency, φ , increases. t The discount offered on the rival’s turf is pˆ A − pA = 2+φ . An increase in φ reduces the discount and brand switching: the in1+φ different consumer on A′ s turf is α(0) = 2(2+φ) , which increases in φ . Reduced brand switching lowers transportation costs benefiting welfare. As prices are also lowered, consumer welfare improves. Conversely, second period profits

Hence, x pA (γ ), pˆ B (γ ) =

p1 = pA1 = pB1 =

which is decreasing in φ . The first period profit of each firm is π1 = p1 /2. In equilibrium, the first period prices are the same, so γ = 0, and using (6) we get the second period prices3

B′ s demand on its turf is



In period one, firm A maximizes the total discounted profit,

ΠA = πA1 + δπA2 (γ ). Inserting πA1 = pA1 DA1 , (7), (9), (10) and





Hence, the best reply is

+γ



,

(8)

pˆ A =

1 1+φ

(t + pB − 2t ψA ) .

which using (4) and (6) gives

γ =

3 (pB1 − pA1 ) (2 + φ) 2 ((1 + 2φ) δ + 3 (2 + φ)) t

.

The indifferent uninformed consumer is x = DA1 = φ



1 2

+γ



1

+ (1 − φ) . 2

(9) 1 , 2

so A′ s demand is (10)

3 It is straightforward to verify that the relevant second-order conditions and non-negativity constraints are fulfilled. Furthermore (1) ensures that the market is covered in equilibrium and that it is not optimal for a firm to deviate to a high price and only serve the informed consumers. Hence, we have shown by construction that an equilibrium exists. 4 The idea is that in a more elaborate model involving uncertainty they would be least interested in the flexibility of two short run contracts.

C. Schultz / Economics Letters 123 (2014) 266–269

B′ s demand and best reply on the turf are still given by (2) and (3). Second period prices are pˆ A =

pB =

(2 + φ) φ

(13)

t,

and the indifferent consumer is

α (γ , ψA ) =

1 + φ + 2γ φ + 2ψA 2 (2 + φ)







.

(14)

+ (1 − φ) (ψB − β0 ) .

′

Prices on B s turf are pA =

2 (ψB − 1) + (1 − 4γ ) φ + 2β0 (1 − φ) 3φ

pˆ B = 1

4ψB − 1 − φ − 2γ φ − 2β0 (1 − φ) 3φ

t;

t,

and the indifferent consumers are

β (γ , ψ) =

1 + 2ψB + φ 2 (2 + φ)

1

+ γ

and β0 =

3

1 + 2ψB + φ 2 (2 + φ)

,

so second period prices on B′ s turf are

 pA =

(2 + φ) φ 

pˆ B =

2ψB − 1

4

− γ

 t

3

and

(2ψB − 1) (1 + φ) 2 − γ 3 (2 + φ) φ

(15)



t.

In the first period, the firms choose short-term contract prices, pA1 , pB1 , long-term contract prices, PA , PB , and the number of longterm contracts ψA and 1 − ψB . The indifferent, informed consumer buys though short-term contracts, is forward looking and switches brand. The indifference condition determining γ is given by (8) with poaching prices from (13) and (15) inserted

γ =

3 (φ (pB1 − pA1 ) (2 + φ) + 2t δ (ψA − (1 − ψB ))) 2φ ((1 + 2φ) δ + 3 (2 + φ)) t

(16)

  ΠA = pA1 DA1 + PA ψA + δ pˆ A DAA + pA DAB . Using PA = pA1 + δ pˆ A we get

     1 1 ΠA = pA1 φ + γ + (1 − φ) + δ pˆ A α (γ , ψA ) 2

      1 1 + δ pA φ β(γ ) − +γ + (1 − φ) β0 − . 2

2

1

φ

+δ

5φ − 2 6φ (φ + 1)



t.

Higher transparency, φ , lowers the price. Long-term contracts lower the first period short-term contract price, compare with (11). Furthermore, 1 2 − φ2 4 1+φ

,

(18)

so the number of long-term contracts, 2ψA , is decreasing in transparency φ . Inserting (18) into (13) gives second period equilibrium prices on A′ s turf pˆ A =

1 2

t

and pB =

1 2 (1 + φ)

t.

Long-term contracts lower second period equilibrium prices, compared with (12). Furthermore, an increase in transparency lowers B′ s poaching price, but does not affect A′ s short-term contract price to repeat customers. As is clear from (13) there is a direct effect lowering the price, and an indirect effect increasing the price: A offers fewer long-term contracts. These effects balance each other. The price reactions increase switching: inserting (18) 2+φ into (14) we find α = 14 1+φ , which is decreasing in φ . Thus total transportation costs increase and welfare decreases. Increasing transparency does not affect firm A′ s second period price to repeat customers but the first period price decreases, making consumers who buy from A in both periods better off. Of course, consumers who switch and experience lower prices in both periods are also better off. Total consumer welfare thus increases in φ . The total profit decreases. Proposition 2. Suppose long-term contracts are available. An increase in transparency lowers long-term contract prices, first period prices and second period poaching prices, while second period prices to repeat customers are unchanged. Firms offer fewer long-term contracts when transparency increases and total welfare falls as switching increases, firms profit fall and consumer welfare increases. Long-term contracts increase α ; thus fewer consumers switch brand and welfare improves. Furthermore, all prices are lower, so consumer welfare improves and profits decrease. The firms are in Prisoners’ Dilemma like situation, a ban on long-term contracts would improve profits. References

.

A′ s total discounted profit is

2



ψA = 1 − ψB =

When more customers are locked into long-term contracts, firm A prices more aggressively on the contestable part of its home turf, α is increasing in ψA . On B′ s turf, the demand for A′ s second period short-term contract is still given by (5). Consumers with x ≥ 1 − ψB have bought B′ s long-term contract. The demand for firm B′ s second period short-term contract is DBB = φ ψB − x pA , pˆ B

equilibrium pA1 = pB1 and ψA = 1 − ψB ; thus p1 = pA1 = pB1 =

(1 − 2ψA ) (1 + φ) + 2γ φ t and (2 + φ) φ 1 − 2ψA + 2γ φ (1 + φ)

269

(17)

Firm A maximizes ΠA w.r.t. pA1 and ψA . Inserting (13), (14) and (16) into (17) and maximizing gives best replies. In a symmetric

Armstrong, M., 2006. Recent developments in the economics of price discrimination. In: Blundel, R., et al. (Eds.), Advances in Economics and Econometrics Theory and Applications, Ninth World Congress. In: Econometric Society Monographs, vol. 42. Cambridge University Press. Fudenberg, D., Tirole, J., 2000. Consumer poaching and brand switching. Rand J. Econ. 31 (4), 634–657. Winter. Fudenberg, D., Villas-Boas, M.J., 2007. Behavior-based price discrimination and customer recognition. In: Economics and Information Systems, Volume 1. Elsevier Science, Oxford. Gu, Y., Wenzel, T., 2011. Transparency, price-dependent demand and product variety. Econom. Lett. 110 (3), 216–219. Schultz, C., 2004. Market transparency and product differentiation. Econom. Lett. 83 (2), 173–178. Schultz, C., 2009. Transparency and product variety. Econom. Lett. 102 (3), 165–168. Sinitsyn, M., 2009. Price dispersion in doupolies with heterogeneous consumers. Int. J. Ind. Organiz. 27, 97–205. Stahl, D.-O., 1989. Oligopolistic pricing with sequential consumer search. Amer. Econ. Rev. 79 (4), 700–712. Varian, H., 1980. A model of sales. Amer. Econ. Rev. 70 (4), 651–659.