A Comparison of the Wholesale Structure and the Agency Structure in Differentiated Markets. Liang Lu

Transcription

1 A Comparison of the Wholesale Structure and the Agency Structure in Differentiated Markets Liang Lu 1

2 Vertically-Related Markets Suppliers and consumers do not deal directly An economic agent who o Purchases from suppliers for resale to final consumers wholesale structure Examples: grocery stores, florists 2

3 Vertically-Related Markets Suppliers and consumers do not deal directly An economic agent who o Helps suppliers and consumers transact and receives a share agency structure Examples: booking.com, ebay (fixed price listing) 3

4 Vertically-Related Markets Suppliers and consumers do not deal directly An economic agent who o Purchases from suppliers for resale to final consumers o Helps suppliers and final consumers transact and receives a fee Price setting 4

5 Wholesale Structure Chicago approach ( ) Contractual obligations Powerless retailers Dobson and Waterson (1999) Differentiation in retailers More concentrated over time o e.g. supermarkets Further significant changes are on the way as a result of Internet retailing Double marginalization 5

6 Agency Structure Characterized by o Supplier pricing o Retailer revenue-sharing Online platforms/e-tailers o Typically large and can dictate contract terms 6

7 Literature Theoretical Device o Gans (2012), Gaudin and White (2013) The Most Favored Nation (MFN) clause o Foros, et al. (2013), Johnson (2013b, 2014) Consumer lock-in o Johnson (2013a) Asymmetric information o Hagiu and Wright (2013), Condorelli et al. (2014) 7

8 Literature Theoretical Device o Gans (2012), Gaudin and White (2013) The Most Favored Nation (MFN) clause o Foros, et al. (2013), Johnson (2013b, 2014) - Baseline comparison Consumer lock-in o Johnson (2013a) Asymmetric information o Hagiu and Wright (2013), Condorelli et al. (2014) 8

9 Johnson (2014) Comparison of wholesale and agency structures Double marginalization under the agency model Nested random-utility model Equilibrium outcomes o P W > P A, π W > π A o π S W > π S A, π R W < π R A Full market coverage assumption 9

10 Foros et al. (2013) Comparison of supplier pricing and retailer pricing under revenue-sharing contract Differentiated demand system by Dobson and Waterson (1996, 2007) Equilibrium outcomes o P S > P R if competitive pressure is higher among retailers than among suppliers 10

11 Literature Empirical o Santos and Wildenbeest (2014) Broader literature Vertical restraints o RPM and consumers relative sensitivity towards competition (Winter, 1993). o Revenue-sharing contracts (Dana and Spier, 2001) Strategic delegation o Principal and agent approach (Bonanno and Vickers, 1988) Theory of intermediaries o Bargaining in networks with asymmetric information (Hagiu, 2006) o Dealer (wholesale) or platform operator (agency) (Belleflamme and Peitz, 2010) 11

12 Research Questions Compare outcomes under wholesale and agency structures To what extent is the agency structure retaileradvantaged? The preferences of suppliers and retailers in terms of structure choice How would levels of differentiation at both layers of the supply and distribution chains determine firms preferences? 12

13 Model Bilateral duopoly o Two suppliers, j = 1, 2 and two retailers, i = 1, 2 o Each supplier j produces a single good j and distributes to both retailers who reach final consumers o Assume zero costs for all firms 13

14 Model Direct demand system (Dobson and Waterson,1996 and 2007) q i j = 1 β 1 γ p j i + γp j i + β(p j i (1 β 2 )(1 γ 2 ) γp j i ) o The parameter γ [0,1) captures level of competition between goods o The parameter β [0,1) captures level of competition between retailers Contractual structures o Wholesale o Agency 14

15 Timing Under wholesale 1. Suppliers simultaneously set wholesale prices w i j 2. Retailers simultaneously set final prices p i j 15

16 Optimization Problems Under wholesale At Stage 2, R i solves max π p 1 i, p 2 R i = max [(p i p 1 i, p 2 i 1 w 1 i )q 1 i + (p 2 i w 2 i )q 2 i ] i At Stage 1, S j solves max j j πsj = max [w j j j 1 q j 1 + w j 2 q j 2 ] w 1, w2 w 1, w2 16

17 Timing Under agency 1. Retailers simultaneously declare the revenue-sharing rates α i [0,1] to suppliers 2. Suppliers simultaneously set final prices p j i. Revenue generated is split according to α i 17

18 Optimization Problems Under agency At Stage 2, S j solves max j j πsj = max [ 1 α j j 1 p j 1 q j α 2 p j 2 q j 2 ] p 1, p2 p 1, p2 At Stage 1,R i solves max α i π Ri = max α i [α i (p i 1 q i 1 + p i 2 q i 2 )] 18

19 Symmetric Equilibrium Under wholesale o w i j w γ o p i j p β, γ o q i j q β, γ Under agency o p i j p i (β, γ, α i ) increasing in α i o Foros et al. (2013) prove that α = α 1 = α 2 is a Nash equilibrium if β > γ o p i p γ o q i j q β, γ 19

20 Equilibrium Outcomes Wholesale (W) Agency (A) Wholesale price (w) 1 γ 2 γ - Revenue sharing rate (α) - (2 γ)(1 β 2 ) 2 γ(1 + β) Final price (p) 1 β 2 γ + 1 γ (2 β)(2 γ) 1 γ 2 γ 20

21 Equilibrium Outcomes Wholesale (W) Agency (A) Final price (p) 1 β 2 γ + 1 γ (2 β)(2 γ) 1 γ 2 γ Demand (q) 1 (1 + β)(1 + γ)(2 β)(2 γ) 1 (1 + β)(1 + γ)(2 γ) Supplier profit (π Sj ) 2 1 γ 2β 1 γ [2β γ(1 + β)] 1 + β 1 + γ 2 β 2 γ 2 (1 + β) 1 + γ 2 γ 2 [2 γ(1 + β)] Retailer profit (π Ri ) 2(1 β) 2(1 β)(1 γ) (1 + β)(1 + γ)(2 β) 2 (2 γ) γ 2 γ [2 γ(1 + β)] Lemma 3. If the retailer market is approaching perfect competition, i.e., β 1, outcomes under wholesale and agency structures are the same. 21

22 Comparison Price & Demand Proposition 1. In equilibrium, final price is lower, quantity demanded is higher under the agency structure than under the wholesale structure, irrespective of levels of differentiation at both layers. 22

23 Comparison Supplier Profit Proposition 2. In equilibrium, π Sj W > π Sj A, a supplier always prefers the wholesale to the agency structure, irrespective of levels of differentiation at both layers. 23

24 Comparison Retailer Profit Observation 1. Suppose that β and γ are equally likely to take up any value over the interval 0,1. There are more combinations of β and γ such that a retailer prefers agency to wholesale structure than those such that a retailer prefers wholesale to agency structure. 24

25 Comparison Retailer Profit Observation 2. When the level of supplier differentiation (competition) is not too low (high), a retailer always prefers agency to wholesale structure, irrespective of own levels of differentiation. 25

26 Imperfect competition Wholesale (W) Supplier profit π Sj / β < 0 if β 1 2 ; > 0 if β > 1 2 π Sj / γ < 0 Retailer profit π Ri / β < 0 π Ri / γ > 0 Lemma 5. Suppose that the wholesale structure is in place. Retailers will unambiguously prefer a market where the level of supplier differentiation (competition) is low (high) and the level of retailer differentiation (competition) is high (low). Suppliers will unambiguously prefer a market where the level of supplier differentiation (competition) is high (low) and the level of retailer differentiation (competition) is very low (high). 26

27 Imperfect competition Price effect VS Substitution effect 27

28 Imperfect competition Wholesale (W) Agency (A) p/ β < 0 - Final price p/ γ < 0 < 0 Demand q/ β < 0 if β 1 2 ; > 0 if β > 1 2 < 0 q/ γ < 0 if γ 1 2 ; > 0 if γ > 1 2 < 0 if γ 1 2 ; > 0 if γ >

29 Conclusion We compare wholesale and agency structures in a simple bilateral duopoly differentiated demand system We find the preferences of suppliers and retailers in terms of structure choice We analyse how these preferences are determined by levels of differentiation at both layers of the market Firms incentives are better aligned under the agency structure Thank you! 29