Designing Price Contracts for Boundedly Rational Customers: Does the Number of Block Matter?

Transcription

1 Designing Price Contracts for Boundedly ational Customers: Does the Number of Block Matter? Teck H. Ho University of California, Berkeley Forthcoming, Marketing Science Coauthor: Noah Lim, University of Houston February 2007 Teck H. Ho

2 Outline Motivation Does the Number of Block Matter? Economic Hypotheses A Behavioral and General Approach February 2007 Teck H. Ho 2

3 Motivation B2C B2B Integration of economics and psychology Combine the strengths of economics and psychology Lack of behavioral data in real B2B settings Study laboratory B2B settings February 2007 Teck H. Ho 3

4 Integration of Economics and Psychology Johnson 2006 February 2007 Teck H. Ho 4

5 Behavioral Economics Models Ho et al February 2007 Teck H. Ho 5

6 Examples of Pricing Contracts Total Cost to Buyer Linear Two-part Tariff Total Cost to Buyer Quantity Three-part Tariff Multi-Block Tariff Quantity February 2007 Teck H. Ho 6

7 A Simple Framework Number of Block Single Multiple No Linear Block-tariff 2B vs. 3B Fixed Fee Yes Two-part Tariff Three-part Tariff February 2007 Teck H. Ho 7

8 Does Number of Block Matter? Number of Block Single Multiple No Linear Block-tariff 2B vs. 3B Fixed Fee Yes Two-part Tariff Three-part Tariff February 2007 Teck H. Ho 8

9 esearch Question Does the Number of Block Matter Empirically? Total surplus generated from trading Division of surplus e.g., which format favors the seller February 2007 Teck H. Ho 9

10 A B2B Market: The Mapping between eal and Laboratory Settings Independent Example Manufacturer seller C = 20 etailer Buyer Price Single Demand = 00 - price Which Type of Pricing Contract to Use? Price Contract Price February 2007 Teck H. Ho 0

11 Integrated Manufacturer and etailer Integrated Manufacturer Profits Manufacturer C = * Assume equal division 800 O etailer Price* = etailer Profits Demand = 00 - price February 2007 Teck H. Ho

12 Linear Price Total Cost to etailer W Linear Quantity Independent Manufacturer C = 20 Manufacturer Profits 600 W*= A O etailer Price*= etailer Profits Demand = 00 - price Total Surplus Integrated > Total Surplus Independent February 2007 Teck H. Ho 2

13 Two-Block Tariff Total Cost to etailer W W2 2-Block Tariff X Quantity Manufacturer C= 20 Manufacturer Profits 600 W, X, W2 = 20 M M=W-W2X etailer Price* = 60 Demand = 00 - Price M 600 etailer Profits February 2007 Teck H. Ho 3

14 Number of Block: 2B vs. 3B Total Cost to etailer 2B w2 Total Cost to etailer w 3B w2 w w0 x Quantity x0 x Quantity W2 = 20 2B & 3B M = W-W2X 2B = W0-W2X0 + W-W2X-X0 3B February 2007 Teck H. Ho 4

15 February 2007 Teck H. Ho 5. evenue Equivalence Strong Manufacturer Profits π M etailer Profits π Y Y Y Y M X X X X M π κ δ π π κ δ π + = + = 600 = = Y X δ δ = = Y X κ κ Constraints: X Y X = 2B ; Y = 3B

16 February 2007 Teck H. Ho 6 2. evenue Equivalence Weak 6 6 X 0 Y Y X δ δ = Y Y Y Y M X X X X M π κ δ π π κ δ π + = + = Constraints: = = Y X κ κ Manufacturer Profits π M etailer Profits π X = 2B ; Y =3B

17 February 2007 Teck H. Ho 7 3. Division Equivalence 0 X Y Manufacturer Profits π M etailer Profits π Y Y Y Y M X X X X M π κ δ π π κ δ π + = + = Y X κ κ = 0 = = Y X δ δ Constraints: X = 2B ; Y = 3B

18 Empirical Equivalence Manufacturer Profits π M 6 X = Y 0 X = 2B ; Y = 3B 6 etailer Profits π February 2007 Teck H. Ho 8

19 Testable Hypotheses Total Pie H H2 M s Share of Pie 00% 67% H3 H4 2 3 Number of Block 2 3 Number of Block February 2007 Teck H. Ho 9

20 Economic Experiments Vary Number of Blocks : -Block Linear Price, 2-Block tariff, and 3- Block tariff Price contracts. Subjects are business students and working managers. Subjects were told the following: Decision-making experiment and they will earn cash according to the decision points they obtain. subjects per session with rounds. 2 sessions per contract. Each subject is randomly matched with another subject only once. They will either be a ED player Manufacturer or BLUE player etailer in each round. ED sells a product to BLUE, who in turn sells it to a group of customers. ED s unit cost is 20. Customers Demand is Quantity =00-Price. February 2007 Teck H. Ho 20

21 Subjects Decisions 2-Block and 3-Block tariffs between-subjects: ED offers BLUE a quantity discount contract. ED chooses X, Y and Break w, w2 and x respectively. In 3-Block contract, we fixed w0 and x0 to control for decision complexity. Total Cost to etailer Total Cost to etailer w2 w w2 w 00 x 8 x Quantity Quantity February 2007 Teck H. Ho 2

22 Subjects Payoffs BLUE observes ED s contract offer of w, w2 and x. BLUE chooses Price, which determines Quantity sold according to Quantity = 00 Price. E.g., For 2-Block tariff: If Quantity Break, ED profits = [X- 20] * Quantity BLUE profits = [PICE X] * Quantity If Quantity > Break, ED profits=[x*break]+[y*quantity Break] [20*Quantity] BLUE profits=[price*quantity] [X*Break] [Y*Quantity Break] BLUE can also eject the contract and both players earn zero points. February 2007 Teck H. Ho 22

23 Students versus Managers Managers Full-time and Part-time MBA students, Stake Size Doubled, Groups of 4, Instructions given out 7 days in advance. 2-Block Tariff Undergrad MBA 2 t-stat N=0 N=36 v 2 Efficiency 80% 83% M s share of total profits 65% 68% -.27 Conditional on retailer accepting contract. February 2007 Teck H. Ho 23

24 Scatter-Plots: 2- versus 3-Block π M 2-Block Tariff π π M 3-Block Tariff π February 2007 Teck H. Ho 24

25 H and H3: - versus 2-Block Theory Actual Theory Actual t-stat Prediction -Block -Block Prediction 2-Block 2-Block 2 v Efficiency 75% 67% 00% 8% H: 5.24* Manufacturer s Share of Profits 67% 64% 00% 65% H3: 0.80 *significant at the 5% level. Conditional on etailer accepting contract. February 2007 Teck H. Ho 25

26 H2 and H4: 2- versus 3-Block Theory 2-Block 3-Block t-stat Prediction 2 v 3 w * Price * Efficiency H2: 2B=3B 8% 95% -6.55* 00% M s Share of Total Profits H4: 2B=3B 00% 65% 73% -4.03* *significant at the 5% level Conditional on etailer accepting contract February 2007 Teck H. Ho 26

27 Empirical egularities Total Pie H H2 M s Share of Pie 00% 67% H3 H4 2 3 Number of Block 2 3 Number of Block February 2007 Teck H. Ho 27

28 Quantal esponse Equilibrium QE Empirical Puzzle : etailer choose to buy in the last block less often in 2-Block vs. 3-block only 60% compared to 83% for accepted contracts, whereas theory predicts retailer doing so all the time. QE Model: Allow etailer to be less than perfectly sensitive to payoffs across blocks i.e., noisily best respond eject Left l 0 U ight Last Block q x q > x r U February 2007 Teck H. Ho 28

29 February 2007 Teck H. Ho 29 QE Model Cont d Assume that the retailer follows a multinomial logit choice rule so that the probability of the retailer choosing ight is Parameter γ captures the sensitivity to differences in monetary payoffs. Manufacturer takes retailer s decision rule into account. Sets the contract by maximizing the following expected profit function: r l r U U U e e e γ γ γ + + r.π M + r l r U U U e e e γ γ γ r l U U e e γ γ + + = Ε M π l M U U U r l l e e e π γ γ γ.

30 eference-dependent Payoffs Total Cost to etailer W X W2 2-Block Tariff Quantity Empirical Puzzle 2: w2 and Price are higher in 2-block vs. 3-Block etailer s wants lower adjacent marginal price it pays to apply to the previous block. Let β be the value of every counterfactual dollar. Example: For 2-Block tariff, etailer s Utility is: U = U r l l U = π r = π β w w2 x if if 0 < q q > x x February 2007 Teck H. Ho 30

31 February 2007 Teck H. Ho 3 Model Estimation Manufacturer s decisions are iid with a bivariate normal density: and are the equilibrium predictions solved numerically of the QE model with counterfactual profits. Estimate common β and contract-specific γ. * w * w * 2 * , ~ w w w w w w it it w w N w w σ σ σ ρ σ σ ρ σ

32 February 2007 Teck H. Ho 32 Likelihood Function Log-Likelihood function for each contract is: =,,,, 2 2 ρ σ σ γ β w w LL where = Σ }.ln ight.ln Left.ln eject 2 ln 2 ln2 { Ω Ω Σ Σ = = r l r r l l r l U U U it U U U it N i T t U U it e e e e e e e e γ γ γ γ γ γ γ γ π w w w w w w σ σ σ ρ σ σ ρ σ and = Ω * 2 2 * w w w w it it

33 Estimation esults Parameters Full Model Nested Model γ = 2B γ 3B =0.2* Nested Model β=0 β γ 2B γ 3B LL *To approximate large value of γ. Figures in parentheses are the t-statistics. February 2007 Teck H. Ho 33

34 Model Predictions: 2 Block Variable w w2 Actual Data Predictions Left ight eject Conditional Efficiency m % 65.3% % 67.9% February 2007 Teck H. Ho 34

35 Model Predictions: 3 Block Variable W w2 Actual Data Predictions Left ight eject Conditional Efficiency m % 72.7% % 77.4% February 2007 Teck H. Ho 35

36 Future esearch A mini field application project at HP Field data B2B pricing contract data from HP Other pricing contracts Two-part tariff vs. quantity discount contract B2C settings mobile phone plans, 3-block tariffs February 2007 Teck H. Ho 36

37 HP Printing Division Go-to-Market Strategy Design and Analysis Business Objective Optimize incentives for IPG new product business Policy Issues Fixed vs % target before discount kicks in 2-block versus 3-block tariffs esearch esults Fixed threshold better quantity discount policy 3-block is better for several retailers Business esults HP adopted all recommendations Experimental Design Stanford students as subjects held at HP Labs One new and one old product in IPG Commercial Value-added eseller Program Demand model calibrated with business inputs eseller competence / sales activity modeling Demand drivers February 2007 Teck H. Ho 37

38 Does Contract Framing Matter? Number of Block Single Multiple No Linear Block-tariff 2B vs. 3B Fixed Fee Yes Two-part Tariff Salient vs. Opaque Three-part Tariff February 2007 Teck H. Ho 38

39 February 2007 Teck H. Ho 39

40 February 2007 Teck H. Ho 40

41 A Tighter Test of H2 Define Z = 600-Total Profits. Let Z be distributed with density fz for Z>0, where fz is exponential with parameter λ. f0=0. Let y be the probability that Z=0. Likelihood function of Z with n observations: L y, λ = n i = { y I Z if Z = 0, where I Z = 0 otherwise + y Z} Key is to test whether model where values of y and λ are equal across the 2 and 3 Block contracts can be accepted. February 2007 Teck H. Ho 4 f

42 Parameter Estimates and L- Tests Parameters Exponential Constraints Exponential y 2B y 3B Unconstrained Model -LL λ 2B y 2B =y 3B * λ 3B LL λ 2B = λ 3B * All estimated parameters are significant. y 2B =y 3B, λ 2B = λ 3B * February 2007 Teck H. Ho 42

43 Testable Hypotheses H: Total channel profits increase as the number of blocks in a price contract changes from to 2. H2: Total channel profits remain unchanged as the number of blocks changes from 2 to 3 H3: Manufacturer s share of total profits increases from 66.7% in the -Block contract to 00% in the 2-Block contract. H4: Manufacturer s share of total profits remain unchanged at 00% as the number of blocks increases from 2 to 3. February 2007 Teck H. Ho 43

44 Empirical egularities. Total profits increases as number of blocks increases from to 2. H supported 2. Total profits increases even as number of blocks increases from 2 to 3 H3 not supported 3. Manufacturer s share of profits does not increase as number of blocks changes from to 2 H2 not supported. 4. Manufacturer s share of profits increases as number of blocks changes from 2 to 3, but still far below the 00% predicted H4 not supported. February 2007 Teck H. Ho 44