March 25, 2006 Teck Ho

Overview of Experiment

• 2 Markets, A and B

• Each Market lasts for 6 rounds

• Each group plays 3 times in Market A and 3 times in Market B

• Each group is matched with another group only once

• In each round, role is either Manufacturer or Retailer

March 25, 2006 Teck Ho

Overview of Both B2B Channel Markets• Manufacturer’s marginal cost is 20• Manufacturer either chooses a simple wholesale

price X (in Market A) or a quantity discount contract: X, Y and Break (integers from 0 to 100) (in Market B)

• X must be greater than Y (since it is quantity discount contract) in Market B

• Retailer chooses to Accept or Reject the offer• If Retailer Accepts, she chooses the Retail Price• Retail Price chosen determines Quantity and payoffs

for both players• If Retailer Rejects, round ends. Both players earn 0

points

March 25, 2006 Teck Ho

Demand Facing the Retailer

• In both markets, Retailer sees a simple linear demand

• Demand = 100 – Retail Price

• If retail price = 20,

demand = 100 – 20 = 80

• If retail price = 50

demand = 100 – 50 = 50

March 25, 2006 Teck Ho

Market A: Computation of Payoffs

M’s payoffs

= [X-20]* QUANTITY

R’s payoffs

= [PRICE – X]*QUANTITY

Total Cost to Retailer

QUANTITYQ

xQ

Quantity Q = 100 – Retail Price

March 25, 2006 Teck Ho

Market A: Sample Linear Price Contract

If Price = 80M’s payoffs = [45 - 20]*20 = 500 R’s payoffs = [80 - 45] *20 = 700

If Price = 55M’s payoffs = [45 - 20] *45 = 1125 R’s payoffs = [55-45] *45 = 450

Total Cost to Retailer

20 45 QUANTITY

X = 45

2000

1000

Price 80 55

March 25, 2006 Teck Ho

Market B: Computation of Payoffs

If QUANTITY < = BREAK, M’s payoffs = [X-20] * QUANTITY R’s payoffs = [PRICE-X] * QUANTITY

If QUANTITY > BREAK, M’s payoffs = [(X - 20) * BREAK] + [(Y-20) * (QUANTITY – BREAK)]R’s payoffs = [PRICE * QUANTITY] – [X * BREAK + Y * (QUANTITY – BREAK)]

Total Cost to Retailer

Q1 Break Q2 QUANTITY

X x Break+ Y x (Q2- Break)

X x Q1

March 25, 2006 Teck Ho

Market B: Sample QD Contract 1

Total Cost to Retailer

X = 50Y = 25BREAK=20

10 20 50 QUANTITY

1750

500

Price 90 50

If QUANTITY = 10 (< = 20), M’s payoffs = [50-20] * 10 = 300R’s payoffs = [90-50] * 10 = 400

If QUANTITY = 50 (> 20), M’s payoffs = [(50 - 20) * 20] + [(25-20) * (50 – 20)]=750R’s payoffs = [50 *50] – [50 * 20 + 25 * (50 – 20)] = 750

March 25, 2006 Teck Ho

Market B: Sample QD Contract 2

Total Cost to Retailer

X = 45Y = 20BREAK=25

20 25 60 QUANTITY

1825

900

Price 80 40

If QUANTITY = 20 (< = 25), M’s payoffs = [45-20] * 20 = 500R’s payoffs = [80-45] * 20 = 700

If QUANTITY = 60 (> 25), M’s payoffs = [(45 - 20) * 25] + [(20-20) * (60 –25)] = 625R’s payoffs = [40 *60] – [45 * 25 + 20 * (60 – 25)] = 575

March 25, 2006 Teck Ho

Deciding the Winner

• Each group’s total earnings is the sum of its earnings either as a manufacturer or a retailer in all six decision rounds

• The group who has the highest total earnings will win a prize of

$40 (Ho & Ho Foundation) + $5 / Group = $100

March 25, 2006 Teck Ho

Simple Rules to Follow

• In each decision round, manufacturers and retailers will be given 5.5 and 3.5 minutes to make their decisions respectively and --a prompt will appear when the time limit expires

• Do not click on the BACK button on the browser to return to a previous page--make sure the value you entered in the decision box is correct before clicking on the CONTINUE button. – Clicking on the BACK button to enter a new value will

not work and may cause the system to behave erratically

March 25, 2006 Teck Ho

Experiment Starts Here

http://128.32.67.154/contractdesign2/

March 25, 2006 Teck Ho

Steps in Designing B2B Contracts

• Figure out the maximum possible pie • Choose a contract structure that makes the maximum

pie achievable (linear versus quantity discount (QD))• Pick the right parameters to achieve the maximum pie

(Linear: X; QD: X, Break,Y)• Pick the right parameters to divide the pie based on

relative bargaining power (Linear: X; QD: X, Break, Y)

• Ensure voluntary and incentive-compatible participation (i.e., retailers will choose the “right way”)

March 25, 2006 Teck Ho

What is the Maximum Pie?

• Suppose manufacturer and retailer work as a team (marginal cost = 20)

• Profits are:(Price – 20)*Quantity = (Price – 20) x (100 – Price)

• Optimal retail price is 60 and quantity = 40

• Profits = 1600

March 25, 2006 Teck Ho

Joint Decision: Optimal Retail Price

SalesQuantity

$60$20

40

Price$100

Quantity = 100 - Price

March 25, 2006 Teck Ho

Which Contract Form?

• Linear Wholesale Price Contract

• Nonlinear Whole Price Contract– Block tariffs

March 25, 2006 Teck Ho

Linear Wholesale Price Contract • Suppose Manufacturer offers Retailer a linear wholesale price

X. Marginal Cost is 20.• Demand is: Quantity = 100 – Price • Manufacturer’s profits = (X-20) * (100 – Price(X)) • Retailer’s profits = (Price – X)* (100 – Price)• Optimal Decisions:

– Price(X) = (100 + X )/2– X=60, Price=80, Quantity = 20– M’s profits = 800, R’s profits = 400– Total profits = 1200

• Total profits are 75% of the maximum possible profits (1600)• Can Quantity Discounts Schemes Increase the Pie?

March 25, 2006 Teck Ho

Independent Channel Members

Manufacturer

Retailer

20

Price

X

Quantity=100-Price

March 25, 2006 Teck Ho

Linear Pricing Contract:

Optimal Retail Price: SalesQuantity

Price (X)= ($100 + X)/2

$X Price$100

Quantity = 100 - Price

100- Price (X)

March 25, 2006 Teck Ho

How to Achieve Maximum Pie?

• Marginal cost to the retailer = 20

• Optimal retail price = 60

March 25, 2006 Teck Ho

Market B: Optimal Design

Total Cost to Retailer

Q1 Break Q2 QUANTITY

X x Break+ Y x (Q2- Break)

X x Q1

• Choose X and Break to divide the pie

• Manufacturer makes (X-20)*Break

Y=20

March 25, 2006 Teck Ho

Market B: Optimal Design

Total Cost to Retailer

X = 45Y = 20BREAK=32

32 QUANTITY

If QUANTITY (< = 32)Price >= 68, Optimal Price = 72.5 M’s payoffs = [45-20] * 27.5 = 687.5

R’s payoffs = [72.5-45] *27.5 = 756.25

If QUANTITY (> 32)Price < 68, Optimal Price = 60 M’s payoffs = [(45 - 20) *32] + [(20-20) * (40 –25)] = 800

R’s payoffs = [60 *40] – [45 * 32 + 20 * (40 – 32)] = 800

March 25, 2006 Teck Ho

Market B: 2-Block Tariffs

• Manufacturer sets Y = 20 to achieve the maximum pie• Retailer chooses Price = 60, Quantity = 40• Manufacturer chooses X and Break to divide the pie

based on the relative bargaining power • Manufacturer earns (X-20)*Break leaving Retailer 1600

– (X-20)*Break• A possible optimal contract:

– X=45, Y=20, Break = 32 (or X = 60, Y=20, Break=20)

– M’s Profits = 800, R’s Profits = 800, Total = 1600

March 25, 2006 Teck Ho

Summary• Figure out the maximum possible pie!

• Choose a contract structure and the right parameters to achieve the maximum pie

• Divide the pie based on bargaining power

• Ensure voluntary and incentive-compatible participation (it is the interest of the retailer to choose accordingly)