Discussions
budsimpson
supplychain15.pptDesigning Supply Contracts: Contract Type and Information Asymmetry
Authors: C. Corbett, C. S. Tang
Presenter: T.J. Hu
Contents
- Introduction
- Literature
- Model
- Supplier's Optimal Supply Contracts
- Comparisons
- Numerical Examples
- Conclusions
- Future Research
Introduction
The Supply Chain
Supplier
Buyer
L(q)
w(q)
p(q)
s
cost c
C ~ F(•)
Supplier's Concerns:
- The types of contracts
- Information about the buyer's cost structure
Three Types of Contracts
1. One-part linear contract: w
2. Two-part linear contract: w, L
3. Two-part nonlinear contract: {w(q), L(q)}
Six Scenarios
Type of contracts
Full information
Asymmetric information
One-part linear: w
F1
A1
Two-part linear: w,L
F2
A2
Two-part nonlinear:
{w(q), L(q)}
F3
A3
Questions to Answer:
- What should supplier do when faced with decreased buyer demand?
- Value of information about the buyer’s cost structure
- Value of more sophisticated contracts
- Which of the above two is more valuable?
- When there is no double marginalization?
Literature
1. Supply Chain Management
2. Economics
Supply Chain Literature
- Deriving optimal ordering policies in the context of a given contract
- Deriving optimal contract parameters given the functional form of that contract
- Coordination within supply chains, the value of information and various alternative contracting schemes
Selected Papers
- Lee, So, and Tang (1998)
Quantify the value of sharing demand information
Demand follows an AR(1) process
- Bourland, Powell and Pyke (1996), Cachon and Fisher (1997), Gavirneri, Kapuscinski and Tayur (1996)
Benefits of information sharing when demand is i.i.d.
- Lee and Whang (1996)
Incentive scheme for a multi-echelon supply chain (central planner, but each echelon uses local information only)
- Corbett (1996, 1998)
Asymmetric information leads to to suboptimal outcomes (without central planner)
that can be implemented by a central planner where each echelon uses local information only and which leaves each party with at least the same expected profit as the classic Clark and Scarf (1960)
Selected Papers (Cont’d)
- Weng (1995)
Quantifies the value of channel coordination
Quantity discounts alone are not sufficient to achieve coordination
- Corbett and de Groote (1997)
Compares various coordination schemes for a 2-level SC
Preferences ordering of these schemes for the supplier, buyer and vertically-integrated firm
- This paper
Quantifying the value of information and the value of more complex contracts
Economics Literature
- Vertical contracting
Two successive monopolists
Double marginalization
- Topics
Comparing total surplus under various schemes
Contract to mitigate the double marginalization issue
Selected Papers
- Tirole (1988) : The Theory of Industrial Organization
- F. Machlup and M. Taber (1960)
Bilateral monopoly, successive monopoly, and vertical integration, Economica, May (1960), 101-119.
- Gal-Or (1991a,b)
In general, neither franchise fees nor retail price maintenance can achieve the integrated solution under asymmetric info
Equilibrium sometimes achieved with linear pricing and franchise fee contract (two supplier)
- Bresnahan and Reiss (1985)
Study the ratio of the profit margins under simple wholesale price with full information
How the ratio depends on the convexity of demand function
Contribution of This Paper
- Combine two strands of theory
building on the basic bilateral monopoly framework offered in economics
asking the normative and more micro-level questions more typical of supply chain literature
measure the cost of sub-optimality (quantification and insights of the differences between the cases)
The Model
The Supply Chain
Supplier
Buyer
L(q)
w(q)
p(q)
s
cost c
Assumptions
- One supplier and one buyer
- One product
- One period contract
- Deterministic demand
- Linear price-demand curve q = a - bp
- a - b (s+ ) 0
- F(c)/f (c) is increasing in c
F/f for Normal Distribution
Supplier’s Problem (S)
- Buyer’s individual rationality constraint
- Buyer’s incentive compatibility constraint
Sequence of Events
- Supplier offers one of the three types of contracts
- Buyer (with c) selects the order quantity q or (w(q), L(q))
- All sales and financial transactions take place simultaneously
Revelation Principle (A3)
- Reformulating the contracts in terms of c, i.e. optimizing over {w(c), L(c)}
- There is an optimal contract under which the buyer will reveal truthfully.
Supplier’s Optimal Supply Contracts
1. Buyer’s problems
2. Supplier’s problems
Buyer’s Problem (B1, B2)
- In B1, set L=0
- In B2, to buyer, L is independent of q
Solutions for B1, B2
Comments on the Solutions
Buyer’s Problem (B3)
Solution for B3
- Revelation Principle FOC evaluates at c
- It tells the supplier how to choose w(•) and L(•).
- SOC holds in the neighborhood of c.
Supplier’s Problems
Optimal Contracts Under Complete Information: Case F1, F2, F3
Contracts with Full Information
Type of contracts
Full information
Asymmetric information
One-part linear: w
F1
A1
Two-part linear: w,L
F2
A2
Two-part nonlinear:
{w(q), L(q)}
F3
A3
Case F1 (SF 1)
- Note: The Supplier knows the buyer’s optimal order quantity q*
Solution for SF 1
Profit and Profit Margins
- Supplier’s profit and profit margin are double those of the buyer!
More on Profit and Margins
- is a local measure of the curvature of the demand curve
- Ref. Bresnahan and Reiss (1985)
Question:
- Is the buyer’s individual rationality constraint satisfied?
- If not satisfied, as we commented before, the buyer won’t order and thus both parties’ profits are zero!
Case F2 (SF 2)
Observations
- With complete info about c, supplier can set the rationality constraint to be binding.
- He then maximizes the joint profits.
Solution for SF 2
Comments on Solutions for SF 2
Interpretation
- It’s optimal for the supplier to set the whole sale price equal to his marginal cost and use the lump sum side payment to extract all profits from the buyer in excess of his reservation profit level.
Case F3 (SF 3)
- Superset of F2
- F2 is optimal given full info on c: buyer only gets minimum level
- Value of addition flexibility is 0
- results carry over from F2
Supplier’s Problems
Optimal Contracts Under Asymmetric Information: Cases A1, A2, A3
Contracts with Asymmetric Information
Type of contracts
Full information
Asymmetric information
One-part linear: w
F1
A1
Two-part linear: w,L
F2
A2
Two-part nonlinear:
{w(q), L(q)}
F3
A3
Case A1 (SA1)
- Note: The Supplier knows the form of the buyer’s optimal order quantity q*
Solution for SA1
Profit and Profit Margins
- Supplier has incentive to induce the buyer to reveal his true cost c. (???)
Question:
- Is the buyer’s individual rationality constraint satisfied, i.e.
- If not satisfied, the buyer won’t order.
Case A2 (SA2)
Observations
- For any given w, the supplier will always choose the lowest L that still satisfies the buyer’s rationality constraint.
- b(c) is decreasing in c necessary and sufficient to set b( ) = infc b(c) b-
Solution for SA 2
Remarks
- If =E(c)=c, case A2 reduces to F2.
- The information asymmetry means the supplier must now offer a larger side payment (or less franchise fee) than in F2, to meet the “worst-case” buyer’s min profit requirements.
- Effectively, need
Question:
- When and what if the expected supplier’s profit is zero?
Case A3 (SA 3)
- Using buyer’s optimal order quantity q* and FOC from B3
Euler’s Equation:
Necessary Conditions
Constrained Problems: Lagrangian
Solution for SA 3
- Based on our assumption, the optimal w is increasing in , whereas in earlier cases, it is decreasing in or E[c].
- From FOC, L is also increasing in .
Buyer’s Tradeoff
- Accepting a higher lump sum payment and a higher unit whole sale price versus
- Accepting a lower lump sum payment and a lower unit whole sale price.
Special Case A3: Uniform Prior
Special Case A3 (Cont’d)
- The unit whole sale price can be interpreted as the average of a constant part and a part decreasing in q, illustrating how w decreases with quantity. Compare: p=a/b - q/b
Comparisons
The Impact of Buyer’s Cost on the Supplier’s Profit Margin
- Buyer’s cost c
Buyer’s profit margin mb
Buyer orders less
Supplier’s profit - How should the supplier respond?
Supplier’s Response
- In case F1, A1, A2:
sacrifices margin for volume
- In F2 and F3:
insensitive
- In A3:
sacrifices volume for margin
“Effective” Wholesale Price
- More precisely, one should take the side payment into account and evaluate the “effective” unit wholesale price as follows:
The Value of Info to the Supplier
- The value of information is (significantly) greater when the supplier has the flexibility to offer two-part contracts.
The Value to the Supplier of Offering Side Payments
- As demand becomes more price-sensitive, the absolute penalty from using only wholesale price without side payments decreases.
- The value of contracting flexibility is greater under full information.
Value of Information v.s. Value of Contracting Flexibility
- Value of information increases with b, while value of contracting flexibility decreases with b. Therefore,
- In more price-sensitive environments, supplier should focus more on obtaining info about the buyer’s costs.
Value of Info v.s. Value of Contracting Flexibility (Cont’d)
F1
F2
A1
A2
Numerical Examples
Conclusions
Conclusions
- Under full information, a supplier will decrease his wholesale price in reaction to a buyer cost increase, maintaining the volume while sacrificing margin.
Conclusions (Cont’d)
- Under asymmetric information, however, the supplier may do the opposite: increase average wholesale price, thus maintaining margin while sacrificing volume.
Conclusions (Cont’dd)
- The value to the supplier of obtaining better information about the buyer’s cost structure increases with the variance of the supplier’s prior distribution about that cost parameter and with price-sensitivity of demand.
Conclusions (Cont’ddd)
- The value of better information is greater when the supplier can offer two-part contracts rather than only one-part contracts, and
- The value of being able to offer two-part contracts rather than one-part contracts is decreasing in price-sensitivity b.
Future Research
….
- In many contracting situations, the supplier starts in case A1:
offering a simple linear wholesale price
with no side payment
without knowing the buyer’s cost structure
Questions to Answer:
- When should the supplier focus on obtaining better information about the buyer’s cost structure?
- When should he offer more sophisticated contracts?
- How would the results change if we introduce stochastic price-sensitive demand?
- What changes if the the supplier cannot observe the price-sensitivity parameter b?
Designing Supply Contracts: Contract Type and Information Asymmetry
Authors: C. Corbett, C. S. Tang
Presenter: T.J. Hu
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