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Designing Supply Contracts: Contract Type and Information Asymmetry

Designing 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.

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Designing Supply Contracts: Contract Type and Information Asymmetry

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  1. Designing Supply Contracts: Contract Type and Information Asymmetry Authors: C. Corbett, C. S. Tang Presenter: T.J. Hu

  2. Contents • Introduction • Literature • Model • Supplier's Optimal Supply Contracts • Comparisons • Numerical Examples • Conclusions • Future Research

  3. Introduction

  4. The Supply Chain s Supplier C ~ F(•) L(q) w(q) Buyer cost c p(q)

  5. Supplier's Concerns: • The types of contracts • Information about the buyer's cost structure

  6. 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)}

  7. Six Scenarios

  8. 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?

  9. Literature 1. Supply Chain Management 2. Economics

  10. 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

  11. 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)

  12. 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

  13. Economics Literature • Vertical contracting • Two successive monopolists • Double marginalization • Topics • Comparing total surplus under various schemes • Contract to mitigate the double marginalization issue

  14. 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

  15. 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)

  16. The Model

  17. The Supply Chain s Supplier L(q) w(q) Buyer cost c p(q)

  18. 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

  19. F/f for Normal Distribution

  20. Supplier’s Problem (S) • Buyer’s individual rationality constraint • Buyer’s incentive compatibility constraint

  21. 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

  22. 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.

  23. Supplier’s Optimal Supply Contracts 1. Buyer’s problems 2. Supplier’s problems

  24. Buyer’s Problem (B1, B2) • In B1, set L=0 • In B2, to buyer, L is independent of q

  25. Solutions for B1, B2

  26. Comments on the Solutions

  27. Buyer’s Problem (B3)

  28. 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.

  29. Supplier’s Problems Optimal Contracts Under Complete Information: Case F1, F2, F3

  30. Contracts with Full Information

  31. Case F1 (SF 1) • Note: The Supplier knows the buyer’s optimal order quantity q*

  32. Solution for SF 1

  33. Profit and Profit Margins • Supplier’s profit and profit margin are double those of the buyer!

  34. More on Profit and Margins •  is a local measure of the curvature of the demand curve • Ref. Bresnahan and Reiss (1985)

  35. 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!

  36. Case F2 (SF 2)

  37. Observations • With complete info about c, supplier can set the rationality constraint to be binding. • He then maximizes the joint profits.

  38. Solution for SF 2

  39. Comments on Solutions for SF 2

  40. 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.

  41. 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

  42. Supplier’s Problems Optimal Contracts Under Asymmetric Information: Cases A1, A2, A3

  43. Contracts with Asymmetric Information

  44. Case A1 (SA1) • Note: The Supplier knows the form of the buyer’s optimal order quantity q*

  45. Solution for SA1

  46. Profit and Profit Margins • Supplier has incentive to induce the buyer to reveal his true cost c. (???)

  47. Question: • Is the buyer’s individual rationality constraint satisfied, i.e. • If not satisfied, the buyer won’t order.

  48. Case A2 (SA2)

  49. 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-

  50. Solution for SA 2

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