A Principal-Agent Model for Product Specification and Production

Authors:Ananth V. Iyer, Leroy B. Schwarz and Stefanos A. Zenios

Presented by N.Prabhakar, for the class ISYE6230- Economic Decision Analysis

The Industry’s New Paradigm-Outsourcing-Year 2001

•Chrysler outsources over 80% of the parts it assembles into cars• Ford, over 65% •GM over 55%.•Cisco System partners provide final assembly for almost half of its switches and routers.•Nearly 80% of Kodak’s reloadable cameras are sourced in Asia

What are the interactions? The buyer (Principal) delegates the

majority of product-specification and production activity to the supplier (Agent), but retains the flexibility to commit a given, observable amount of an internally-available resource (e.g., engineering hours) to help the supplier.

The supplier, in turn, allocates his resource (e.g., engineering hours) to produce the finished product

What are the decisions?

Both the Supplier’s resource allocation and capability are assumed to be hidden from the Buyer The Principal’s problem is to determine a menu of (resource-commitment, transfer-price) contracts to minimize his/her total expected cost

OEM’s (*Principal) decisions vs. Supplier’s (*Agent) decisions

Production cost(Payoff function):Depends on Resource commitment made by the

Buyer x1 Production cost(Payoff

function):Depends on The supplier’s allocated resource x2

Supplier’s capability φ ∈ [φ, φ] φ denotes the least-capable supplier φ the most-capable.

What defines the strategy?

Determine a menu of contracts (x1(φ), t(φ)) φ∈[φ,φ]to minimize the buyer’s total expected cost

The resources provided bythe two parties are not necessarily measured in the same units.

buyer’s beliefs about the supplier’s capability are reflected in: π(φ)t(φ) is the transferprice paid to the supplier that chooses resource commitment option x1(φ).

Interaction Principal and Agent Buyer moves first and offers a contract that

consists of buyer resource commitment and corresponding transfer price.

In the second step, the supplier chooses among all options offered the pair (of resource commitment and price) that maximizes his total payoff.

The buyer provides the resource commitment chosen by the supplier, the supplier chooses his resource allocation, incurs the cost, and delivers the final product to the buyer.

Finally, the buyer pays the supplier.

The buyer knows φ, and chooses x1 and x2 in order to minimize total cost. The problem is as follows: For each φ ∈ [φ, φ], find x1(φ) and x2(φ) to minimize the

production cost▪ V (x1(φ), x2(φ), φ)▪ subject to 0 ≤ x1(φ) ≤ R.

The optimal (first-best) choice of the two inputs for each type φ ∈ [φ, φ] will be denoted x∗1(φ) and x∗2(φ), respectively.

Proposition 1 The optimal solution is: x∗1(φ) = R Vx2(R, x∗2 (φ), φ) = 0 for each φ ∈ [φ, φ]

Single-Party Problem: First-Best

Single Resource-Commitment Contract In this contract,

Buyer single resource-commitment and price, Buyer x1 and a price t,

Supplier (upon acceptance) chooses x2(φ) that minimizes his/her total cost, for a specific x1. Then

Buyer’s problem is to determine x1 ∈ [0,R] and to

minimizet,x1tsubject to the participation constraint,

Max x2[t − V (x1, x2, φ)] ≥ u¯ for each φ ∈ [φ, φ]

u¯ is the minimum needed benefit for supplier

(A)

Single Resource-Commitment Contract(contd.)

Buyer x1 = capacity constraint R, else he/she would forego some cost savings.

In response to this, a supplier of type φ x2 that minimizes the production cost V (R, x2, φ).This coincides with first-best x∗2 (φ).

The Transfer price t. First, it follows from (A) that t must ensure the participation of the supplier with the highest cost (i.e. lowest capability φ = φ). Hence, the price offered by the buyer is equal to this supplier’s cost; that is,

t = u¯+ V (R, x∗2(φ), φ) Note that a supplier with a capability φ > φ is left with a

profit (surplus) that reflects his cost advantage over the least capable (i.e. highest cost) supplier.

Single Resource-Commitment Contract(contd.)

This contract induces First-best choices both parties, but the price paid by the buyer must be enough to cover the cost of the least-capable supplier.

Therefore, the buyer cannot exploit any of the cost savings achieved by a more capable supplier.

Screening Contracts

 Worker knows his ability and can acquire credentials or somehow signal that ability to the employer before being offered a wage, then the problem is signaling.

In a Screening game the employer offers a wage level first, then the worker chooses the amount of credentials he will acquire and accepts or rejects a contract for a wage level. It is called Screening, because the worker is screened by the employer in that the offers may be contingent on the skill level of the worker.

In the first case, the assumption is that ˜ Vx1φ(x1, φ) ≤ 0 for all x1 and φ. Buyer’s efforts and the Supplier’s capabilities are complements: More Buyer resources increase the magnitude of the Supplier’s

marginal cost-reduction capability (i.e., it decreases ∂ ˜ V (x1,φ)∂φ ).

More Buyer resources increase the cost advantage of more capable Suppliers.

In the second case, the assumption is that ˜ Vx1φ(x1, φ) ≥ 0 for all x1 and φ. Buyer’s efforts and the Supplier’s capabilities are substitutes: More Buyer resources decrease the magnitude of the

supplier’s marginal cost-reduction capability (i.e., it increases ∂ ˜ V (x1,φ) ∂φ ).

More resources diminish the cost advantage of the more capable suppliers.

Resource-Commitment Screening Contract: Two –cases :Complements, Substitutes

Resource-Commitment Screening Contract (Contd.)

Given complements, the optimal menu of contracts separates less capable suppliers by committing fewer resources compared to the resources that would be committed to a more capable supplier.

Given substitutes, the optimal menu of contracts coincides with the single resource-commitment contract

The analysis proceeds in two main steps: First, for any given menu of resource-

commitment options (x1(φ))φ∈Φ, find the transfer price menu (t(φ))φ∈Φ that will implement it; i.e., make it desirable for a type-φ supplier to choose the pair.

Next, obtain the menu of resource commitment options that when implemented with the pricing mechanism from step 1 that minimizes the buyer’s total expected cost.

Resource-Commitment Screening Contract (Contd.)

The nature of the non-linear transfer payment system provides an important insight.

The total price for a supplier of type φ is equal to the reservation profit margin u , total cost of production when the supplier chooses the desired resource commitment x1(φ), plus an information rent.

The information rent is increasing in the supplier’s capabilities, hence makes it attractive for the supplier to reveal his capabilities by the choice he makes.

Resource-Commitment Screening Contract (Contd.)

Second step of the analysis, which is to identify the menu that will minimize the buyer’s expected total cost when implemented with the pricing mechanism.

The problem can be reduced to: Find a menu of resource-commitments (x1(φ))φ∈Φ to minimize:

Step 2Resource-Commitment Screening Contract (Contd.)

P(φ) is the cumulative density function for the supplier’s capabilities

Step 2Resource-Commitment Screening Contract (Contd.)

This highlights a trade off: The Buyer wants the Supplier to choose a resource level that minimizes total production cost but also wants to extract some of the cost savings. To achieve this he/she has to offer the supplier an information rent.

The information rent that would implement the first-best decisions is excessive. Hence, the menu designed by the buyer proposes a resource commitment that may be different from first-best; one that may increase the direct product development cost compared to first-best but with smaller information rents.

•If, on the other hand, the buyer’s resource and supplier’s capability are substitutes, then theoptimal screening contract coincides with the single resource-commitment contract.•One can say more by considering the hybrid complements/substitutes . In that case, it can be shown that the optimal contract is derived by separating the region of types into two parts: the region of complements and the region of substitutes. The solution is obtained by pasting together the pieces corresponding to the two parts.

Resource-Commitment Screening Contract (Contd.)

Insights from Propositions Buyer’s optimal commitment of resources

depends on Supplier capability: In the case that Supplier capability and Buyer

resources are Substitutes, increasing the Buyer’s involvement achieves two objectives: ▪ it reduces the total cost of product specification and

production and the corresponding information rents.

▪ The increased involvement by the buyer reduces the supplier’s marginal capability that drives the information rents. It follows that it is optimal for the buyer to use all her resources irrespective of the supplier’s capability.

Insights from Propositions In the case of Complements, Buyer resources can increase

the supplier’s marginal capability and that will increase the information rents.

Thus, the buyer finds it advantageous to restrain his/her involvement in order to effectively price-discriminate: The Buyer provides contracts with limited involvement (low x1) and contracts with a more extensive involvement (higher x1) but, potentially, at a price discount (lower t).

Then, the more capable supplier finds it advantageous to choose the more extensive involvement at a lower price because he can better integrate this involvement in his processes and achieve larger cost reductions.

Therefore, even though the Price paid to a more-capable supplier is lower than the one paid to a less-capable one, the former is left with a higher surplus because he takes advantage of the buyer’s involvement.

Current scope of this Research

Ford Opens the Door for Contract Manufacturing in Automotive  

“Today we’re thinking and behaving like a consumer-electronics company,” said Derrick Kuzak, Ford Motor Co. group vice president of global product development, in January, as he introduced the company’s second-generation SYNC system, known as the MyFord platform.Indeed, Ford is taking a consumer-electronics-oriented approach with MyFord, not only in the connectivity solution’s features but also in the company’s use of a Electronics Manufacturing Services (EMS) provider to make the system. By employing an EMS contract manufacturer, rather than a traditional automotive supplier, Ford is behaving like most modern consumer electronics firms, which predominately outsource the production and design of their products to contract manufacturers. With Ford increasingly seen as a trendsetter in the vehicle Infotainment industry, the move could open up the automotive market to EMS providers and Original Design Manufacturers (ODMs)—and threaten the position of established automotive electronics suppliers.

“In a break from tradition, Ford with its MyFord system has chosen to partner with Flextronics, a Singapore-based EMS provider that is not part of the established Tier-1 automotive supplier base,” said Richard Robinson, principal analyst for automotive infotainment at iSuppli. “By doing this, Ford’s infotainment team has taken a page from top-tier consumer electronics OEMs, developing a product that leverages a reference platform from a contract manufacturer, rather than making the system from scratch. The EMS reference design approach has beenused for years in the manufacturing of consumer devices, including cell phones and Portable Navigation Devices (PNDs), so why not in automotive infotainment?”

Contract manufacturers in 2009 accounted for only 5.5 percent of the global automotive electronics business.

Link to article: http://www.isuppli.com/News/Pages/Ford-Opens-the-Door-for-Contract-Manufacturing-in-Automotive.aspx

THANK YOU

Appendix A

Calculation and Propositions in details in Appendix A

The constraints of the Model?Resource constraint 0 ≤ x1 ≤ R R=Total resource available to Buyer

The total production cost is V (x1, x2, φ) and is assumed to be decreasing in x1 and φ and is jointly convex in x1 and x2, the supplier will choose his resource allocation x2 only after he decides which pair (x1(φ), t(φ)) to select. This reflects the implicit assumption that the supplier has the flexibility to allocate his resources at the last stage of the interaction

Incentive-compatibility constraint i.e., that a supplier of type φ will choose buyer resource-commitment level x1(φ),

t(φ) − minx2 V (x1(φ), x2, φ) ≥ t(ˆφ) − minx2V (x1(ˆφ), x2, φ) for all ˆ φ ∈ [φ, φ]Participation constraint; i.e., that the supplier’s payoff will exceed the prevailing expected payoff in the marketplace,

t(φ) − minx2 V (x1(φ), x2(φ), φ) ≥ u¯ for each φ ∈ [φ, φ]

Assumptions of the Model The buyer’s committed resource, x1, is assumed to

be costless to the buyer and to decrease the supplier’s production cost. There are three reasons behind this assumption: To examine mechanisms that the buyers can utilize in order

to reduce the “agency costs” in the buyer-supplier relationship, buyer resources can provide a mechanism to efficiently screen suppliers of different capabilities. By assuming these resources to be costless to the buyer we focus on their impact on agency costs. The second reason

Analytical tractability: with this assumption, the analysis of the problem is streamlined.

Empirical: At Ford and at many buyers such resources are costless in the short-to-medium term.

Buyer can determine the optimal level for the supplier’s resource allocation in the case where the supplier’s capability is known.

Buyer is familiar with the technological aspects of the production process but not with the exact parameters of the technology

Assumptions of the Model

Single-Party Problem: First-Best

Propositions-Step 1Resource-Commitment Screening Contract (Contd.)

Given Hybrids,

Resource-Commitment Screening Contract (Contd.)

Resource-Commitment Screening Contract (Contd.)

In the case of complements, the buyer’s ability to offer a menu of contracts reduces the supplier’s surplus compared to the single resource commitment contract. In other words, the buyer exploits her involvement in the product development project to extract some of the supplier’s surplus.

While the supplier with a high level of capability retains more of the surplus than the less capable supplier, he is worse off compared to the case of a single resource-commitment contract.

Additional Insights from Propositions