We consider a monopolist which produces a single product and it either sells or servicizes its product to the consumers. In the following, we introduce the consumer and product charac- teristics, and then discuss consumers’ and firm’s decisions. Table B.1 in online appendix B.3 summarizes the parameters and decision variables of our model.
3.3.1 Consumer and Product Characteristics
Consumers differ in their valuation of the product. There are two consumer segments, θi,
i = H, L, where θH and θL show the valuations of high and low end segments, respectively. We assumeαθH =θLwhereα∈(0,1) andθL=θ. The mass of potential customers isM and
β ∈(0,1) shows the fraction ofθH consumers.
Here,θirepresents consumer segmenti’s utility from the first use, then the product’s utility deteriorates with each use. The deterioration rate depends on the product durability, δ, that is, it will be slower for products with higher levels of durability. Specifically, the consumer
marginal utility per unit use is θi− δt, i= H, L, where δt shows the drop in marginal utility after tunits of use.
There is a cost of operating the product. This cost includes the maintenance and all other costs incurred to keep the product operational. When the consumers own the product (which is the case under selling), the consumers incur the operating cost; otherwise, when the firm owns the product (which is the case under servicization), the firm incurs the operating cost.1 For copiers the operating cost includes maintenance, toners, papers etc. For instance, University of California Davis and Oregon State University have adopted servicization contracts for their copier needs (U.C.D, 2014; O.S.U, 2014). The consumers and the firm may differ in their
1
If we relax this assumption and assume that consumers bear a part of the operating cost under servicization, our results remain unaltered.
operational efficiency to operate the product, that is, for the same amount of use the firm can incur higher or lower total operating cost than the consumers. For example, in its failed deal attempt with University of Texas at Houston, Interface carpet stated a higher maintenance cost per square feet than UT’s own established janitorial service, (Olivia and Quinn 2003). Furthermore, as Bardhi and Eckhardt (2012) points out, when a consumer does not own the product, her use behavior toward the product changes. When a consumer owns the product she has incentive to use the product properly because misuse of the product will increase her product maintenance cost. This incentive disappears in servicization model as the firm bears the operating cost, as a result the firm may incur a higher operating cost for the same use level. On the other hand, the economies of scale may lower operating cost for the firm.
Since more durable products require less maintenance and are expected to lose their energy efficiency slower, we assume that the operating cost is decreasing in product durabilityδ. In addition, we assume that total operating cost is increasing in useτ in a convex manner. Because as the product is used more it may require more frequent repairs and may lose material and energy efficiency. In order to capture all these features, we use the following operating cost functions: when the consumer or the firm owns the product, they incur an operating cost
mcτ2
2δ ,i=c, f, where mc and mf denote the operating cost parameters, respectively. mc can be lower or higher than mf as explained above. We study an alternative cost model through a numerical study in the Appendix B, where the operating cost is not correlated with product durability. We show that our key results continue to hold.
3.3.2 Consumer and Firm Decisions
In this section, we introduce the consumers’ and firm’s problems first for selling strategy, then for servicization strategy.
In selling strategy, on the demand side, each consumer first decides whether to purchase the product. If typeθi consumer buys the product, she then determines her level of useτ, to maximize her utility:
Ur(θi) = max τ Z τ 0 (θi− t δ)dt− mcτ2 2δ −p. (3.1)
Marginal utility per unit use is integrated over use to obtain consumer’s utility in equa- tion (3.1), then total operating cost mcτ2
2δ and the product price p are deducted. Once the marginal utility per unit use, the product provides, drops below the marginal operating cost per unit use, the consumer stops using the product, and the product is disposed. There is no disposal cost or salvage value.
On the supply side, the firm determines the product durability δ. We assume that pro- duction cost is convex in product durability and is equal to cδ2, where c is a positive scaling parameter. The firm then sets the selling price p. Because the high valuation segment has a higher willingness-to-pay serving only the low valuation segment is never optimal. Let πr,B∗
andπr,H∗ denote the manufacturer’s optimum profit when it sells to both segments and only to
θH segment, respectively. If πr,B∗ ≥ πr,H∗ , the manufacturer sells to both segments; otherwise it sells only to high valuation segment. π∗r,B and πr,H∗ are given by:
πr,B∗ = maxp,δ(p−cδ2)M, (3.2)
s.t Ur(θL)≥0.
πr,H∗ = maxp,δ(p−cδ2)M β, (3.3)
s.t Ur(θH)≥0.
We normalize the reservation utility of both segments to zero. If the firm sells to both segments, low valuation segmentθLmust receive at least its reservation utility, i.e.,Ur(θL)≥0. Similarly, if the firm sells only to the high valuation segmentθH, high valuation segment must capture at least its reservation utility, Ur(θH)≥0.
In servicization strategy, on the demand side, the consumers choose one of the contract options offered by the firm, including not receiving any service. Each contract option specifies a use-price pair, i.e., (τi, Fi),i=H, L. Consumers choosing the contract (τi, Fi) use the product forτi units and pays the firm Fi.
On the supply side, the firm determines the product durability δ and the parameters of the menu contract (τi, Fi), i=H, L. Similar to selling strategy, because the high valuation segment has a higher willingness-to-pay, inducing only the low valuation segment to purchase the service is never optimal. If the firm induces both segments to purchase the service, the
menu must satisfy the following individual rationality and incentive compatibility constraints. IRi : Z τi 0 (θi− t δ)dt−Fi≥0, i:H, L (3.4) ICi : Z τi 0 (θi− t δ)dt−Fi≥ Z τj 0 (θi− t δ)dt−Fj, i6=j,and i, j:H, L. (3.5)
Otherwise, if the firm induces only high valuation segment to accept the offer, then the con- tract only needs to satisfy individual rationality constraint of the high valuation segment, i.e.,
Uv(θH)≥0. Letπv,B∗ andπ∗v,N denote the manufacturer’s optimum profit when it serves both segments and only the θH segment, respectively. Then,
π∗v,B = max δ,Fi,τi,i=H,L X i=H,L (Fi− mfτH2 2δ −cδ 2)Q i, (3.6) s.t, IRi, ICi i=H, L. πv,H∗ = max δ,FH,τH (FH − mfτH2 2δ −cδ 2)Q H, (3.7) s.t, IRH.
whereQL= (1−β)M andQH =βM. The firm serves both segments ifπ∗v,B≥πv,H∗ ; otherwise, it serves only θH segment.