Channel Decision-Making
Eyal Biyalogorsky
Graduate School of Management
University of California Davis, Davis, CA 95616
eyalog@ucdavis.edu
Oded Koenigsberg
Columbia Business School
Columbia University, New York, NY 10027
ok2018@columbia.edu
2008
1
Channel Decision-Making
Abstract
In many industries firms have to make quantity decisions before knowing the exact state of
demand. In such cases, the channel members have to decide who will own the units until demand
uncertainty is resolved. The decision about who should retain ownership depends on the balance
of benefit and risk to each member. Ownership, after all, is costly. Whichever member owns the
units accepts the risk of loss if more units are produced than can be sold. But ownership also
grants firms the flexibility to respond to demand, once it becomes known, by adjusting price.
In this study, we analyze ownership decisions in distribution channels and how those
decisions are affected by demand uncertainty. We model demand based on micro-modeling of
consumer utility functions and capture demand uncertainty related to market size and price
sensitivity. The study demonstrates three important conclusions. First, as long as the degree of
uncertainty about market size is intermediate, the retailer and the manufacturer both benefit when
the manufacturer maintains ownership of the units. Second, when there is substantial uncertainty
about market size, the retailer and the channel are better off if the retailer retains ownership but
the manufacturer will still prefer to maintain ownership. Thus, there is potential for channel
conflict under these conditions. Finally, the pass-through rate varies with the degree of
uncertainty regarding price sensitivity. The optimal pass-through rate is less than 100% when
there is little uncertainty regarding price sensitivity. The rate increases with an increase in
uncertainty regarding price sensitivity and can exceed 100% if the uncertainty is great enough.
Key words: Channels of distribution; Demand uncertainty; Lead time; Pricing; Pass-through.
2
1. Introduction
One of the important tasks facing firms in setting up distribution channels is organizing
different flows through the channel to ensure the best possible performance. Coughlan et al.
(2006) identified eight generic activities that must be considered: physical possession,
ownership, promotion, negotiation, financing, risk, ordering, and payment. In this paper we
investigate how the ownership flow in a channel should be organized. Ownership is the power to
exercise control over an asset (Grossman and Hart 1986). In a distribution channel, one of the
ownership decisions is which member should own (control) the inventory carried by the
channel—the manufacturer or the retailer—and under what conditions.1
Ownership matters in a channel when demand is uncertain. The firm that owns the units in
the channel can adjust its actions in response to new information regarding actual demand by
consumers. For example, if a manufacturer retains ownership of the units in the channel and
finds that demand for the product is higher than expected, it can increase the wholesale price in
response. Conversely, a channel member that does not own the units has limited ability to
respond to new information. If the manufacturer transfers ownership of the units to the retailer
before learning that demand is higher than expected, the manufacturer loses the ability to
increase its wholesale price in response. Thus, ownership conveys the ability to respond to
changes in the market (Grossman and Hart 1986).
Ownership, however, is risky, and hence costly. The owner is liable for any unsold units,
which can be costly if demand turns out to be low. This risk can prompt each channel member to
prefer not to own the units (Cachon 2004; Netessine and Rudi 2004). Thus, it is not clear a priori
1
Another aspect of ownership in a channel is vertical integration—whether channel members should be independent
entities. This issue has received extensive attention in the literature (see, for example, McGuire and Staelin (1983))
and is not dealt with in this paper.
3
what sort of ownership arrangement is in the best interest of the retailer, the manufacturer, and
the channel under a particular set of conditions.
The literature on channels has largely ignored the issue of ownership of the units in a
channel. In many cases, changes in ownership follow changes in the physical location of the
units, so there appears to be an implicit assumption that models of inventory location also
explain the ownership decisions in the channel. Models of inventory location address where to
physically locate the units to generate logistical and cost efficiencies. The basic idea behind these
models is that a cost is incurred in handling inventory (there are warehousing, shipping, and
handling costs) and that the cost varies according to the level in the channel that carries the
inventory. Therefore, optimally locating the inventory can reduce overall costs in the channel. In
a single-manufacturer multiple-retailer setting, for example, it may be more efficient to pool and
locate inventory centrally with the manufacturer (Anupindi and Bassok 1999).
Ownership, however, is conceptually distinct from the physical location of the units
(Coughlan et al. 2006). Many internet retailers use drop-shipping arrangements in which they
take ownership of units that remain physically in manufacturer or distributor warehouses and are
shipped directly from those warehouses to the final consumers (Wall Street Journal 2003;
Netessine and Rudi 2006). In consignment arrangements, units that are stored on the retailer’s
premises are still owned by the supplier (Dong, Dresner, and Shankar 2005; Rubinstein and
Wolinsky 1987; Valentini and Zavanella 2003; Wang, Jiang, and Shen 2004). Thus, inventorylocation models are not sufficient to understand the optimal ownership arrangements in a channel
of distribution.
In this paper we examine a channel facing demand uncertainty and determine which
member in the channel—the manufacturer or the retailer—should retain ownership of the units.
4
Our model adds to the literature by exploring the incentives for manufacturers and retailers to
own the units in a channel when ownership is not tied to the physical location of the units.
We develop a model in which a manufacturer sells its product to a retailer that then sells
the units to consumers. Channel members initially are uncertain regarding two dimensions of
demand for the product—market size and price sensitivity—and must produce the units before
subsequently receiving information that resolves the uncertainty. By taking ownership of the
units, a channel member controls what is done with them when the demand uncertainty is
resolved. We model demand based on micro-modeling of consumer utility functions and
incorporate uncertainty regarding both market size and price sensitivity. The cost of physically
handling the units is set at the same amount in each structure so that the physical location of the
units is immaterial to the ownership decisions in the model. This setting enables us to determine
whether and when the benefit of ownership, in the form of the ability to respond to new
information regarding demand, outweighs the risk.
We find that the benefit of owning the units outweighs the cost when the amount of
uncertainty regarding market size is sufficiently large. In addition, the benefit of ownership tends
to be greater for the manufacturer than for the retailer. As a result, one can distinguish between
three different regions based on the amount of demand uncertainty: When the amount of demand
uncertainty regarding market size is large, both the manufacturer and the retailer prefer to own
the units, leading to potential conflict in the channel. In contrast, when the degree of uncertainty
is low, both the manufacturer and the retailer prefer to sell all of the units regardless of the
realization of demand uncertainty. Consequently, the benefit from ownership is small and it does
not make much difference who owns the units in the channel. If the amount of demand
uncertainty is intermediate, however, both the manufacturer and the retailer prefer to have the
5
manufacturer retain ownership. The retailer is willing to forego ownership because the small
benefit it would obtain does not offset the effect that the manufacturer inability to respond to the
new information has on its decisions, and therefore on the retailer’s profits.
By explicitly modeling demand uncertainty regarding both market size and price
sensitivity, we also shed some light on how channel pass-through is affected by demand
uncertainty. We find that the pass-through of price reductions increases with the retailer’s initial
uncertainty about customers’ price sensitivity. If the retailer is certain about price sensitivity, the
pass-through is less than 100% (regardless of uncertainty about market size). The pass-through
rate increases as uncertainty about price sensitivity increases. If that uncertainty is sufficiently
large, the pass-through rate can surpass 100%.
The remainder of this paper is organized as follows. In the next section we describe the
previous literature and in section 3 we lay out the model and our assumptions and present our
basic analysis. We introduce and discuss our results in Section 4 and conclude in Section 5.
6
2. Related Literature
The decision regarding ownership flow in a channel comes down to the benefit and cost
associated with postponing the transfer of ownership from the manufacturer to the retailer until
after demand uncertainty is resolved. Intuitively, the ability to wait and make decisions after
demand is known should be valuable, hence the interest in designing processes that allow
decision postponement (Van Meighem and Dada 1999). Most of the postponement literature
concentrated on product-design strategies (see, for example, Lee and Tang (1996)) but there has
been some work on the effect of different ordering arrangements between retailers and
manufacturers. Ferguson (2003) looked at how a retailer postponing the ordering decision
(without changing the retail price, which was exogenous) affects the manufacturer’s production
decision. Cachon (2004) showed that offering advance-purchase discounts and allowing the
retailer to place some orders before and some orders after demand is known can help to
coordinate the channel when demand is uncertain. Netessine and Rudi (2004, 2006) investigated
how demand uncertainty affects the use of drop shipping, in which the manufacturer/wholesaler
owns and stocks the inventory and ships units directly to customers at the retailer’s direction. A
common theme in these papers is that prices are exogenous and only the production decision is
considered. In contrast, our focus is on the effect that the ability to respond to new information
by changing prices ex post (while production decisions must be taken ex ante) has on channel
members.
While the literature generally points to the benefits of the ability to delay decisions until
demand is known, other papers point out that the changes in firms’ initial decisions in response
to the added flexibility from postponement may not always be beneficial. Iyer and Padmanabhan
(2000) asked when a manufacturer should offer flexible terms of trade to a retailer that faces
7
demand uncertainty and showed that there are times when a manufacturer will offer rigid rather
than flexible terms. Similarly, Iyer and Bergen (1997) found that manufacturers may not be
better off under quick-response channel arrangements and that rigid rather than flexible
arrangements may improve quick-response arrangements. In a setting of a single manufacturer
and multiple competing retailers, Iyer, Narasimhan, and Niraj (2007) investigated how improved
information affects the manufacturer’s preference regarding where to keep the inventory. They
found that, with more reliable information, the manufacturer prefers to hold the inventory only if
the retail market is very competitive.2 Our results bear some similarity to these works. In our
model, if the retailer has ownership, the manufacturer strategically changes its pricing in such a
way that under some conditions the retailer prefers that the manufacturer will retain ownership.
Shifting ownership of units in the channel from the retailer to the manufacturer and vice
versa also shifts the risk. This is somewhat similar to other mechanisms, including return policies
(Mantrala and Raman 1999; Marvel and Peck 1995; Padmanabhan and Png 1997) and
guaranteed profit margins (Mantrala, Basuroy, and Gajanan 2005), which provide for risksharing between retailers and manufacturers. Such mechanisms, however, provide for risksharing without shifting a participant’s control over the units in the channel. In contrast,
changing ownership shifts both risk and control, and it is the question of who should control and
have the decision rights over the units that is central to this study.
The work most closely related to the current study is a paper by Taylor (2006). Taylor,
studied a setting that is similar to our model. Among the questions he posed was when a
manufacturer should sell to a retailer—whether early or late in the selling season. He showed that
the manufacturer always (weakly) prefers to sell late rather than early. One can interpret the sale2
This may be partly due to an increase in manufacturer power as the retail market becomes more competitive. Iyer
and Villas-Boas (2003) showed in a channel-bargaining model that only a powerful manufacturer will voluntarily
8
timing decision in Taylor as a decision about when to transfer ownership of the units in the
channel from the manufacturer to the retailer. Thus, Taylor’s result is equivalent to our part B of
proposition 1 in Section 4, which describes manufacturer preferences regarding ownership of
units in the channel. Unlike Taylor’s work, our model captures demand uncertainty regarding
both market size and price sensitivity. We later show that the nature of the demand uncertainty
affects the results in important ways. We also differ from Taylor in viewing the ownership
decision as a strategic choice for the channel rather than only for the manufacturer. Thus, we
consider issues affecting incentives for the retailer while Taylor’s model included a constraint
that the retailer had to be no worse off under manufacturer ownership than under retailer
ownership. Our model enabled us to determine whether there are situations in which channel
members agree that the retailer should retain ownership even if incentives to the manufacturer
(considered in isolation) are such that the manufacturer strictly prefers to retain ownership. This
explains when and why we see ownership rights given to retailers. In addition, we explore how
pricing and promotion decisions are affected by the nature of the demand uncertainty and the
presence of lead time in the channel.
3. Model and Analysis
We consider a bilateral channel in which a risk-neutral manufacturer sells its product to a
risk-neutral retailer that then sells it to consumers. In the beginning, the manufacturer and the
retailer each have some symmetrical and exogenous uncertainty about demand. Then, at a later
point, they learn true demand for the product in the market. Production decisions must be made
before the firms learn the true demand state but pricing decisions can be made after.
offer a return policy.
9
This setting is typical of industries, such as fashion and toys that must commit to a
production quantity very early in the planning cycle. In the fashion industry, for example, lead
time between the start of production and availability of those units for sale can be as long as
twelve months (Fisher and Raman 1996). In these industries, production decisions are typically
made under conditions of more severe uncertainty than are pricing decisions, and changing the
initial production plan at a later point in time is very costly when possible at all (see, for
example, Caruana and Einav (2005), Fisher and Raman (1996), Johnson (2001), and Schleifer
(1993)).
Given these conditions, it is natural to ask which member of the channel, the manufacturer
or the retailer, should have ownership of the units produced until the pricing decision must be
made. If the manufacturer retains ownership, it can adjust the wholesale price in response to the
lowered demand uncertainty but also risks being stuck with units that cannot be sold or can be
sold only at a deeply discounted price. The retailer can always adjust the retail price as it learns
more about demand. If the retailer takes ownership of the units, the wholesale price charged by
the manufacturer is fixed and the retailer reaps most of the windfall if demand turns out be high,
at the cost of getting stuck with unwanted units if demand turns out to be low.
The sequence of events in the model is as follows: Under the retailer ownership scenario,
the retailer assumes ownership of the units before the uncertainty is resolved (Figure 1a). The
manufacturer sets a linear per-unit wholesale price while uncertainty remains regarding demand3
and the retailer decides how many units to order. The units are produced and delivered to the
3
We consider in this analysis only linear per-unit wholesale arrangements. This is a reasonable starting point in
view of the wide use of such arrangements in practice (Lariviere and Porteus 2001) and because it is the optimal
outcome expected of bargaining in channels under uncertainty (Iyer and Villas-Boas 2003). In addition,
understanding firms’ incentives under linear contracts is a necessary first step in determining whether more complex
arrangements such as side payments and nonlinear prices are called for.
10
retailer. After the firms learn the true demand conditions, the retailer sets the retail price. Any
unsold units are scrapped. Under this scenario, the retailer bears the cost of unsold inventory.
Under the manufacturer ownership scenario, the manufacturer retains ownership of the
units until the uncertainty is resolved (see Figure 1b) and the retailer places its order with the
manufacturer only after learning what the true demand in the market is. The manufacturer
decides how many units to produce based on its estimate of how many units the retailer will
order and while uncertainty about demand remains. After the firms learn the true demand
condition, the manufacturer sets the wholesale price and the retailer places orders with the
manufacturer and sets the retail price. The manufacturer ships the requested units to the retailer
and scraps any leftover units. Under this scenario, the manufacturer bears the cost of unsold
inventory.
As a reference, we also depict in Figure 1 (see Figure 1c) the sequence of events when
there is no lead time in the channel. In that case, production takes place after the demand
uncertainty has been resolved and both wholesale and retail prices are set after demand is known.
Note that ownership in this case does not matter because all decisions are made after the
uncertainty is resolved.
Insert Figure 1
Demand Uncertainty
We model demand and uncertainty in the following manner: Let φ be consumers’
valuation of the service provided by the product. We assume that φ is distributed uniformly in the
interval [0,
1
β
]; that there are α consumers in the market, each independently drawn from the
11
distribution of φ; and that each consumer uses at most one product.4 From these assumptions, the
quantity demanded as a function of price, p, is
q = α Pr[φ ≥ p] = α [1 − Pr[φ ≤ p]] = α (1 −
p
) = α (1 − β p).
1/ β
Thus, the market demand function q is given by
q = α (1 − βp ) ,
(1)
where α represents market size and β represents consumer price sensitivity.
There are two possible sources of uncertainty: (1) the firm may be uncertain about the
exact number of consumers in the market, α ; and/or (2) the firm may be uncertain about
consumers’ valuation of the product, which in this case means uncertainty regarding the upper
bound of the valuation distribution. Uncertainty regarding consumer valuation is reflected as
uncertainty regarding the price sensitivity in the market, β .
Note that, in contrast to the usual linear demand function formulation, in equation 1 we
keep α as a multiplicative term outside the parentheses. This is done to avoid confounding the
effects of potential market size (number of consumers) and price sensitivity. It is common to
write the preceding demand function in reduced form as q = α − β ' p with β ' = αβ and to model
uncertainty as an additive linear error term on α while keeping β ' fixed. Such an approach
confounds uncertainty regarding the number of consumers and their valuation of the product
because keeping β ' fixed requires that β must change in negative correlation to α . This
confounding causes problems in interpretation of the mathematical results. To avoid this, we use
the demand formulation in equation 1.
4
These assumptions lead to a linear demand-function formulation. We also conducted an analysis using an
exponential demand formulation. All of the results of the linear case hold for the exponential case as well. Details
are available from the authors upon request.
12
We assume that the manufacturer and the retailer are uncertain about both market size and
price sensitivity and capture uncertainty for both as a discrete two-state distribution. We denote
parameters related to the high-demand state with a subscript h and parameters related to the lowdemand state with a subscript l. Thus, channel members are uncertain about the number of
potential consumers in the market. Market size can be large (αh) with probability θ1 or small (αl)
with probability (1–θ1) where αh> αl. Channel members are also uncertain about consumer price
sensitivity; price sensitivity can be strong (βl) with probability θ2 or weak (βh) with probability
(1–θ2) where βl > βh.5 Note that as the differences between the high demand state and low
demand state increase, the standard deviation (which is a measure of uncertainty) of market size
and/or price sensitivity increases.
Costs
Regarding costs, we assume that there is a constant marginal cost of production, c per unit;
the retailer’s marginal cost is zero; the holding cost is zero,6 and the unsold units are scrapped
with no cost or value to either the manufacturer or the retailer.
Analysis
We analyze the two scenarios of manufacturer and retailer ownership as a game between a
manufacturer and a retailer where the manufacturer acts as the Stackelberg leader and the retailer
as the follower. The analysis is straightforward; the details are omitted here and can be found in
the appendix. The equilibrium outcomes of the analysis are given in Table 1.
INSERT TABLE 1
5
See Marvel and Peck (1995) for a similar approach for modeling uncertainty.
All the results directly extend to the case of a positive symmetric holding cost, h>0. Details are available from the
authors upon request.
6
13
4. Results
4.1. Who Should Own the Units in a Channel?
Retaining ownership of the units in a channel until uncertainty is resolved exposes a firm
to the risk of not being able to sell all the units. If the optimal sale quantity turns out to be
smaller than the number of available units by Δ , then the firm wastes money (c Δ for a
manufacturer that retains ownership and w Δ for a retailer that retains ownership). On the other
hand, owning the units provides a firm with another degree of freedom in responding to eventual
demand conditions. For example, a manufacturer that owns the units can adjust the wholesale
price according to revealed demand. If, on the other hand, ownership is first transferred to the
retailer, the manufacturer must fix the wholesale price before demand is revealed and cannot
adjust it later. The added flexibility is useful if the firm finds it profitable not to sell all the
available units when demand is low. The firm can then restrict the quantity sold by setting a
higher price. For example, the manufacturer can set a higher wholesale price that results in the
retailer ordering (and selling) fewer than the number of units available in inventory.
These two forces affect the manufacturer and the retailer differently. The cost of wasting a
unit is smaller for the manufacturer than for the retailer since c < w . The manufacturer also cares
more about the flexibility afforded by ownership since that is the only way the manufacturer can
respond to revealed demand while the retailer can always change the retail price. Intuitively,
these differences lead to different decisions by the manufacturer and the retailer regarding when
and how much to restrict sales in the low-demand state. Therefore, it matters who owns the units
in a channel.
14
We find that channel members’ decisions regarding ownership of the units in the channel
depend on the difference in market size between the high-demand and the low-demand state. Let
k = 1−
βh βl c
; then:
β lθ1 (1 − θ 2 ) + β hθ1θ 2
Proposition 1: (A) Retailer profits are greater under retailer ownership when there is a
large difference in market size (
αl k
< ) and under manufacturer ownership when there is an
αh 2
intermediate difference in market size (
k αl
<
< k ). When the difference in market size is small,
2 αh
retailer profits are the same regardless of ownership ( k <
αl
).
αh
(B) Manufacturer profits are greater under manufacturer ownership when the difference
in market size is sufficiently large (
αl
< k ). Manufacturer profits are the same regardless of
αh
ownership when the difference in market size is small ( k <
αl
).
αh
(C) Total channel profits are greater under retailer ownership when the difference in
market size is large (
αl k
< ) and under manufacturer ownership when there is an intermediate
αh 2
difference in market size (
k αl
<
< k ). Channel profits are the same regardless of ownership
2 αh
when the difference in market size is small ( k <
αl
).
αh
INSERT TABLE 2
Several important implications derive from proposition 1. First, it does matter who owns
the units in a channel. Specifically, it matters when the potential difference in market size is large
15
enough (see Table 2). For intermediate differences in market size, the manufacturer should retain
ownership of the units. Since this arrangement also benefits the retailer, it is reasonable to expect
that the manufacturer and retailer can reach an arrangement that keeps ownership with the
manufacturer. When there is a large difference in market size, the retailer would like to have
ownership of the units. However, in this case the manufacturer’s interest differs from the
retailer’s interest in that the manufacturer prefers to retain ownership. Since total channel profits
are greater under retailer ownership, there are potential arrangements that would make everyone
better off and let the retailer assume ownership. This may explain cases in which we observe
retailer ownership in practice. Of course, the fact that an agreement is possible does not mean
that the parties will reach one, and so there is the potential for channel conflict under these
conditions.
To illustrate the importance of these results, consider one possible set of parameters:
βl=0.04, βh=0.02, θ1=θ2=0.5, and c=4. In this case, if expected market size in the low-demand
state is 78% or less than that of the high-demand state, it matters who owns the units in the
channel. If the low-demand market size is even smaller (39% or less of the high-demand market
size), the manufacturer and the retailer will have opposing interests regarding ownership of the
units. The profit implications are substantial. For example, if αh=200 and αl=60, the
manufacturer’s profit is 48% higher under manufacturer ownership than under retailer
ownership, but the retailer’s profit is 98% higher under retailer ownership than under
manufacturer ownership.
To understand what drives this result, one must realize that it matters who owns the units in
the channel only if the firm that owns the units finds it optimal to restrict sales in a low-demand
16
case to less than the available inventory.7 Obviously, it is always optimal to sell all units in highdemand conditions. If it is also optimal to sell all units in low-demand conditions, then there is
no waste from not selling all the units and there is no benefit from the flexibility to react to
demand conditions while bearing the cost of unsold units. When α l is close enough to
αh ( k <
αl
), the difference in market size is small enough that it is always optimal to sell all the
αh
units in both the low-demand and the high-demand states (see Table 1).8 Therefore, it does not
matter who owns the units.
Next, consider what happens when the difference in market size increases as αl decreases
(holding αh constant). Clearly there comes a point at which it is no longer optimal to sell all the
units if market size turns out to be small. The wholesale price decreases faster than the retail
price when αl decreases. The manufacturer’s marginal contribution from selling more units in the
low-demand state becomes negative for values of α l < kα h . Therefore, the manufacturer wants to
restrict sales when α l < kα h . To do that, the manufacturer must have control over the units in the
channel and therefore wants to retain ownership. As a consequence, sales in the high-demand
state increase over the optimal quantity and sales in the low-demand state decrease when the
manufacturer does not hold the inventory. It turns out that, for values of
k αl
<
< k , the added
2 αh
contribution for the retailer in the high-demand state is larger than the loss in contribution from
the low-demand state. Therefore, the retailer is better off (as, obviously, is the channel) under
these conditions when the manufacturer owns the units.
7
Notice that the production quantity is the same regardless of whether the manufacturer or the retailer owns the
units. Therefore, it does not affect the question of ownership.
8
Assuming optimal production quantities.
17
When the difference between the demand states is very large,
αl k
< , the manufacturer is
αh 2
still better off owning the units; however, the retailer and the channel are better off if the retailer
owns the units. When the manufacturer owns the units, the retailer gives up some potential
contribution in the high-demand state (compared to when the retailer owns the units) because the
manufacturer increases the wholesale price when demand is high. This is compensated by the
additional contribution the retailer gains in the low-demand state when the manufacturer reduces
the wholesale price. However, when
αl k
< , this compensation is not sufficient (think what
αh 2
happens, for example, when αl=0; there are no sales in the low-demand state and the retailer
gains nothing from letting the manufacturer own the units) and the retailer is therefore better off
owning the units. The channel is better off when the retailer owns the units because the retailer
sells more units in the low-demand state.
It is interesting that the decision whether to own the units depends only on the uncertainty
regarding market size and does not depend on uncertainty regarding price sensitivity. The reason
that uncertainty regarding price sensitivity does not affect the ownership decision is that changes
in price sensitivity affect only the price—they do not affect the optimal sale quantity. Since
ownership matters only if a firm wants to restrict sales in the low-demand condition and price
sensitivity does not impact the optimal sales quantity, price sensitivity does not affect the
ownership decision.
The critical threshold k = 1 −
βh βl c
, which determines when ownership
β lθ1 (1 − θ 2 ) + β hθ1θ 2
matters and when the manufacturer and retailer both want to own the units, is the ratio of the
actual production quantity to the number of units the manufacturer would like to sell ex-post
18
when market size turns out to be large. Thus (1–k) can be thought of as a measure of the
reduction in quantity produced because of demand uncertainty on the part of channel members.
The greater the reduction in production, the fewer units the channel carries and, therefore, the
benefit of ownership is reduced and ownership matters only at larger potential differences in
market size. Not surprisingly, demand uncertainty leads to lower production the higher the
production cost ( c ), the higher the consumers price sensitivity levels ( β l and β h ) and the higher
the probability that consumers are more price sensitive θ2. Thus, k increases with θ1 and
decreases with c , β l , β h and θ2.
4.2. The Effect of Lead Time on Profits
As expected, under uncertain demand conditions, the presence of lead time (the situation in
Figure 1a and 1b) reduces total channel profits and the manufacturer profits relative to a channel
without lead time (Figure 1c). In addition, under uncertain demand conditions and in the
presence of lead time, retailer profit and consumer surplus are reduced compared to the same
situation without lead time, except:
Proposition 2: When market size is uncertain, retailer profit are greater with lead time
than without lead time under retailer ownership if
cβ h β l
cβ h β l [2 − θ1[2 − cβ h + cθ 2 ( β h − β l )] −
]
θ1[ β l (1 − θ 2 ) + θ 2 β h ] α l k
<
< and consumer surplus are
(1 − θ1 )[(3 − cβ h )(1 + cβ h ) β l + θ 2 ( β h − β l )(3 + c 2 β h β l )]
αh 2
greater with lead time than without lead time under retailer ownership if
cβ h β l
cβ h2 β l [2 − θ1[2 − cβ h + cθ 2 ( β h − β l )] −
]
α k
θ1[ β l (1 − θ 2 ) + θ 2 β h ]
< l < .
2
(1 − θ1 )[(3 − cβ h )(1 + cβ h ) β l β h + θ 2 ( β h − β l )[ β h (15 + β h β l c ) − 4 β l ]] α h 2
Surprisingly, under specific conditions, the retailer and consumers can be better off. The
retailer is better off because the wholesale price is lower with lead time than without it when the
retailer owns the units (see Table 1). This lower wholesale price is obviously beneficial to the
19
retailer. If the preceding condition holds, this effect is stronger for the retailer than the cost of
assuming ownership (because of excess inventory if demand is low) when faced with lead time.
Consumer surplus is greater because retailer ownership generates more sales when market size is
small. And although sales are reduced when the market size is large, the total effect is to increase
consumer surplus under the right conditions. This counterintuitive result underscores the
importance of the decision about ownership of units in the channel. It demonstrates that, even
with the overall inefficiencies and waste resulting from lead time, consumers and the retailer
may be better off when lead time is present when the retailer owns the units. This occurs because
the manufacturer in this case cannot respond to actual demand. Therefore, some channel
coordination problems are mitigated by uncertainty about demand and the fact that the retailer
controls the units in the channel.
Finally, note that neither ownership structure fully solves the coordination problem in the
channel. Channel profits under both ownership arrangements are lower than profits from the
integrated channel. Nonetheless, ownership decisions do have an effect on total channel profits,
which comes closer to the integrated-channel level when (1) the retailer owns the units and
αl k
k α
< and (2) when the manufacturer owns the units and < l < k . Under manufacturer
αh 2
2 αh
ownership the losses due to coordination failure are 25%. These losses are lower under retailer
ownership when the retailer prefers to own the unit. For instance, for the values used in the
example in section 4.1 (βl=0.04, βh=0.02, θ1=θ2=0.5 and c=4), under retailer ownership when
αl=60, αh=200, the profit loss is only 17% compared to 25% under manufacturer ownership.
4.3 Pricing and Passthrough
In this section we turn our attention to understanding how demand uncertainty and the
separation of production and pricing decisions affect pricing and passthrough in the channel. The
wholesale and retail prices in our model can change in response to actual demand conditions.
20
One way to think about these price changes is in the spirit of Gerstner and Hess (1991)—as the
static analog of a dynamic model of promotions.9 Thus, the change in retail and wholesale prices
between demand states can be interpreted as the offering of consumer and trade promotions,
respectively. We find that:
Proposition 3: Retail and wholesale price discounts are deeper in a channel with lead time
than in a channel without lead time.
The presence of lead time has two effects on pricing decisions: (1) because the quantity
produced is smaller than the desired sale quantity when demand is strong, the price when
demand is strong is higher under lead time than under no lead time; and (2) the production cost is
sunk when the firm makes the pricing decision. Therefore, the sales quantity when demand is
weak is higher and the corresponding price is lower with lead time than without lead time.
Obviously, the difference in price between situations of strong and weak demand is larger with
lead time than without lead time.
We now turn our attention to understanding how the passthrough rate is affected by the
nature of the demand uncertainty facing the channel. We find that:
Proposition 4: (A) In the absence of uncertainty regarding price sensitivity (i.e., when the
channel faces only market-size uncertainty,) the passthrough is less than 100%.
(B) When there is uncertainty regarding price sensitivity, the passthrough rate increases as
the potential difference in price sensitivity increases, and, for sufficiently large differences in
price sensitivity, the passthrough rate is higher than 100%.
This result shows that the passthrough rate depends on how much price sensitivity in the
market can change. The more that price sensitivity can change, the higher the resulting
passthrough rate and, importantly, this can lead to passthrough rates that exceed 100%.
To understand this result, consider the effect that market-size and price-sensitivity
uncertainties have on the demand functions. If price sensitivity is known, uncertainty regarding
9
One such model is of perishable products with iid demand over periods.
21
market size leads to the demand function being steeper (rotated counterclockwise) in the lowdemand state than in the high-demand state (see Figure 2, top panel). As a result, for the same
number of units to be sold, the wholesale price must change more than the retail price and passthrough is less than 100%. In contrast, if market size is known, uncertainty regarding price
sensitivity leads to the demand function being less steep (rotated clockwise) in the low-demand
state than in the high-demand state (see Figure 2, bottom panel). In that case, for the same
number of units to be sold, the wholesale price must change less than the retail price and passthrough is greater than 100%. The passthrough rate when there is uncertainty regarding both
market size and price sensitivity is a combination of these two effects. As the potential difference
in price sensitivity increases, the price-sensitivity effect becomes more dominant and the
passthrough rate increases until at a certain point it passes 100%.
Insert Figure 2
5. Conclusion
One of the decisions faced in organizing a channel of distribution is assignment of
ownership of the inventory of units in the channel. Previous research on this question
concentrated on cost and efficiency considerations related to the physical location of the
inventory in the channel. We instead focus on the decision rights that ownership provides and
suggest that the assignment of these decision rights is another important aspect that firms should
consider when determining ownership. The decision rights conferred by ownership can benefit a
firm because it provides flexibility in how the firm can respond to changes in market conditions.
We show that this flexibility is indeed valuable and may lead firms to seek ownership when the
benefits of such flexibility exceed the potential costs of ownership.
22
We consider the situation of a monopolistic channel consisting of a manufacturer and a
retailer that are uncertain a priori about demand conditions in the market. When there is a large
degree of uncertainty regarding market size (the potential difference in market size is large), we
find that the manufacturer and the retailer each prefer to own the units in the channel, which can
lead to conflict. When the degree of uncertainty is intermediate both members of the channel
prefer to have the manufacturer own the units. Further, when the difference is small or the
uncertainty is only regarding price sensitivity, it does not matter who owns the units. We also
find that uncertainty affects the passthrough rate in the channel. The passthrough rate is below
100% when firms know the consumers’ price sensitivity. The rate increases with the level of
uncertainty regarding price sensitivity and can even exceed 100% if the degree of uncertainty
regarding price sensitivity is high.
These findings have important managerial and theoretical implications. They point to the
importance of the decision about who will own the units in the channel. They thus provide
another important explanation for why we observe different arrangements regarding ownership
of units in channels and under what conditions those arrangements should be used.
Our model demonstrates that ownership, while potentially costly, also confers valuable
added flexibility in decision-making. Indeed, we find that the manufacturer prefer to retain
ownership even though it is costly and that, under some conditions, the retailer wants to have
ownership as well. These results suggest that strategic considerations are important in addition to
any cost and/or efficiency considerations in deciding who should own the units in a channel10. If
the manufacturer’s and retailer’s costs do not differ greatly, strategic considerations may
dominate and the manufacturer (at least) may be better off if it maintains ownership.
10
Obviously, in case of asymmetric costs (inventory holding costs and salvage value) the firm that is more efficient
has higher incentives to maintain ownership.
23
Our model results also provide another explanation for the empirical phenomenon of
passthrough rates that range from less than 100% to much greater than 100%. Empirical research
on passthrough rates has reported values ranging from 0% to more than 200% (Chevalier and
Curhan 1976; Walters 1989; Armstrong 1991). Previous studies explained the large range of
observable pass-through rates and, in particular, the less intuitive values of rates greater than
100% as resulting from different demand-function shapes for different products (Bulow and
Pfleiderer 1983; Blattberg and Neslin 1990; Tyagi 1999).11 We provide a complementary
explanation by showing that the amount of uncertainty regarding consumer price sensitivity
affects the passthrough rate and that a large amount of uncertainty can result in passthrough rates
that exceed 100%.
The basic tension in our model is between the benefit ownership confers through greater
flexibility in decision-making and the potential cost of ownership in the form of overstocks and
inventory risks. Thus, our model is suited for situations in which direct variable costs are
substantial, making the potential cost of ownership large. This is true for products such as cars,
durable consumer goods, clothes, and toys. On the other hand, the model does not effectively
capture situations in which direct variable costs are relatively small or even nonexistent, as is the
case for wholly digital products. In those situations, the cost of overstock is very low and,
therefore, issues associated with making the production decision before demand is known are not
as important.
We assume in the model that there is only one production run that takes place before the
firms learn about demand. This corresponds well to situations in which replenishment orders
cannot be fulfilled during the selling season (see, for example, Fisher et al. (1994) and Moon
(2002)) but it is clearly a simplification of situations in which firms can place replenishment
11
Neslin, Powell, and Stone (1995) also explained rates greater than 100% using a “loss leader” argument.
24
orders. The ability to have an additional production run in response to actual demand may affect
ownership choices as well as other decisions, such as the initial quantity ordered by the retailer.
Multiple production runs also may lead to situations in which the manufacturer and the retailer
simultaneously own some of the units. For example, the manufacturer may, in such situations, try
to limit the number of units the retailer can order before the uncertainty is resolved. In this paper,
we conceptualize ownership of the units in the channel as a simple either/or construct.
Our model uses the common assumption that firms are risk-neutral (or at least that they
should be risk-neutral). It is interesting to consider how different risk attitudes might affect the
results. Ex ante, for the manufacturer (retailer), the difference in profit between the two demand
states varies more when the manufacturer (retailer) owns the units. Thus, risk-averseness tends to
reduce the expected benefit of ownership. As a consequence, one would not expect there to be a
region of indifference regarding ownership if firms are risk-averse. Instead, in that case, both
firms will prefer not to own the units. In addition, it will require greater benefit from ownership
for firms to prefer to own the units. Thus the regions in which the manufacturer and retailer both
want to own the units will be at higher levels of uncertainty in the risk-averse case than in the
risk-neutral case (the critical threshold k will be lower).12 A full analysis of the effect of risk
attitude is beyond the scope of the paper; nonetheless, it appears that risk-averseness, while
weakening the results somewhat, does not affect the overall structure of the findings.
A natural follow-up question is whether the manufacturer or the retailer will actually retain
ownership of the units in the channel, especially in cases where their interests differ.13 Since the
channel’s profits are greater under retailer ownership when both the retailer and the manufacturer
want to retain ownership, the efficiency criterion suggests that the retailer will assume
12
The effects for a risk-seeking firm are the opposite of those for the risk-averse firm.
25
ownership. Indeed, if one allows side payments between the retailer and the manufacturer, it is
easy to construct an arrangement that makes everyone better off under retailer ownership, thus
guaranteeing it. Although the efficiency criterion is appealing in theory, in practice it may not be
so easy to reach such arrangements. For example, it is well known in the literature addressing the
double marginalization channel-coordination problem that two-part tariffs can coordinate the
channel (Moorthy 1987) but such arrangements are not commonly observed in practice (except
in franchising; see Desai and Srinivasan (1996)). Thus, it is not clear which channel member will
actually retain ownership when the retailer and manufacturer incentives differ. It appears that the
ownership question presents another coordination issue for channel members.
These issues, as well as other questions relating to the effect of competition and risksharing arrangements (such as return policies) on ownership decisions, require additional followup research. This paper provides the beginnings of an understanding of the implications of
ownership for the channel and of the effects of the presence of lead time and demand uncertainty
on decision-making by channel members.
13
Our model obviously does not directly address this question since we do not model the decision within the
channel regarding ownership, only the incentives of the channel members to retain ownership.
26
6. References
Anupindi, R., and Bassok Y., (1999), “Centralization of Stocks: Retailers vs. Manufacturer,”
Management Science, 45(2), 178–191.
Armstrong, M. K., (1991), “Retail Response to Trade Promotions: An Incremental Analysis of
Forward Buying and Retail Promotion,” doctoral dissertation, University of Texas, Dallas.
Blattberg, R. C., and Neslin A., (1990), Sales Promotions: Concepts, Methods and Strategies,
Prentice Hall, NJ.
Bulow, J. I., and Pfleiderer P., (1983), “A Note on the Effect of Cost Changes on Prices,” Journal
of Political Economy, 91(1), 182–185.
Cachon, G., (2004), “The Allocation of Inventory Risk in a Supply Chain: Push, Pull, and
Advance-Purchase Discount Contracts,” Management Science, 50(2), 222–238.
Caruana, G., and Einav L., (2005), “Quantity Competition with Production Commitment: Theory
and Evidence from the Auto Industry,” working paper, Stanford University.
Chevalier, M., and Curhan R. C., (1976), “Retail Promotions as a Function of Trade Promotions:
A Descriptive Analysis,” Sloan Management Review, 18(3), 19–32.
Coughlan, A. T., Anderson E., Stern L. W., and El-Ansary A. I., (2006), Marketing Channels, 7th
ed., Prentice Hall, Upper Saddle River, NJ.
Dong, Y., Dresner M., and Shankar V., (2005) “Delegation and Replenishment in Distribution
Channels,” Working paper.
Desai, P. S., and Srinivasan K., (1996), “Aggregate versus Product-Specific Pricing: Implications
for Franchise and Traditional Channels,” Journal of Retailing, 72(4), 357–382.
Ferguson, E. M., (2003), “Commitment Time Issues in a Serial Supply Chain with Forecast
Updating,” Naval Research Logistics, (50), 917–936.
Fisher, M. L., and Raman A., (1996), “Reducing the Cost of Demand Uncertainty through
Accurate Response to Early Sales,” Operations Research, 44(1), 87–99.
Fisher, M. L., Hammond J. H., Obermeyer W. R., and Raman A., (1994), “Making Supply Meet
Demand in an Uncertain World,” Harvard Business Review, May–June, 83–93.
Gerstner, E., and Hess J. D., (1991), “A Theory of Channel Price Promotions,” American
Economic Review, (81), 872–886.
Grossman, S. G., and Hart O. D., (1986), “The Costs and Benefits of Ownership: A Theory of
Vertical and Lateral Integration,” Journal of Political Economy, 94(4), 691–719.
Iyer, A. V., and Bergen M. E., (1997), “Quick Response in Manufacturer-Retailer Channels,”
Management Science, 43(4), 559–570.
Iyer, G., and Padmanabhan V., (2000), “Product Lifecycle, Demand Uncertainty, and Channel
Contracting,” working paper, University of California, Berkeley.
Iyer, G., and Villas-Boas M. J., (2003), “A Bargaining Theory of Distribution Channels,” Journal
of Marketing Research, (40), 80–100.
27
Iyer, G., Narasimhan C., and Niraj R., (2007), “Information and Inventory in a Distribution
Channels,” Management Science, 53(10), 1551-1561.
Johnson, M. E., (2001), “Learning from Toys: Lessons in Managing Supply Chain Risk from the
Toy Industry,” California Management Review, 43(3), 106–124.
Lariviere, M. A., and Porteus E., (2001), “Selling to the Newsvendor: An Analysis of Price-Only
Contracts,” Manufacturing Service Operations Management, (3), 293–305.
Lee, H. L., and Tang C. S., (1996), “Modeling the Costs and Benefits of Delayed Product
Differentiation,” Management Science (43), 40–53.
Mantrala, M. K., and Raman K., (1999), “Demand Uncertainty and Supplier’s Returns Policies for
a Multi-Store Style-Good Retailer,” European Journal of Operations Research, 115(2), 270–
284.
Mantrala, M. K., Basuroy S., and Gajanan S., (2005), “Do Style-Goods Retailers’ Demands for
Guaranteed Profit Margins Unfairly Exploit Vendors?” Marketing Letters, 16(1), 53–66.
Marvel, P. H., and Peck J., (1995), “Demand Uncertainty and Returns Policies,” International
Economic Review, (36), 691–714.
McGuire, T., and Staelin R. (1983), “An Industry Equilibrium Analysis of Downstream Vertical
Integration,” Marketing Science, 2(2), 161–191.
Moon, Y., (2002), Electronic Arts Introduces The Sims Online, Harvard Business School Case 9503-008.
Moorthy K. S., (1987), “Managing Channel Profits—Comment,” Marketing Science, 6(4), 375–
379.
Neslin, S. A., Powell S. G., and Stone L. S., (1995), “The Effects of Retailer and Consumer
Response on Optimal Manufacturer Advertising and Trade Promotion Strategies,”
Management Science, 41(5), 749–766.
Netessine, S., and Rudi N., (2004), “Supply Chain Structures on the Internet and the Role of
Marketing-Operations Interaction,” in Supply Chain Analysis in an E-business Era, D. SimchiLevi, S. D. Wu and M. Shen, eds., Kluwer.
Netessine, S., and Rudi N., (2006), “Supply Chain Choice on the Internet,” Management Science,
52(6), 844–864.
Padmanabhan, V., and Png I. P. L., (1997), “Manufacturer’s Return Policies and Retail
Competition,” Marketing Science, 16(1), 81–94.
Rubinstein, A., and Wolinsky A., (1987), “Middlemen,” The Quarterly Journal of Economics,
102(3), 581–593.
Schleifer, A. Jr., (1993), L.L. Bean, Inc., Harvard Business School Case 9-893-003.
Taylor, A. T., (2006), “Sale Timing in a Supply Chain: When to Sell to the Retailer,”
Manufacturing and Service Operations Management, 8(1), 23–42.
Tyagi, R. K., (1999), “A Characterization of Retailer Response to Manufacturer Trade Deals,”
Journal of Marketing Research, 36(3), 510–516.
28
Valentini, G., and Zavanella L., (2003), “The Consignment Stock of Inventories: Industrial Case
and Performance Analysis,” International Journal of Production Economics, 81–82, 215–224.
Van Meighem, J., and Dada M., (1999), “Price versus Production Postponement: Capacity and
Competition,” Management Science, 45, 1631–1649.
Wall Street Journal, (2003), “B-to-B—Looking Big: How Can Online Retailers Carry So Many
Products? The Secret Is Drop-Shipping,” April 28, 7.
Walters, R. G., (1989), “An Empirical Investigation into Retailer Response to Manufacturer Trade
Promotions,” Journal of Retailing, 65(2), 253–272.
Wang Y., Jiang L., and Shen Z. J., (2004), “Channel Performance under Consignment Contract
with Revenue Sharing,” Management Science, 50(1), 37–47.
29
Table 1: Equilibrium Outcomes
Retailer Ownership
αl <
Price (large market size)
Price (small market size)
αh
2
(1 −
β hβ lc
)
β l θ 1 (1 − θ 2 ) + β h θ 1θ 2
cβ h
⎧1 3
⎪ 4 [ β + θ [ β (1 − θ ) + θ β ] ] if β l
⎪
l
l
1
2
2 h
⎨
1
3
β
c
l
⎪ [ +
] if β h
⎪⎩ 4 β h θ1[ β l (1 − θ 2 ) + θ 2 β h ]
Wholesale price
(large market size)
Wholesale price
(small market size)
NR
αh
4
[1 −
β h βl c
]
β lθ1 (1 − θ 2 ) + β hθ1θ 2
αl
Sales (small market size)
α l < α h (1 −
β hβ lc
)
β l θ 1 (1 − θ 2 ) + β h θ 1θ 2
cβ h
⎧1 3
⎪ 4 [ β + θ [ β (1 − θ ) + θ β ] ] if β l
⎪
l
l
1
2
2 h
⎨
1
3
β
c
l
⎪ [ +
] if β h
⎪⎩ 4 β h θ1[ β l (1 − θ 2 ) + θ 2 β h ]
2
cβ h
⎧1 1
⎪ 2 [ β + θ [ β (1 − θ ) + θ β ] ] if β l
⎪
l
l
1
2
2 h
⎨
cβ l
⎪1 [ 1 +
] if β h
⎩⎪ 2 β h θ1[ β l (1 − θ 2 ) + θ 2 β h ]
4
[1 −
α l > α h (1 −
β hβ lc
)
β l θ 1 (1 − θ 2 ) + β h θ 1θ 2
No Lead Time
α l [θ 2 β h + β l (1 − cβ h − θ 2 )]
⎧ 1
⎪ 2β [2 − 2[α (1 − θ ) + α θ ][ β (1 − θ ) + θ β ] ] if β l
⎪ l
1
2
2 h
h
l 1
l
⎨
α l [θ 2 β h + β l (1 − cβ h − θ 2 )]
⎪ 1 [2 −
] if β h
2[α h (1 − θ1 ) + α lθ1 ][ β l (1 − θ 2 ) + θ 2 β h ]
⎩⎪ 2β h
⎧ 3 + cβ l
⎪ 4 β if β l
⎪
l
⎨
⎪ 3 + cβ h if β
h
⎪⎩ 4 β h
⎧ 3 + cβ l
⎪ 4 β if β l
⎪
l
⎨
⎪ 3 + cβ h if β
h
⎪⎩ 4 β h
α hα l [θ 2 β h + βl (1 − cβ h − θ 2 )]
⎧ 1
⎪ 2α β [2α h − [α (1 − θ ) + α θ ][ β (1 − θ ) + θ β ] ] if β l
⎪ h l
h
l 1
l
1
2
2 h
⎨
α hα l [θ 2 β h + βl (1 − cβ h − θ 2 )]
⎪ 1 [2α −
] if β h
h
[α h (1 − θ1 ) + α lθ1 ][ β l (1 − θ 2 ) + θ 2 β h ]
⎩⎪ 2α h β h
⎧1 + cβ l
⎪ 2 β if β l
⎪
l
⎨
⎪1 + cβ h if β
h
⎪⎩ 2 β h
α hα l [θ 2 β h + βl (1 − cβ h − θ 2 )]
⎧ 1
⎪ 2α β [2α l − [α (1 − θ ) + α θ ][ β (1 − θ ) + θ β ] ] if β l
⎪ l l
h
l 1
l
1
2
2 h
⎨
α hα l [θ 2 β h + βl (1 − cβ h − θ 2 )]
⎪ 1 [2α −
] if β h
l
[α h (1 − θ1 ) + α lθ1 ][ β l (1 − θ 2 ) + θ 2 β h ]
⎩⎪ 2α l β h
⎧ 1
⎪ 2 β if β l
⎪ l
⎨
⎪ 1 if β
h
⎪⎩ 2 β h
αh
Indifference
α h [θ 2 β h + β l (1 − cβ h − θ 2 )]
⎧ 1
⎪ 2β [2 − 2[α (1 − θ ) + α θ ][β (1 − θ ) + θ β ] ] if β l
⎪ l
h
l 1
l
1
2
2 h
⎨
α h [θ 2 β h + β l (1 − cβ h − θ 2 )]
⎪ 1 [2 −
] if β h
⎪⎩ 2β h
2[α h (1 − θ 1 ) + α l θ 1 ][β l (1 − θ 2 ) + θ 2 β h ]
⎧ 3
⎪ 4β if β l
⎪ l
⎨
⎪ 3 if β
h
⎪⎩ 4β h
⎧ 1
⎪ 2β if β l
⎪ l
⎨
⎪ 1 if β
h
⎪⎩ 2β h
β l β h c + θ1 β l + ( β h − β l )θ1θ 2
2β l β h
Sales (large market size)
Manufacturer Ownership
β h βl c
]
β lθ1 (1 − θ 2 ) + β hθ1θ 2
α hα l [θ 2 β h + β l (1 − cβ h − θ 2 )]
⎧α
4[α h (1 − θ1 ) + α lθ1 ][ β l (1 − θ 2 ) + θ 2 β h ] ⎪⎪
h (1 − cβ l )
if β l
4
⎨
⎪α h (1 − cβ l ) if β
h
⎪⎩
4
α hα l [θ 2 β h + β l (1 − cβ h − θ 2 )]
4[α h (1 − θ1 ) + α lθ1 ][ β l (1 − θ 2 ) + θ 2 β h ]
αl
4
30
⎧1 + cβ l
⎪ 2 β if β l
⎪
l
⎨
⎪1 + cβ h if β
h
⎪⎩ 2 β h
⎧α l (1 − cβ l )
if β l
⎪⎪
4
⎨
⎪α l (1 − cβ l ) if β
h
⎪⎩
4
Production (ordering) quantity
Retailer profit
αh
β h βl c
[1 −
]
β lθ1 (1 − θ 2 ) + β hθ1θ 2
4
α h [ β h ( β l c − θ1θ 2 ) − θ1β l (1 − θ 2 )]2
8θ1β h β l [ β l (1 − θ 2 ) + θ 2 β h ]
CS 1
Consumer surplus
Where, Π R1 =
β h βl c
[1 −
]
β lθ1 (1 − θ 2 ) + β hθ1θ 2
4
Π R2
Π R1
Manufacturer profit
αh
ΠM2
CS 2
1
(1 − cβ )α i
4
α hα l [θ 2 β h + β l (1 − cβ h − θ 2 )]2
16β h β l [α h (1 − θ1 ) + α lθ1 ][β l (1 − θ 2 ) + θ 2 β h ]
(1 − cβ i ) 2 α i
16β i
α hα l [θ 2 β h + β l (1 − cβ h − θ 2 )]2
8β h β l [α h (1 − θ1 ) + α lθ1 ][β l (1 − θ 2 ) + θ 2 β h ]
(1 − cβ i ) 2 α i
8β
α hα l [θ 2 β h + β l (1 − cβ h − θ 2 )] 2
32β h β l [α h (1 − θ 1 ) + α l θ 1 ][β l (1 − θ 2 ) + θ 2 β h ]
(1 − cβ i ) 2 α i
32 β i
4θ1α l (1 − θ1 )[ β l (1 − θ 2 ) + θ 2 β h ]2 + α h [ β h ( β l c − θ1θ 2 ) − θ1β l (1 − θ 2 )]2
,
16θ1β h β l [ β l (1 − θ 2 ) + θ 2 β h ]
4θ1αl (1 − θ1 )[βl (1 − θ2 ) + θ2 β h ][β h βl + θ 2 (4β h2 − 5βh βl + β l2 )] + α h β h [β h ( βl c − θ1θ 2 ) − θ1βl (1 − θ 2 )]2
CS1 =
32θ1β h2 βl [βl (1 − θ 2 ) + θ 2 βh ]
Π R2 =
θ1α l (1 − θ1 )[ βl (1 − θ 2 ) + θ 2 β h ]2 + α h [ β h ( βl c − θ1θ 2 ) − θ1βl (1 − θ 2 )]2
,
16θ1β h β l [ β l (1 − θ 2 ) + θ 2 β h ]
ΠM 2 =
θ1α l (1 − θ1 )[ βl (1 − θ 2 ) + θ 2 β h ]2 + α h [ β h ( β l c − θ1θ 2 ) − θ1β l (1 − θ 2 )]2
and
8θ1β h β l [ β l (1 − θ 2 ) + θ 2 β h ]
CS 2 =
α hα l [θ 2 β h + β l (1 − cβ h − θ 2 )]
4[α h (1 − θ1 ) + α lθ1 ][ β l (1 − θ 2 ) + θ 2 β h ]
θ1α l (1 − θ1 )[ β l (1 − θ 2 ) + θ 2 β h ]2 + α h [ β h ( β l c − θ1θ 2 ) − θ1β l (1 − θ 2 )]2
.
32θ1β h β l [ β l (1 − θ 2 ) + θ 2 β h ]
31
,
Table 2: Ownership Structure Preferences
αl k
<
αh 2
k αl
<
<k
2 αh
Manufacturer’s
preference
Retailer’s preference
Manufacturer
ownership
Retailer ownership
Total channel profit
is greater under
Retailer ownership
Manufacturer
ownership
Manufacturer
ownership
Manufacturer
ownership
32
k<
αl
αh
Indifferent
Indifferent
Indifferent
Figure 1a: Retailer Ownership
Retailer
orders
product
Retailer sets
retail price
Retailer scraps
unsold units
t
Manufacturer sets
wholesale price
Figure 1b: Manufacturer Ownership
Retailer orders
products and sets
retail price
t
Manufacturer
produces
units
Manufacturer
sets wholesale
price
Manufacturer
scraps unsold
units
Figure 1c: No Lead Time Case
Retailer orders
products and sets
retail price
t
Manufacturer
produces units &
sets unit price
Uncertainty
resolved
33
P,w
1
Figure 2: Pass-through and Demand Uncertainty
β
Retailer
Reaction Curve
ΔP
Δw
Consumer
Demand
q
*
P,w
1
1
ΔP
αl
αh
2
2
αl
αh
q
βh
βl
Retailer
Reaction Curve
Δw
Consumer
Demand
q
*
α
2
34
α
q