Competing Under Financial Constraints∗
Guillem Ordóñez-Calafı́†
University of Warwick
February 20, 2016
Abstract
This paper extends a model of trade credit to study the interaction between financial
constraints and product market competition. The non-contractibility of a retailer’s
investment limits the line of credit that its supplier is able to extend. Then, input
prices regulate both the retailer’s input demand and the quantity of input that it can
borrow. Credit rationing arises in equilibrium when the retailer’s competitive pressure
is sufficiently strong. I show that financial constraints act as a commitment device
that induce the supplier to lower input prices and increase the retailer’s aggressiveness
in the product market. As a result, both the retailer and the supplier can be more
profitable due to presence of financial constraints.
JEL classification: G32, L11, L13
Keywords: Trade credit, financial constraints, product market competition
∗
Special thanks to my supervisors John Thanassoulis and Jacob Glazer and also to Dan Bernhardt.
I also thank Pablo Beker, Vicente Cuñat, Gonzalo Gaete, Christian Laux, Rocco Macchiavello, Volker
Nocke, Giulio Trigilia and the participants at the MTWP Warwick; SMYE; Network of Industrial Economics
DSC; European Finance Association DT; TSE-MaCCI ENTER and Econometric Society EWM for helpful
comments. Financial support from the ESRC is gratefully acknowledged.
†
Department of Economics, University of Warwick. g.ordonez-calafi@warwick.ac.uk
1
Introduction
Firms’ limited access to credit is a widespread phenomenon. Among other effects, the lack of
credit reduces companies’ investment, thereby shaping both production chains and the market structure. Moreover, input prices and product market competition determine investment
profitability and in turn, whether firms are financially constrained. Despite the reciprocal
effect of market structure and financial constraints, the literature has often approached the
two mechanisms separately. The main purpose of this paper is to study the interaction between these elements in a unified setting. I show that a financially constrained retailer can
be at a competitive advantage due to the need to honour its debt. Moreover, I propose a
relation between input price discrimination and the presence of financial constraints.
I extend the model of trade credit in Burkart and Ellingsen (2004) to study the commercial
relation between a supplier and a financially constrained retailer. Trade credit occurs when
a supplier allows a customer to delay payment for goods already delivered. Hence, it can
be seen as a financial transaction where the supplier becomes a lender and the retailer
acts as a borrower. Evidence shows that this is an important source of firms’ finance even
in countries with well-developed financial systems (see, for instance, Rajan and Zingales
1995 and Giannetti 2003). There is extensive literature analysing both the rationale for
trade credit and its price relative to other forms of credit (see Klapper et al. 2012 and
references therein). While not neglecting the importance of these questions, I enrich a model
of trade credit to study the interaction between input pricing, product market competition
and financial constraints.
I consider a supplier (he) extending trade credit to a competitive retailer (she). The
retailer’s investment in the retail market is not contractible. Thus, limited liability creates
an incentive to divert the product and obtain private benefits rather than honour the debt.
As a consequence, the supplier must reduce the volume of credit extended to ensure that
retailer’s repayment is incentive compatible. Notably, the line of credit offered by the supplier
is a combination of volume of input and input price. Therefore, the supplier’s price policy
determines both the retailer’s input demand and the quantity of input that can be extended
in credit. The retailer is financially constrained when she cannot obtain the loan that she
wants even though she is willing to pay it back (Tirole 2006). Hence, in equilibrium credit
rationing arises endogenously.
It is well known that product market competition has a profit destruction effect that
reduces firms’ ability to raise funds (see Tirole 2006, for a comprehensive approach). More
specifically, competitive pressure reduces the profitability of the investment and increases
incentives to divert, thereby raising the agency costs of the financial transaction. This effect
1
is captured in my model, where I use the number of retailer’s competitors to characterise
the conditions under which she is financially constrained. Importantly, financial constraints
both determine and are affected by the supplier’s price policy. With low competitive pressure
there is no credit rationing and the vertical relation between the supplier and the retailer is
characterized by double marginalization. Conversely, higher competition leads to financial
constraints. Then, the retailer exhausts all credit and as a consequence, the delegation
problem of double marginalization vanishes.
My main result shows that both the retailer and the supplier can be more profitable due to
credit rationing. This occurs for intermediate levels of competitive pressure, when financial
constraints bind but are not severe. The line of credit becomes a commitment device that
makes it profitable for the supplier to lower input prices and induce higher aggressiveness of
the retailer in the product market. Hence, even though the retailer obtains less credit than
in the absence of contractual frictions, she borrows a higher quantity of input. The retailer
has further gains because competitors reduce their output, becoming less profitable than if
their rival was self-financed. This result is in contrast to the common view that financial
constraints reduce profits and lead to underinvestment (see, for instance, Holmstrom and
Tirole 1997 and the long literature that follows).
The linearity of wholesale prices is a key element to the mechanism driving the main
result. This (standard) assumption generates double marginalization over the vertical chain.
I show that financial constraints eliminate double marginalization and allow the supplier to
regulate the retailer’s investment exempt of delegation problems. In a natural extension,
I relax the linear assumption and characterize the optimal contract. Then, the supplier is
always negatively affected by the contractual frictions. Notably, I show that an optimal
contract can be implemented with a two part tariff such that the retailer is never financially
constrained. Thus, financial constraints may not arise in equilibrium despite agency problems. This result opens a door to the analysis of the relation between price discrimination
(linear versus non-linear pricing) and credit rationing.
The remainder of the paper is structured as follows. Section 2 revises the related literature. Section 3 describes the model and Section 4 presents the equilibrium analysis without
characterizing the input price. Section 5 derives the supplier’s price policy under linear
pricing and compares the market outcome with a setting where there is no credit rationing.
Section 6 relaxes the linearity assumption and Section 7 concludes.
2
2
Related Literature
I extend the model of trade credit in Burkart and Ellingsen (2004) in two directions. I
introduce product market competition in the retail market so as to make the retailer’s input
demand endogenous. While the effects of suppliers’ competition on the extension of trade
credit are analysed, for instance, in Petersen and Rajan (1997), McMillan and Woodruff
(1999), Fisman and Raturi (2004) and Fabbri and Klapper (2014), the effects of retailers’
competitive pressure have drawn little attention. Furthermore, I assume that the supplier is
a monopolist. As a result, input prices endogenously determine the line of credit. Numerous
papers argued that trade credit can be used by suppliers to price discriminate, offering longer
terms to favoured clients (see, e.g., Wilner 2000; Fisman and Raturi 2004; Giannetti et al.
2011). In this paper input prices do not provide a rationale for trade credit. Instead, they
determine the volume of input that can be extended in credit given the presence of financial
constraints. As Giannetti et al. (2011) note, it is still not clear whether a supplier would
reduce input prices to credit-constrained customers. I answer this question.
The forces interacting here are similar to the studies where ex ante strategic decisions
provide a first-mover advantage in the product market. This is the case, for example, of investment capacity in Dixit (1980). Financial contracts have also been proposed as a strategic
commitment that alters product market outcomes. Fershtman and Judd (1987) analyse the
incentive contracts that principals (owners) will choose for their agents (managers) in an
oligopolistic context. Most notably, Brander and Lewis (1986) show that a firm may want
to choose its financial structure so as to commit to being aggressive in the product market.
The present paper differs from previous contributions on that the retailer does not have a
first-mover advantage. I propose a setting where the commitment device is given by the
presence of financial constraints. As a consequence, both the supplier and the retailer only
benefit from it when agency costs are sufficiently high.
My results reconcile opposite findings about the effects of leverage on firms’ ability to
compete in the product market, which are comprehensively reviewed in Cestone (1999).
Companies can be at a competitive advantage due to the presence of financial constraints.
However, if competition is severe, credit rationing reduces profits and may prevent a company from entering the market. Therefore, my results are also relevant to the study of the
impact of financial constraints on firms’ investment. Extensive literature contributed to the
common wisdom that credit rationing reduces profits and leads to underinvestment (see, for
instance, Holmstrom and Tirole 1997 or Nocke and Thanassoulis 2014). In contrast, I show
that financial constraints can provide a commitment device that leads to higher levels of
investments and profits.
3
3
The Model
I describe the model in four parts. These are as follows:
Vertical Relation. Consider a penniless retailer (she) that wishes to enter a retail
market. For this, she needs to borrow input from a supplier (he), i.e. to obtain trade
credit. Hence, we omit the presence of banks. In the spirit of Burkart and Ellingsen (2004),
neither this nor the no-wealth assumptions affect the main results. In particular, relaxing
either or both assumptions would only reduce the amount of trade credit that the retailer
requires. The supplier faces a unit production cost of cu and has all the bargaining power. In
particular, he sets an input price T (·) and the retailer borrows a quantity I, thereby incurring
a debt T (I). To ease presentation, I assume that each unit of input can be transformed into
a unit of output in the retail market.
Markets. The retailer can only obtain trade credit from her supplier. This provides a
simple setting for our analysis. Nonetheless, imperfect competition in the upstream market
would not change the main insights. Downstream, the retailer competes à la Cournot in
a market with an inverse demand function P (Q) = M − Q, where Q represents the total
quantity of good that is sold. The market features N homogeneous firms that we call
incumbents. Firm i ∈ {0, 1, 2, . . . , N } produces qi and each firm has the same unit cost c.
Modelling identical incumbents simplifies our setup and lets us exploit the vertical relation
as a function of the competitive pressure in a simple way.
Moral Hazard and Financial Constraint. Following Burkart and Ellingsen (2004),
assume that sales revenues are verifiable, but neither input purchase nor investment decisions
are contractible. A moral hazard problem arises because the retailer has limited liability and
can divert resources that were destined for sale into private benefits. As a consequence,
debt is honoured only to the extent of market revenues and the retailer enjoys these only
after honouring all repayment obligations. Let qe ∈ [0, I] be the retailer’s output in the
downstream market. The remaining I − qe goes to non-contractible uses that generate a
private payoff of β ∈ (0, cu ) per unit of input. Hence, diversion of resources is inefficient.
The retailer’s utility is
πe = max
n
M−
XN
i=1
qi − q e
o
qe − T (I), 0 + β (I − qe )
(1)
This profit function makes it optimal for the retailer borrowing ”infinite” amounts of
input that she then diverts. To prevent this, the supplier can set a limit L to the volume of
input that he extends in credit, so that I ≤ L. The retailer is financially constrained when
her desired investment exceeds the amount of input that she can borrow, L.
Timing. First, the supplier offers a contract {T (·), L} and the retailer borrows I ≤ L.
4
Hence, the supplier incurs a production cost cu I and the retailer incurs a debt T (I). Second,
incumbents and retailer simultaneously launch qi and qe ≤ I in the retail market while
I − qe is diverted. Importantly, incumbents do not observe either the supplier’s offer or
the transaction with the retailer. Thus, even though the supplier anticipates the retailer’s
demand, our game has a unique stage.
4
Equilibrium Analysis
I start with two preliminary results that simplify the subsequent analysis. I first establish
that the retailer never invests so little as to pay only a fraction of the debt, T (I). In the
retailer’s objective function (1), honouring the debt partially does not generate any utility the value of the maximand is still zero. Instead, when the same resources are diverted, the
retailer obtains β > 0 per unit. Lemma 1 follows from the assumption that market revenues
are contractible:
Lemma 1 Honouring the debt is an all-or-nothing decision for the retailer.
The second result shows that the retailer never allocates input to uses that generate
non-contractible private benefits. This implies that the supplier offers a contract so that the
retailer honours her debt. Furthermore, it also rules out a situation where, despite honouring
the debt, the retailer allocates some input to alternative uses. To see this, notice that for
repayment to be incentive compatible, the retailer’s profits in the market must be πe ≥ βL.
Hence, the supplier cannot extract any surplus from input destined to alternative uses since
these generate β per unit. Moreover, since cu > β, each unit of input that is not invested in
the retail market reduces the supplier’s profits.
Corollary 2 All input borrowed by the retailer is invested in the retail market, i.e. qe = I.
In sum, given the contract offered by the supplier, the retailer always honours the debt
and never allocates input into alternative uses. Next, we use these results to characterize
the best responses of each agent.
4.1
Best Replies
Incumbents. The profits of incumbent i are πi = M −
I can represent the best response of any incumbent as
qi∗ (qe ) =
M − qe − c
, ∀i
N +1
5
P
q
−
q
−
q
qi − cqi . Thus,
−i
i
e
−i
(2)
Retailer. By Corollary 2, the objective function in (1) collapses to πe = (M − N qi − qe ) qe −
P
T (qe ), where I use the symmetry of incumbents’ responses to represent i qi = N qi . The
retailer best replies to both incumbents’ output qi and the supplier’s offer {T, L}. Suppose,
for now, that repayment is incentive compatible. Then,
(
qe∗ (qi , T, L)
=
qe∗ (qi , T ) =
L
M −N qi −T 0 (qe )
2
if qe∗ (qi , T ) ≤ L
otherwise
(3)
The first line in (3) represents the case where the retailer is not financially constrained.
Incumbents’ reaction and input price lead to an optimal investment that is below the credit
line offered by the supplier. This is in contrast to the second line, where the retailer cannot
obtain as much credit as she wishes. Then, the concavity of profits in the retail market
implies that she exhausts the line of credit, i.e. qe = L.
Supplier. The supplier offers a contract {T (qe ), L}. Importantly, the line of credit
L makes the retailer indifferent between investing and diverting. Note that higher credit
provides the retailer incentives to divert, generating a loss for the supplier. Conversely, a
lower L can have either of two effects. If the retailer is not constrained - the first line in
(3), then reduced credit would have no impact in equilibrium. Instead, if the constraint is
binding - the second line in (3), a lower L is strictly dominated: by increasing L marginally,
the retailer borrows more input and will repay, increasing the supplier’s profits. This allows
to characterize the line of credit as follows:
(
πe (qe∗ (qi ,T ))
if βqe∗ (qi , T ) < πe (qe∗ (qi , T ))
β
(4)
L(qi , T ) =
πe (L(qi ,T ))
otherwise
β
The first line in (4) represents the case where the unconstrained investment is more
profitable than diverting the same quantity of input. The constraint L(qi , T ) is the input
that, when diverted, generates revenues that equal market profits. Thus, the retailer, whose
best response corresponds to the first line in (3), is indifferent between investing qe∗ (qi , T ) or
diverting a higher volume of input, L(qi , T ). The second line in (4) captures the case where
investing optimally in the retail market is less profitable than diverting the same quantity of
input. Then, the retailer is constrained and her response corresponds to the second line in
(3), where qe∗ (qi , T, L) = L(qi , T ). This argument reduces the supplier’s problem to his price
policy:
maxT {T − cu qe (T )}
(5)
s.t. (3) and (4)
Therefore, the tariff determines both the retailer’s best response and the line of credit.
6
The solution to the supplier’s problem is characterized under both linear and non-linear
assumptions in sections 4 and 5. Next, we describe the two possible outcome of this game.
4.2
Delegation and Financial Constraints
Two types of equilibria can emerge. To better understand the underlying mechanisms,
I first abstract from the supplier’s price policy and present these two outcomes without
characterizing the tariff.
First, suppose that the financial constraint does not bind. This is captured by the first
lines in both (3) and (4). Then, best responses of market participants lead to
qen (T ) =
M − T 0 (qe )(N + 1) + cN
N +2
and
qin (T ) =
M − 2c + T 0 (qe )
N +2
(6)
If, instead, the retailer is financially constrained, the second lines in both (3) and (4) apply.
Then, the market outcome is
qec (T )
T (L)
+ β (N + 1) + cN
= L(T ) = M −
L
and
qic (T ) = β − c +
T (L)
L
(7)
The difference between the two equilibria reveals a key feature of the model. When the
financial constraint does not bind, the supplier faces a delegation problem. In particular, the
tariff determines the retailer’s demand for input (and her investment in the retail market)
by regulating her marginal cost. The process is also known as double marginalization.
Conversely, if the retailer is financially constrained, her demand equals the line of credit
L(qi , T ). Hence, the supplier can regulate the retailer’s investment through the financial
constraint and as a result, the delegation problem vanishes.
The rest of the paper studies the supplier’s pricing strategy and the corresponding outcome as a function of the number of incumbents, N . By introducing exogenous variation on
the competitive pressure, I characterize the conditions under which each equilibrium arises.
Proposition 3 If cu + β > c, the retailer cannot enter the market (L = 0) for N ≥ N ≡
M −β−cu
.
cu +β−c
Proof : Trade requires πu = T (qe ) − cu qe ≥ 0 and πe = (M − N qi − qe )qe − T (qe ) ≥ βqe .
Suppose the retailer gathers all surplus, so T (qe ) = cu qe . Then, it must be that
(M − N qi − qe )qe − cu qe ≥ βqe . Using incumbents’ best response (2), the condition
reads qe ≤ M − (cu + β) (N + 1) + cN . Then qe ≥ 0 can only be satisfied if N ≤ N .
7
Assumption 1: cu + β > c
Therefore, either the supplier is not ”too” efficient relative to the incumbents and/or
revenues in alternative markets are sufficiently high. The assumption is made so as to focus
on the interesting insights generated by the model. I want to consider the case where, due to
financial constraints, the retailer’s entrance might not be feasible. Notably, this holds when
the supplier and incumbents are equally efficient (c = cu ).
5
Linear Prices
Suppose that the supplier must choose a constant wholesale price, so T (qe ) = wqe . In most
settings w affects the market outcome by regulating the retailer’s input demand. Here, it
also specifies the relative profitability of the downstream market with respect to diverting.
Therefore, by setting w the supplier determines both qe∗ (qi , T ) and L(qi , T ), thereby deciding
whether the retailer is financially constrained. The next proposition characterizes the two
types of equilibria:
Proposition 4 When the retailer is not financially constrained, input price and output are
determined by double marginalization:
wn (qi ) =
M − N q i − cu
M − N q i + cu
⇒ qen (qi ) =
2
4
If the retailer is financially constrained, input price leads to the output of a market participant
with a unit cost cu + β:
wc (qi ) =
M − N q i − β + cu
M − N q i − β − cu
⇒ qec (qi ) = Lc (qi ) =
2
2
Proof : Unconstrained setting: The retailer’s marginalization is captured by the first
line in (3), which yields qe∗ (qi , T ) = [M − N qi − wn ] /2. The supplier incorporates his
customer’s best reply and solves (5), which simplifies to maxwn {(wn − cu ) qe∗ (qi , T )}.
This is the first marginalization. The solution yields wn (qi ). Plugging this into qe∗ (qi , T )
one obtains qen (qi ).
Constrained setting: By the second line in (3), qe = L. Furthermore, the second line
in (4) can be written as L = [M − N qi − L − wc ] L/β, which pins down the line of
credit: L(wc ) = M − N qi − wc − β. The supplier then solves the problem in (5), which
reads maxwc {(wc − cu ) L(wc )}. The solution is wc (qi ). Plugging this into L(wc ) yields
L(qi ), which is the investment of a participant with cost β + cu .
8
With no credit rationing, the vertical relation is characterized by standard double marginalization. Instead, if the retailer is financially constrained, he sets a price so as to generate
a demand (constraint) that corresponds to the investment of a market participant with
marginal cost cu + β. Thus, the effect of credit rationing is twofold. On the one hand, the
financial constraint erases the supplier’s delegation problem because the retailer exhausts all
credit, so she does not marginalize. On the other hand, it imposes a unit agency cost of β
to the supplier. Then, the wholesale price generates the demand (constraint) of a market
participant with unit cost cu + β.
Proposition 4 shows that a constrained retailer always faces a lower input price, i.e.
wc (qi ) < wn (qi ). Nonetheless, her output can be either higher or lower than in the absence
of constraints. The reason is the different response of the constrained and the unconstrained
outputs to competitive pressure: |∂qen /∂qi | < |∂Lc /∂qi |. This relation is depicted in Figure
1.
2
Lc (qi )
1
qen (qi )
qi
0
1
2
3
4
Figure 1: Retailer’s best replies under both double marginalization qen (qi ) and financial
constraints Lc (qi ).M = 10, cu = 2, c = 2, β = 0.8 and N = 2
I described the two outcomes of the model under linear pricing. Next, I characterize
the conditions under which either outcome arises as an equilibrium. To this end, I conduct
comparative statics on the number of incumbents. Higher competition in the retail market
reduces the relative profitability of investing and worsens the agency problem. Therefore,
comparative static results hold for β as for N since they have similar effects on the vertical
relation.
u
u
Proposition 5 Let N1 ≡ Mcu−4β−c
< N2 ≡ Mcu−3β−c
. Pure strategy Nash Equilibria leads to
+3β−c
+2β−c
the following outcome as a function of competitive pressure downstream:
- If N < N1 the retailer is not financially constrained and does not use all credit available;
- If N ∈ [N1 , N2 ] the retailer is not financially constrained, but exhausts the line of credit;
9
- If N > N2 the retailer is financially constrained.
Proof : We first show that the unconstrained outcome cannot be an equilibrium for N >
N1 . The wholesale price in the unconstrained setting is wn (qi ) in Proposition 4. Using
incumbents’ best response qin (T ) in (6), we obtain wn = [2 (M + cN ) + cu (2 + N )] /(4+
3N ). Plug this into the retailer’s responses in both (6) and in (7) - using wn = T 0(qe )
and wn = T (L)/L respectively, and see that qen (wn ) < L(wn ) if and only if N < N1 .
This implies that the unconstrained outcome cannot be sustained for N > N1 .
Analogously, we now show that the constrained outcome cannot be an equilibrium for
N < N2 . The wholesale price in the unconstrained setting is wc (qi ) in Proposition 4.
Using incumbents’ best response in (6), we obtain wc = [M + cu − β (N + 1) + cN ] /(N +
2). Plug this in the retailer’s responses in both (6) and in (7) and see that qen (wc ) >
L(wc ) if and only if N > N2 , which implies that the constrained outcome is not an
equilibrium for N < N2 .
When N ∈ [N1 , N2 ] neither the constrained nor the unconstrained outcomes are an
equilibrium. Furthermore, it holds that qen (wn |N1 ) = L(wc |N2 ) = β. The supplier’s
price policy for N ∈ (N1 , N2 ) consists of wm so that qen (wm ) = L (wm ) = β. This
is wm = [M − β (N + 2) + cN ] /(N + 1). A higher price w0 > wm leads to qen (w0 ) >
L (w0 ), but then it is optimal to set wc < w0 . Analogously, a lower price w00 < wm
yields qen (w0 ) < L (w0 ) but then it is optimal to set wn > w00 .
The first part of Proposition 5 shows the case where the downstream market is relatively
profitable and the retailer has little incentives to divert. Then the constrained outcome is
not an equilibrium because the optimal price is too high to make the retailer constrained:
qe (wc ) < L(wc ). This holds for a small number of incumbents, since qen (wn ) ≤ L(wn ) if
and only if N ≤ N1 . Conversely, the third part describes the case where high competitive
pressure leads to the constrained outcome. The little profitability of the market makes the
price for an unconstrained retailer so low that qen (wn ) ≥ L(wn ). Analogously, the constrained
outcome is an equilibrium only for sufficient competitive pressure because qen (wc ) ≥ L(wc ) if
and only if N ≥ N2 .
The second part of the proposition characterizes an equilibrium where the retailer’s demand for input equals the line of credit. Thus, even though the retailer exhausts all credit, she
is not financially constrained. The supplier sets wm so that qen (wm ) = L(wm ) = β. A higher
price constraints the retailer, but the optimal price for a constrained retailer wc is lower.
In contrast, a lower price increases the constraint beyond the retailer’s demand. However,
the optimal price for an unconstrained retailer wn is higher. Notably, when N ∈ (N1 , N2 )
10
the retailer’s output is unaffected by competitive pressure. Hence, the supplier internalizes
the full cost of higher competition by reducing the wholesale price and makes the retailer
relatively more aggressive.
Figure 2 compares the equilibrium of our game (solid ) with a benchmark case where
there is no moral hazard (dotted ), i.e. β = 0 and so L → ∞. The left panel presents the
output of the retailer as a function of the competitive pressure N whereas the right panel
plots her profits. Changes in the slope of the solid line identify the thresholds N1 , N2 and
N . The figure reveals a significant region where the retailer makes higher profits due to the
contractual frictions. With low competitive pressure (N ≤ N1 ) the retailer is not financially
constrained and her output is that of a benchmark case with no moral hazard. Conversely,
when the constraint binds (N2 < N ), output is equal to that of a market participant with
a unit cost cu + β. For sufficiently low levels of competition, investment under financial
constraints exceeds that in a setting with double marginalization.
1
1
qe
0
N1
N2
πe
0
N
N1
N2
N
Figure 2: Output and profits of the retailer under moral hazard (solid ) versus perfect contractibility (dashed ). M = 10, cu = 2, c = 2, β = 0.8.
When the constraint binds the supplier can regulate the retailer’s demand with no
marginalization. Then, the retailer’s profits are those that make repayment just incentive
compatible: πe = βL. Hence, the constraint allows the supplier to extract all retailer’s surplus except an agency cost of β. As shown by Figure 2, for intermediate levels of competition
the retailer is more aggressive and more profitable than in the benchmark case with double
marginalization. This effect vanishes when competition is higher because of Assumption 2:
the effective marginal cost of the supplier cu +β makes it is less competitive than incumbents.
Figure 3 plots both the supplier’s profits and his price policy. The left panel shows that
the supplier can also become more profitable due to the contractual frictions. The right panel
shows that the retailer faces a lower wholesale price when it is optimal for her to exhaust all
credit and thus, when the delegation problem vanishes. Even though the retailer’s output
can be higher due to financial constraints, the volume of debt, defined as the product of
11
input price and quantity of input borrowed, is never higher.
4
πu
1
w
3
0
c
N1
N2
0
N
N1
N2
N
Figure 3: Supplier profits and wholesale price under moral hazard (solid ) versus perfect
contractibility (dashed ). M = 10, cu = 2, c = 2, β = 0.8.
I conclude the section highlighting the possibility that financial constraints provide the
retailer with competitive advantage. This occurs for intermediate levels of competitive pressure, when constraints are binding but not severe. Then, the supplier sets an input price
that makes his retailer more aggressive in the product market. As a result, both retailer and
supplier make higher profits than in a situation with no moral hazard. Contrary, incumbent
companies in the retail market lower their output and thus become less profitable due to
their rival’s financial constraints.
6
Optimal Contracts
I now study the case where the supplier has no constraints on his contracts. This eliminates
double marginalization. Hence, in the absence of diversion opportunities the retailer makes
zero profits. However, for β > 0 the supplier must grant the retailer β per unit of input
extended in credit so as to ensure that she will honour her debt.
Proposition 6 Under optimal contracting, the retailer exhausts all credit (qe = L) and
makes a profit πe = βL. The supplier offers a credit line L equal to the investment of a
market participant with unit cost cu + β and obtains the profits of ”that” participant.
Proof : The supplier extracts all retailer’s surplus except that needed to make repayment incentive compatible. Thus, πe = βqe . Since retailer’s profits are proportional
to the quantity of input borrowed, she exhausts all credit, so qe = L and πe = βL.
Because qe = L, the supplier can offer a quantity of input equal to the investment
that maximizes his profits and then extract surplus with a fixed fee. His problem is
12
maxL(qi ) {πu = F (qi ) − [β + cu ] L(qi )} with F (qi ) = [M − N qi − L(qi )] L(qi ). The FOC
yields L(qi ) = [M − N qi − β − cu ] /2.
Because the retailer’s profits are proportional to the volume of input borrowed, she always
exhaust the line of credit. Hence, the supplier can regulate the retailer’s investment through
L and subsequently extract her surplus to the extent that she becomes indifferent between
investing and diverting. As a consequence, the supplier’s delegation problem vanishes. This
equilibrium is equivalent to the one obtained with linear pricing when the retailer is credit
constrained, i.e. for N > N2 . There, the supplier uses the constraint to induce his optimal
investment free of delegation problems, which equals that of a market participant with a
unit cost cu + β.
Proposition 6 characterizes the investment and profits of both the supplier and retailer,
but it does not propose a pricing scheme. Notably, in our setting this is relevant for the
existence of financial constraints. For instance, if an optimal contract is implemented with a
fixed fee, then the retailer is financially constrained. In particular, since the marginal input
price is zero, her input demand always exceeds the line of credit offered by the retailer.1
Next, I show that an optimal contract can be implemented with a two-part tariff such that
the retailer is never financially constrained:
Proposition 7 An optimal contract can be implemented with a two-part tariff T = F +
wqe such that the retailer is never financially constrained. The line of credit L equals the
investment of a market participant with unit cost cu + β and the tariff is
F (qi ) =
(M − N qi − β − cu ) (M − N qi − 3β − cu )
, w (qi ) = β + cu
4
Proof : The retailer’s input demand under no constraints is qe∗ (qi , T ) = [M − N qi − w] /2
- see equation (3), whereas the optimal investment for the supplier is qe (qi ) = [M − N qi − β − cu ] /2
- see proof of Proposition 6. The two quantities are equal for w(qi ) = β + cu . Then
F (qi ) = [M − N qi − qe (qi ) − β − w(qi )] qe (qi ) captures retailer’s market revenues except for (i) the agency cost βqe (qi ) and (ii) the unit price w(qi )qe (qi ).
The unit price w (qi ) in Proposition 7 generates an input demand equivalent to the
investment of a market participant with unit cost cu + β. Then, the fixed fee extracts the
retailer’s surplus that makes repayment just incentive compatible. Importantly, the line of
credit equals the retailer’s input demand, i.e. L(qi ) = qe∗ (qi , T ), implying that she is not
Equation (3) shows that when the marginal price is zero, the retailer’s input demand is qe∗ (qi ) =
[M − N qi ] /2. Furthermore, in the proof of Proposition 6 it is shown that L (qi ) = [M − N qi − β − cu ] /2.
1
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financially constrained. Hence, given the tariff in Proposition 7, the retailer would only
demand a higher quantity of input with the intention of diverting.
The contract in Proposition 7 highlights the link between input pricing and financial
constraints. It is shown that, despite the presence of moral hazard and the consequent
need for a limited line of credit, the retailer might never be financially constrained. A key
element is that with no contractual restrictions, the supplier can regulate input demand and
financial constraints independently. This is in contrast with linear pricing, where the unit
price determines both input demand and the financial constraints.
The literature has often used linear pricing to represent situations where suppliers cannot
prefectly discriminate in prices and as a result, retailers are left with a positive surplus.
Hence, my results suggest a relation between suppliers’ ability to discriminate and retailers’
financial constraints. In particular, in Section 3 it is shown that if the moral hazard problem
is severe (high competeition downstream) a supplier restricted to linear pricing makes the
retailer financially constrained. However, this need not to be the case with two-part tariffs.
Figure 4 plots the contract in Proposition 7 as a function of the number of incumbents
N . When N ∈ N2 , N the supplier sets a negative fixed fee at the expense of a relatively
high unit price. Note that N2 , N corresponds to the levels of competitive pressure for
which a retailer facing linear prices participates in the market but is financially constrained.
Hence, in order to generate the optimal demand and make repayment incentive compatible,
the supplier must compensate the retailer with a lump sum transfer. Notably, the effect
vanishes when β → 0 and as a result, N2 → N .
β + cu
w
cu
1
0
F
N1
N2
N
Figure 4: Two-part tariff T = F + w implementing an optimal contract such that there are
no financial constraints. M = 10, cu = 2, c = 2, β = 0.8 (solid ) and β = 0 (dashed ).
I finish by noticing two key features of the two-part tariff described in Proposition 7. First,
in our setting a transfer from the supplier to the retailer must be made ex-post. Otherwise,
it provides additional incentives for the retailer to divert. Thus, we implicitly assume that,
14
unlike the retailer, the supplier can commit to honouring his obligations. Second, financial
constraints might not exist despite the retailer’s opportunity to divert if the supplier can fully
discriminate in prices. As a consequence, the presence of agency costs becomes noticeable
only through input prices and firms’ profits.
7
Concluding Remarks
This paper extends a model of trade credit to study the interaction between financial constraints and product market competition. Competitive pressure for the retailer lowers the
profitability of her investment. Hence, when investment is not contractible, competition
increases incentives to divert, thereby reducing the credit that the supplier is able to extend.
The line of credit is a combination of input price and quantity of input. Therefore, the supplier’s price policy not only determines the retailer’s input demand, but also the quantity of
input that can be extended in credit. As a consequence, in equilibrium financial constraints
arise endogenously.
I show that both the retailer and the supplier can be more profitable due to the presence
of financial constraints. The line of credit becomes a commitment device that makes it
profitable for the supplier to lower input prices and induce higher aggressiveness of the
retailer in the product market. Hence, even though the retailer obtains less credit than
in the absence of contractual frictions, she borrows a higher quantity of input. This is in
contrast to the common view that credit constraints lead to underinvestment and reduce
companies’ profits. The previous result is obtained under a linear pricing assumption. I
then relax this assumption and show that the supplier may offer a two-part tariff such that,
despite agency problems, the retailer is never financially constrained. This suggests a relation
between the supplier’s ability to price-discriminate (linear versus non-linear tariffs) and the
presence of financial constraints.
15
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