We show that returns policies do increase manufacturer profitability by attenuating price competition between retailers. This effect holds only in the presence of end-user demand uncertainty. The conditions under which a returns policy raises the manufacturer's profit are weaker when retailing is a duopoly than when retailing is a monopoly. This suggests that returns policies serve both to dampen competition and resolve demand uncertainty.channels, competition, returns, pricing

I.P.L. Png

V. Padmanabhan

English

Research Papers in Economics

 
© 2003-04, V. Padmanabhan and I.P.L. Png  1
 
 
Returns Policies and Retail Price Competition 
 
V. Padmanabhan and I.P.L. Png
∗ 
 
January 2004 
 
                                         
∗ INSEAD, Singapore, and National University of Singapore.   Corresponding author: 
[insert your details].  We thank Hao Wang for helpful comments.     
© 2003-04, V. Padmanabhan and I.P.L. Png  2
Introduction 
Marketing, operations management, and economics researchers have been 
interested in the conditions under which returns policies may coordinate channels 
and supply chains (Pasternack 1985; Marvel and Peck 1995; Padmanabhan and 
Png 1995; Kandel 1996; Tsay 2001; Cachon and Lariviere 2002; Granot and Yin 
2002). 
 
Padmanabhan and Png (1997) showed that with demand uncertainty, a 
returns policy could improve manufacturer profitability under certain conditions.  
They further claimed that, even in the absence of end-user demand uncertainty, a 
returns policy could raise manufacturer profitability by dampening price 
competition between retailers.  However, this claim was disproved by Wang 
(2003), who showed that returns policies do not change manufacturer profitability 
when demand is certain and retailing is competitive. 
 
In this paper, we show that returns policies do increase manufacturer 
profitability by attenuating price competition between retailers, but, that this effect 
holds only in the presence of end-user demand uncertainty.  Interestingly, the 
conditions under which a returns policy raises the manufacturer's profit are 
weaker when retailing is a duopoly than when retailing is a monopoly.  This 
suggests that returns policies serve both to dampen competition and resolve 
demand uncertainty. 
 
Setting 
Let the information structure and sequence of actions be as follows.  Initially, all 
parties are uncertain about the state of primary demand, which could be low or 
high ( l = θ  or h respectively).  The probability of demand being low isλ . 
 
In the first stage, the manufacturer sets a distribution policy comprising a 
wholesale price w and whether to accept returns.  In the second stage, the 
retailers independently order stocks i s .  We assume that the true state of the 
primary demand is revealed to all parties after the second stage.  Then, in the third  
© 2003-04, V. Padmanabhan and I.P.L. Png  3
stage, the retailers independently set prices, θ i p ,  h l i , , 2 , 1 = = θ .1  
     
Let demand at retailer 1 be  
θ θ θ θ γ β α 2 1 1 p p q + − = ,      (1) 
where the demand is more sensitive to the retailer’s own price than the 
competitor’s price in the sense that 
γ β > ,           ( 2 )  
and likewise for retailer 2.  Information is symmetric: specifically,λ ,  θ α ,β , and γ 
are known to all. 
 
No Returns 
In this case, the manufacturer sets a wholesale price w and does not accept 
unsold stock.  Assume that, in stage 3, if demand is high, both retailers price to 
sell their entire stock, while if demand is low, both leave some stock unsold.  
Below, we derive a condition sufficient for this to be true. 
 
By (1), if demand is low, retailer 1’s sales are 
l l l l p γ p β α q 2 1 1 + − = .       (3) 
By assumption, the retailers set price such that some stock will be unsold.  Since 
unsold stock has no salvage value, retailer 1 would set price to maximize revenue 
   ] [ 2 1 1 1 l l l l l p γ p β α p R + − = .      (4) 
The first-order condition is 
   0 2 2 1 = + − l l l p γ p β α .       (5) 
Similarly, retailer 2 would set price to maximize revenue, and its first-order 
condition would be 
0 2 1 2 = + − l l l p γ p β α .       (6) 
Solving (5) and (6), we have retailer 1’s price if demand is low, 
   l l α
β
γ
p
β
γ β
⎥
⎦
⎤
⎢
⎣
⎡
+ = ⎥
⎦
⎤
⎢
⎣
⎡ −
2
1
2
4
1
2 2
,    
or 
  
γ β
α
α
γ β
γ β
p
l
l l −
=
−
+
=
2 4
2
2 2 1 ,      (7) 
                                         
1 Another approach would be to assume that retailers set prices before the state of demand 
is revealed (Marvel and Peck 1995; Dana and Spier 2001; Marvel and Wang 2003).  
© 2003-04, V. Padmanabhan and I.P.L. Png  4
which, is also retailer 2’s price in the case of low demand.  Substituting (7) in (3), 
  
γ β
βα
γ β
α
γ β α q
l l
l l −
=
−
− − =
2 2
] [ 1 .     (8) 
 
By assumption, if demand is high, both retailers price to sell their entire 
stock.  Then the sales of retailers 1 and 2 are 
1 2 1 1 s p γ p β α q h h h h = + − = ,      (9) 
2 1 2 2 s p γ p β α q h h h h = + − = .      (10) 
Solving,  
1 2 1 1 ] [ s s p γ α
β
γ
p β α h h h h = − + + − .     (11) 
In equilibrium, 2 1 s s = , hence 
  
γ β
s α
p
h
h −
−
=
1
1 ,         ( 1 2 )  
and, likewise, for  h p2 .         
 
  In stage 2, the retailers choose stocks  i s  to maximize expected profit given 
the wholesale price w set by the manufacturer.  Retailer 1’s expected profit is 
   1 1 1 1 1 ] 1 [ ws s p λ q p λ h l l − − + .      (13) 
The first-order condition with respect to  1 s  is 
   w s α
γ β
λ
h = −
−
−
] 2 [
1
1 , 
or 
   ]
1
[
2
1
1 w
λ
γ β
α s h −
−
− = .        ( 1 4 )  
  In stage 1, the manufacturer sets w to maximize profit 
   ]
1
][ [ ] [ 2 1 w
λ
γ β
α c w s c w h N −
−
− − = − = Π .     (15) 
The first-order condition with respect tow is 
   0 ] 2 [
1
= −
−
−
− c w
λ
γ β
αh , 
hence, 
   ⎥
⎦
⎤
⎢
⎣
⎡
+
−
−
= c
γ β
α λ
w
h ] 1 [
2
1 .        ( 1 6 )  
  
© 2003-04, V. Padmanabhan and I.P.L. Png  5
 Substituting  for  win (14), we have 
   ]
1
[
4
1
1 c
λ
γ β
α s h −
−
− = .        ( 1 7 )  
In equilibrium, we require that, if demand is low, both retailers leave some stock 
unsold,  1 1 s q l ≤ .  By (8) and (17), this implies that 
  ,
2 1 4
1
γ β
βα
λ
γ β
α
−
≥ ⎥ ⎦
⎤
⎢ ⎣
⎡
−
−
−
l
h c  
i.e., the high demand should exceed the low demand by at least the following 
extent, 
  c l h λ
γ β γ β
βα α γ β
−
− −
≥ − −
1
] 2 ][ [
4 ] 2 [ .     (18) 
 
Substituting for win (15), the manufacturer’s profit is 
   ⎥ ⎦
⎤
⎢ ⎣
⎡
−
−
− ⎥
⎦
⎤
⎢
⎣
⎡
−
−
−
= Π c
λ
γ β
α c
γ β
α λ
h
h
N 1
] 1 [
4
1 .     (19) 
Substituting from (17) in (11), retailer 1’s price when demand is high, 
⎥ ⎦
⎤
⎢ ⎣
⎡
−
−
+
−
= c
λ
γ β
α
γ β
p h h 1
3
] [ 4
1
1 .     (20) 
 
 
Full Returns 
In this case, the manufacturer sets a wholesale price w and gives each retailer a 
full refund for unsold stock.  In the Appendix, we show that, condition (18) 
implies that, in stage 3, if demand is high, both retailers price to sell their entire 
stock, while if demand is low, both leave some stock unsold.   
 
By (1), if demand is low, retailer 1’s sales are 
l l l l p γ p β α q 2 1 1 + − = .        ( 2 1 )  
By assumption, the retailers set price such that some stock will be unsold.  Since 
the manufacturer accepts full returns of unsold stock, retailer 1 would set price to 
maximize profit 
   ] ][ [ ] [ 2 1 1 1 1 l l l l l l p γ p β α w p q w p + − − = − .     (22) 
The first-order condition is 
   0 2 2 1 = + + − w β p γ p β α l l l ,      (23) 
and, similarly, for retailer   
© 2003-04, V. Padmanabhan and I.P.L. Png  6
0 2 1 2 = + + − w β p γ p β α l l l .      (24) 
Solving (23) and (24), we have retailer 1’s price if demand is low, 
  
γ β
w β α
p
l
l −
+
=
2
1 ,       ( 2 5 )  
and likewise for retailer 2.  Substituting  l l p p 2 1 = in (21), retailer 1’s sales are 
   ] ] [ [
2
1 w γ β α
γ β
β
q l l − −
−
= ,      (26) 
and likewise for retailer 2.  
  
By assumption, if demand is high, both retailers price to sell their entire 
stock.  Then the sales and prices of retailers 1 and 2 are given by (9)-(14).  
 
  In stage 2, the retailers choose stocks  i s  to maximize expected profit given 
the wholesale price w set by the manufacturer.  Retailer 1’s expected profit is 
  
, ] 1 [ ] [
] ][ 1 [ ] [
1
1
1 1
1 1 1 1
s w
s
q w p
s w p q w p
h
l l
h l l
⎥
⎦
⎤
⎢
⎣
⎡
−
−
−
− + − =
− − + −
γ β
α
λ λ
λ λ
   (27) 
after substituting from (12).  The first-order condition with respect to  1 s  is 
   ] ] [ [
2
1
1 w γ β α s h − − = .     (28) 
 
  In stage 1, the manufacturer sets w to maximize profit 
{} {} , ] ] [ [ ] [ ] 1 [ ] [
2
2
2 ] 1 [ 2 2
2 2
1 1 1
c w w w w w
cs ws wq
h h l
l R
γ β α γ β α λ γ β α
γ β
λβ
λ λ
− − − − − − + − −
−
=
− − + = Π
 (29) 
after substituting from (26) and (28). The first-order condition with respect tow is 
  {} {}. 0 ] [ ] [ 2 ] 1 [ ] [ 2
2
2
= − + − − − + − −
−
c w w h l γ β γ β α λ γ β α
γ β
λβ  
Re-arranging terms and simplifying, we have 
 
.
] ] 1 [ 2 [ 2
] 2 [
] ] 1 [ 2 ][ [ 2
] 2 ][ 1 [ 2
] ] 1 [ 2 ][ [ 2
] ][ 2 [ ] 2 ][ 1 [ 2
c
c
w
h l
h l
γ λ β
γ β
γ λ β γ β
α γ β λ λβα
γ λ β γ β
γ β γ β α γ β λ λβα
− −
−
+
− − −
− − +
=
− − −
− − + − − +
=
   (30) 
 
 Substituting  for  w in (28), the stock is  
© 2003-04, V. Padmanabhan and I.P.L. Png  7
  .
] ] 1 [ 2 [ 4
] 2 ][ [
] ] 1 [ 2 [ 4
2 ] ] 1 [ ] 1 [ 2 [
1 c s
l h
γ λ β
γ β γ β
γ λ β
λβα α γ λ β λ
− −
− −
−
− −
− − − +
=    (31) 
In the Appendix, we show that, by (18), l q s 1 1 ≥ .   Substituting for w in (25), 
.
] ] 1 [ 2 ][ ][ 2 [ 2
] ][ 2 [ ] 2 ][ 1 [ 2
2
2
1 γ λ β γ β γ β
β γ β γ β βα γ β λ α λβ
γ β
α
− − − −
− − + − − +
+
−
=
c
p
h l l
l  (32) 
Substituting for w in (26), 
.
] ] 1 [ 2 ][ 2 [ 2
] ][ 2 [ ] 2 ][ 1 [ 2
2
2
1 γ λ β γ β
β γ β γ β βα γ β λ α λβ
γ β
βα
− − −
− − + − − +
−
−
=
c
q
h l l
l  (33) 
Substituting from (31) in (11), 
.
] ] 1 [ 2 ][ [ 4
] ][ 2 [ ] ] 1 [ 3 ] 3 [ 2 [ 2
1 γ λ β γ β
γ β γ β α γ λ λ β λβα
− − −
− − + − − − +
=
c
p
h l
h  (34) 
 
 
Full vis-à-vis No Returns 
The following Table compares the profit-maximizing wholesale price, and 
equilibrium retail prices and quantities under the two scenarios of full and no 
returns.  The difference in the manufacturer’s profit in the two scenarios depends 
on a balance among the following:  
•  With returns, the wholesale price is higher and the retailers order larger 
stocks; 
•  However, with returns, in the event of low demand, retailers return 
unsold stock and the manufacturer must bear the cost of these items. 
     
 
 
 
 
 
 
 
 
 
 
 
  
© 2003-04, V. Padmanabhan and I.P.L. Png  8
 
Table: Equilibrium with No and Full Returns2 3 
  No Returns    Full Returns 
w 
⎥
⎦
⎤
⎢
⎣
⎡
+
−
−
c
γ β
α λ h ] 1 [
2
1   < c
h l
] ] 1 [ 2 [ 2
] 2 [
] ] 1 [ 2 ][ [ 2
] 2 ][ 1 [ 2
γ λ β
γ β
γ λ β γ β
α γ β λ λβα
− −
−
+
− − −
− − +  
h q s 1 1 =
 
]
1
[
4
1
c
λ
γ β
αh −
−
−   < c
l h
] ] 1 [ 2 [ 4
] 2 ][ [
] ] 1 [ 2 [ 4
2 ] ] 1 [ ] 1 [ 2 [
γ λ β
γ β γ β
γ λ β
λβα α γ λ β λ
− −
− −
−
− −
− − − +
l p1  
γ β
αl
− 2
  <
] ] 1 [ 2 ][ ][ 2 [ 2
] ][ 2 [ ] 2 ][ 1 [ 2
2
2
γ λ β γ β γ β
β γ β γ β βα γ β λ α λβ
γ β
α
− − − −
− − + − − +
+
−
c h l
l
 
l q1  
γ β
βαl
− 2
  >
] ] 1 [ 2 ][ 2 [ 2
] ][ 2 [ ] 2 ][ 1 [ 2
2
2
γ λ β γ β
β γ β γ β βα γ β λ α λβ
γ β
βα
− − −
− − + − − +
−
−
c h l
l
 
h p1   ⎥ ⎦
⎤
⎢ ⎣
⎡
−
−
+
−
c
λ
γ β
α
γ β
h 1
3
] [ 4
1   >
 
] ] 1 [ 2 ][ [ 4
] ][ 2 [ ] ] 1 [ 3 ] 3 [ 2 [ 2
γ λ β γ β
γ β γ β α γ λ λ β λβα
− − −
− − + − − − + c h l
 
 
 
For tractability, we focus on the case where the marginal cost of the 
product,  0 = c .  Substituting in (19), 
  .
] [ 4
] 1 [
2
γ β
α λ
−
−
= Π
h
N         ( 3 5 )  
Substituting  0 = c  in (29) and (30) 
  , ] ] 1 [ 2 [
2
] 1 [
2
2 2 w w h l R γ λ β
γ β
γ β
α λ α
γ β
λβ
− −
−
−
−
⎭
⎬
⎫
⎩
⎨
⎧
− +
−
= Π  (36) 
and 
  .
] ] 1 [ 2 ][ [ 2
] 2 ][ 1 [ 2
γ λ β γ β
α γ β λ λβα
− − −
− − +
=
h l w       ( 3 7 )  
Substituting (37) in (36) and simplifying, we obtain 
                                         
2  We omit the proofs of these results as they are mere algebraic substitutions.  The 
exception is the proof that  h p1  is higher with no returns.  Equation (12) defines the price 
h p1  without and with returns.  Since the stock is lower without returns, (12) implies that 
the price would be higher.  
3  In the case of  0 = γ , these variables equal the corresponding terms in Padmanabhan 
and Png (1997), Table 3.  
© 2003-04, V. Padmanabhan and I.P.L. Png  9
  .
] ] 1 [ 2 ][ 2 ][ [ 4
] ] 2 ][ 1 [ 2 [
2
γ λ β γ β γ β
α γ β λ λβα
− − − −
− − +
= Π
h l
R      ( 3 8 )  
 
  Comparing (38) with (35), the difference in the manufacturer’s profit with 
and without returns,  0 ≥ Π − Π N R  if 
{} , 0 ] ] 1 [ 2 ][ 2 ][ 1 [ ] 2 ][ 1 [ 2
2 2
≥ − − − − − − − + h h l α γ λ β γ β λ α γ β λ λβα  
which simplifies to 
  . 0 ] 2 ][ 2 ][ 1 [ 2
2 ≥ − − − + h h l l α α α γ β λ λβα      ( 3 9 )  
Accordingly, we have the following result. 
 
Proposition 1.  If the extent to which the high demand exceeds the low demand 
satisfies 
 
] 2 ][ 1 [
2 ] 2 [
2 γ β λ
λβ
α
α α α
− −
≤
−
l
l h h ,      (40) 
and the marginal cost of the product,c, is sufficiently low, then the 
manufacturer’s profit is higher with a returns policy than no returns. 
 
 
Retail Market Structure 
In a similar setting of demand uncertainty but with a monopoly retailer, 
Padmanabhan and Png (1997) showed that the manufacturer’s profit would be 
higher with a returns policy than no returns if the marginal cost of the product, 
0 = c  and the demand parameters satisfied the condition, 
 
] 1 [ ] 1 [
2 / 1 λ λ
λ
χ
− − −
≤ ,        ( 4 1 )  
where  l h α α χ / ≡ .  Using the same substitution, (40) can be simplified as 
 
] 2 ][ 1 [
2
2
2
γ β λ
λβ
χ χ
− −
≤ − , 
or 
  1
] 2 ][ 1 [
2
] 1 [
2 +
− −
≤ −
γ β λ
λβ
χ ,     (42) 
or 
  ), ( 1
2 ] 1 [
2
2 / 1
λ
λγ γ β λ
λγ γ β
χ X ≡ + ⎥
⎦
⎤
⎢
⎣
⎡
+ − −
+ −
≤      ( 4 3 )   
© 2003-04, V. Padmanabhan and I.P.L. Png  10
say. 
 
 Note  that,  with  0 = γ , 
 
] 1 [ ] 1 [
1
1
1
) ( 2 / 1
2 / 1
λ λ
λ
λ
λ
− − −
= + ⎥ ⎦
⎤
⎢ ⎣
⎡
−
= X .     (44) 
Further, the right-hand side of (42) is increasing in γ , and so,  ) (λ X  is increasing 
in γ , and thus, for  0 ≥ γ , 
 
] 1 [ ] 1 [
1
2 ] 1 [
2
) ( 2 / 1
2 / 1
λ λ
λ
λγ γ β λ
λγ γ β
λ
− − −
> + ⎥
⎦
⎤
⎢
⎣
⎡
+ − −
+ −
≡ X .   (45) 
Therefore, the condition (40) for the returns policy to increase the manufacturer 
profit when retailing is a duopoly is weaker than the corresponding condition (41) 
when retailing is a monopoly.  
 
 
Concluding Remarks 
Here, we have shown that, in a setting of end-user demand uncertainty and retail 
duopoly, a returns policy would raise the manufacturer’s profit if the marginal cost 
of the product is sufficiently low and the demand parameters satisfy particular 
conditions.  Further, these conditions are weaker than the corresponding 
conditions for a returns policy to raise manufacturer profit with a retail monopoly.  
This shows that the returns policy serve both to dampen retail competition and 
resolve demand uncertainty.  
 
  Intuitively, the returns policy effectively sets a floor to the retail price when 
demand is low and so, attenuates price competition and raises the retailers’ profits.  
This enables the manufacturer to set a higher wholesale price.  Further, by 
eliminating any cost of excess inventory, the returns policy encourages retailers to 
order larger stocks.    
 
From the manufacturer’s viewpoint, the disadvantage of the returns policy 
is the cost of items returned in the event that demand is low.  Provided that the 
cost of the product is sufficiently low and the high demand is not too much larger 
than the low demand, the advantages of the returns policy outweigh the 
disadvantage.  
© 2003-04, V. Padmanabhan and I.P.L. Png  11
References 
 
Cachon, Gérard P. and Martin A. Lariviere, “Supply Chain Coordination with 
Revenue-Sharing Contracts: Strengths and Limitations”, Management Science, 
forthcoming. 
 
Granot, Daniel, and Shuya Yin, “On the Effectiveness of Returns Policies in the 
Price-Dependent Newsvendor Model”, Working Paper, Sauder School, 
University of British Columbia, November 2002. 
 
Kandel, Eugene, “The Right to Return”, Journal of Law and Economics, Vol. 3 No. 1, 
April 1996, 329-355. 
 
Marvel, Howard and James Peck, “Demand Uncertainty and Returns Policies”, 
International Economic Review, Vol. 36 No.3, 1995, 691-714. 
 
Marvel, Howard, and Hao Wang, “Inventories, Return Policy, and Equilibrium 
Price Dispersion under Demand Uncertainty”, Working Paper, China Center 
for Economic Research, Beijing University, June 2003. 
 
Padmanabhan, V. and I.P.L. Png, “Returns Policies: Make Money by Making 
Good”, Sloan Management Review, Vol. 37 No. 1, Fall 1995, 65-72. 
 
Padmanabhan, V. and I.P.L. Png, “Manufacturers Returns Policies and Retail 
Price Competition”, Marketing Science, Vol. 16 No. 1, 1997, 81-94. 
 
Pasternack, Barry A., “Optimal Pricing and Return Policies for Perishable 
Commodities”, Marketing Science, Vol.4 No.2, 1985, 166-176. 
 
Tsay, Andrew A., “Managing Retail Channel Overstock: Markdown Money and 
Return Policies”, Journal of Retailing, Vol. 77 No. 4, 2001, 457-492. 
 
Wang, Hao, “Do Return Policies Intensify Retail Competition?” Marketing Science, 
forthcoming. 
 
  
© 2003-04, V. Padmanabhan and I.P.L. Png  12
 
Appendix 
By (26) and (28), with full returns, in the low demand state, retailers will leave 
some stock unsold, i.e.,  l q s 1 1 ≥  if  
0 ] [ 2 ] 2 [ ] ] [ [ 2 ] 2 ][ ] [ [ ≥ − + − − = − − − − − − w w w l h l h γ γ β βα α γ β γ β α γ β γ β α . 
Substituting from (30), this condition simplifies to  
c l h ] 2 ][ [ ] 2 4 [ 2 ] ] 1 [ 4 ][ 2 [ γ β γ β γ α λγ γ β β α γ λ β γ β − − ≥ + − − − − − . (A1) 
 
 By  (18),   
  c l h λ
γ β γ β
βα α γ β
−
− −
≥ − −
1
] 2 ][ [
4 ] 2 [ .     (18) 
Now, 
, ] 2 4 [ 2 ] 4 ][ 2 [
] 4 [ 4 ] 4 ][ 2 [ 4 ] 2 [
l h
l h l h
α λγ γ β β α λγ γ β γ β
α λγ γ β β α λγ γ β γ β βα α γ β
+ − − + − − <
+ − − + − − < − −
 (A2) 
and 
  c c ] 2 ][ [
1
] 2 ][ [
γ β γ β γ
λ
γ β γ β
− − >
−
− − .     (A3) 
Substituting (A2) and (A3) in (18), we obtain (A1), which proves that  l q s 1 1 ≥ . 

Demand Uncertainty and Returns Policies”,

Inventories, Return Policy, and Equilibrium Price Dispersion under

Managing Retail Channel Overstock: Markdown Money and Return Policies”,

Manufacturers Returns Policies and Retail Price

On the Effectiveness of Returns Policies in the Price-Dependent Newsvendor Model”, Working Paper,

Optimal Pricing and Return Policies for Perishable Commodities”, Marketing Science,

Returns Policies: Make Money by Making Good”,

The Right to Return”,

Returns Policies and Retail Price Competition

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Returns Policies and Retail Price Competition

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