Pricing Strategy for GM Food: Impact of Consumer Attitude Heterogeneity and GMO Food Labelling

Abstract

We consider how a marketer of a GM food product should price it in response to the requirement of GMO food label in the near future and its effect on consumers' heterogenous attitude. We examine how the GM food pricing is affected by different consumer attitudes towards GM-food (Like, Uninformed, and Dislike), the GMO food labelling to be enforced, and price competition. On the one hand, the GM food seller should expect to raise price after the GMO food labelling to cover the additional cost incurred on labelling. On the other hand, the seller may need to reduce price after labelling as the Uninformed consumers' attitude may change and become negative once the labelling is available. The tradeoff of these two effects yields interesting results. For example, we find that a monopolist GM food seller may choose to charge a high price, i.e., charge a premium for the GM-traits, and maintain at this price even after the labelling is enforced. Managerial implications and future research directions are discussed.

Full text

Forthcoming in Annals of Operations Research
Pricing Strategy for GM Food: Impact of Consumer
Attitude Heterogeneity and GMO Food Labelling
Rong Li, Amiya K. Basu
Whitman School of Management, Syracuse University, Syracuse, NY 13244, rli138@syr.edu, abasu@syr.edu
We consider how a marketer of a GM food product should price it in response to the requirement of GMO
food label in the near future and its effect on consumers’ heterogenous attitude. We examine how the GM
food pricing is affected by different consumer attitudes towards GM-food (Like, Uninformed, and Dislike),
the GMO food labelling to be enforced, and price competition. On the one hand, the GM food seller should
expect to raise price after the GMO food labelling to cover the additional cost incurred on labelling. On the
other hand, the seller may need to reduce price after labelling as the Uninformed consumers’ attitude may
change and become negative once the labelling is available. The tradeoff of these two effects yields interesting
results. For example, we find that a monopolist GM food seller may choose to charge a high price, i.e., charge
a premium for the GM-traits, and maintain at this price even after the labelling is enforced. Managerial
implications and future research directions are discussed.
Key words : GM food; consumer attitude towards GM food; pricing; GMO Food Labelling
1. Introduction and Motivation
Genetically Modified (GM) food have been growing in diversity and volume. For example, the
Hawaiian Rainbow papaya was developed by researchers from Cornell University and the University
of Hawaii since 1984 to save the Hawaii papaya, which began suffering the devastating papaya
ringspot virus in the 1950s. Commercialized in 1998, the Hawaiian Rainbow papaya, together with
other GM papaya, counted as 82% of the Hawaii papaya production in 2009 and sold all over the
world (USDA/NASS 2009). Similar virus-resistant food includes squash and plum. Recently, the
Arctic apple, a GM food with non-browning trait, started its sales in midwest supermarkets.
While some knowledgeable consumers may be able to identify GM food products and understand
the relevant biotechnology, most consumers are unable to do that. Even with GM food labelling,
1

:Impact of Consumer Attitude Heterogeneity on Pricing Strategy for GM Food
2Article forthcoming in Annals of Operations Research
which is to be enforced in different formats per the GMO food labelling law signed in July 2016
(USDA progress on GMO food labeling law), consumers’ attitudes towards GM food may still vary.
Note that consumers form their attitudes via the media, peer influence, their own background and
experience, etc. As covered by the news and shown in the survey studies by Boccia (2016) and Vec-
chione et al. (2015), there are three types of consumer attitudes toward GM food. Some consumers
like GM food, appreciating the bioengineering technology and benefit of second generation of GM
food with new traits (GM-traits), e.g., non-browning, better nutrient profiles, virus-resistant, more
digestible, increased food yield to alleviate world hunger; some consumers dislike GM food, sus-
pecting sustainable issues and potential health risks; and the rest are uninformed or indifferent
about GM food due to insufficient information provided on food labels. The population of these
three types of consumers, Like-GM, Dislike-GM, and Uninformed, may depend on location, gender,
knowledge, and GMO labeling.
Food pricing is generally an important strategy and should consider consumers’ purchasing
behavior. The marketing literature has shown that consumer knowledge plays an important role
in purchase behavior (Sujan 1985,Alba and Hutchinson 1987,Basu and Vitharana 2009). In the
context of GM food, the consumer knowledge displays new (unique) features that have not been
examined in the literature: the consumer attitude toward GM food not only differs significantly
(Like, Dislike and Uninformed), but also may be affected by the upcoming enforcement of the
GMO food labelling law (Uninformed changing to Like or Dislike). Thus, the GM-food pricing is
worth studying, especially when in practice the GM food sellers are fearing the negative impact of
the labelling law. We hope to help them proactively respond to the GMO food labelling law.
Specifically, we consider how a marketer of a GM food product should price it in response to
the requirement of GMO food label in the near future and its effect on consumers’ heterogenous
attitude. We examine how the GM food pricing is affected by different GM-food consumer attitudes,
GMO food labelling, and price competition. We start by considering a monopolist seller of a GM
food product who aims to optimize his expected profit through optimal pricing before and after

:Impact of Consumer Attitude Heterogeneity on Pricing Strategy for GM Food
Article forthcoming in Annals of Operations Research 3
the GMO food labelling enforcement. We consider two cases: dynamic-pricing and fixed-pricing.
Under dynamic-pricing (fixed-pricing), the seller is (is not) allowed to adjust price after the GMO
food label is required. We will then consider how duopoly competition affects the GM food pricing
before and after GMO food labelling.
Due to the additional cost incurred for the GMO food labelling (or the labelling), the GM
food seller should expect to raise price after the labelling to cover the additional cost. But since
consumers’ attitude may change and become negative once the labelling is available, the seller may
need to reduce price after labelling. For a monopolist GM food seller, we find that the labelling will
not affect price if it was optimal for the seller to target Like-GM consumers only before labelling
under dynamic-pricing. In this case, the seller will use a same high price before and after the
labelling; the seller will charge a premium for the GM-traits. The labeling may reduce price if it
was optimal for the seller to target Uninformed consumers and most of these consumers will dislike
GM food upon reading the GMO label. In this case, the seller will start with a medium price and
then reduce the price after labelling. Under fixed-pricing, when the population of Uninformed or
Dislike-GM consumers is large enough, it is optimal for the seller to charge the high or medium
price (i.e., not to offer discount for the GM-traits) and incur profit loss after the labelling. When
(duopoly) competition is considered, we find that competition hurts both sellers and the Nash
Equilibrium (NE) prices are symmetric. Regardless of dynamic or fixed pricing, both sellers are
more likely to charge the low price; that is, both sellers are more likely to offer a discount for the
GM-traits.
The rest of the paper is organized as follows. In Section 2, we introduce our customer choice
model for GM-food. We then use this model to analyze the GM food supplier’s pricing decision for
the monopoly case in Section 3and for the competitive case in Section 4. Finally, we conclude the
paper with summarized results and future research directions in Section 5. All proofs are contained
in the online supplement.

:Impact of Consumer Attitude Heterogeneity on Pricing Strategy for GM Food
4Article forthcoming in Annals of Operations Research
2. Customer Choice Model
We assume that a customer would purchase at most one unit of the GM food product. She would
purchase if her surplus, defined as reservation price minus price, is at least zero.
We make the following assumptions for the reservation prices of customers. For a given customer,
her reservation price depends on her attitude towards GM food and the characteristics of the
food itself (including the GM-traits such as non-browning, better nutrient profiles, more digestible,
virus-resistant, increased food yield to alleviate world hunger, etc.). Note that some of these GM-
traits are visible to consumers (e.g., “preservative free” on the package of Arctic apple slices), while
others are invisible (e.g., Hawaiian Rainbow papaya are virus-resistant). Uninformed consumers
are either lack of knowledge to identify or indifferent to GM food, and thus pay for the food
characteristics only and have the medium reservation price, M. Note that Mrepresents what an
average consumer is willing to pay for the food product with the GM-traits (regardless knowing it
is GM or not). Like-GM consumers, however, are knowledgeable enough to identify the product as
GM and appreciate the bioengineering contribution, and thus have the highest reservation price,
H.Dislike-GM consumers are also knowledgeable enough to identify the product as GM, but dislike
the GM technology for concerns of potential health risks and sustainability issues, and thus have
the lowest reservation price, L, where 0 < L < M < H .
For customer demand, we assume that the demand comes from the three types of consumers.
We denote the market size of each type of consumers, Like-GM, Dislike-GM, and Uninformed
consumers, before GM food label is enforced by qH,qL, and qM, respectively. We normalize the
total market size to 1 and thus qH+qL+qM= 1. Upon the enforcement of GMO food labeling, the
market size remains the same, and the Uninformed consumers will be informed and may join the
Like-GM or Dislike-GM groups. We let qMH ,qM L, and qM M , where qMH +qM L +qMM =qM, denote
the size of Uninformed consumers becoming Like-GM, Dislike-GM, and remaining as Uninformed
(indifferent) to GM food, respectively, upon the provision of GM food labels. Note that qM M
represents the portion of the Uninformed consumers who are indifferent to GM food.

:Impact of Consumer Attitude Heterogeneity on Pricing Strategy for GM Food
Article forthcoming in Annals of Operations Research 5
3. Monopolistic Pricing Model
The monopolistic firm produces this GM food product at unit cost c > 0 and sells at Pbl ≥cbefore
GMO food labeling is enforced. After the GMO food labeling enforcement, the firm will incur
additional printing cost and, more importantly, logistics cost associated with supplying the food
with the right GM labels required by each individual state. Thus the firm will produce this GM
food product at a higher unit cost cl> c and may sell at the same price Pal =Pbl := Por a different
price Pbl 6=Pal. We refer to the former case as the fixed-pricing scenario and the latter as the
dynamic pricing scenario. For both scenarios, the firm should set the price to maximize his profit,
earned from all the three types of consumers. For simplicity, we assume that the duration of before
and after labelling is the same. This assumption, however, will only affect the results for the fixed
pricing model.
3.1. Dynamic Pricing Model
Before GMO food labeling is enforced, the firm should set the optimal price P∗
bl to maximize his
profit Πbl(Pbl ) as follows. Without loss of generality, we assume that when different prices result
in a same profit, the firm would use the higher price.
If and if P∗
bl Optimal Profit Πbl(P∗
bl)
c≥M H (H−c)qH
L≤c<M (H−M)qH≥(M−c)qMH(H−c)qH
L≤c<M (H−M)qH<(M−c)qMM(M−c)(qH+qM)
c<L (H−M)qH≥(M−c)qM, (H−c)qH≥L−c H (H−c)qH
c<L (H−M)qH<(M−c)qM, (M−c)(qH+qM)≥L−c M (M−c)(qH+qM)
c < L L −c > max{(H−c)qH,(M−c)(qH+qM)}L L −c
After the enforcement of GM food labeling, the firm should set the optimal price P∗
al to maximize
his profit Πal(Pal ) as follows.

:Impact of Consumer Attitude Heterogeneity on Pricing Strategy for GM Food
6Article forthcoming in Annals of Operations Research
If and if P∗
al Optimal Profit Πal(P∗
al)
cl≥M H (H−cl)(qH+qMH )
L≤cl< M (H−M)(qH+qMH )≥(M−cl)qM M H(H−cl)(qH+qMH )
L≤cl< M (H−M)(qH+qMH )<(M−cl)qM M M(M−cl)(qH+qMH +qM M )
cl< L (H−M)(qH+qMH )≥(M−cl)qM M , (H−cl)(qH+qM H )≥L−clH(H−cl)(qH+qMH )
cl< L (H−M)(qH+qMH )<(M−cl)qM M , (M−cl)(qH+qM H +qMM )≥L−clM(M−cl)(qH+qM H +qMM )
cl< L L −cl>max{(H−cl)(qH+qMH ),(M−cl)(qH+qM H +qMM )}L L −cl
As shown in these tables, when setting the price for each stage, the firm should first compare
the variable cost with the possible prices to guarantee a positive profit, i.e., to identify the feasible
prices, and then compare the profit under different feasible prices to choose the optimal. Since H,
Mand Lcould be optimal for each stage under the correspondingly conditions, there are many
different pricing-combinations for the two stages, e.g., Hto H,Hto M, and Mto Letc.
On the one hand, since GMO food labeling raises the variable cost (cl≥c), to cover it the firm
may need to raise price after labeling. on the other hand, the labeling may inform the Uninformed
consumers and change their attitude to Like-GM or Dislike-GM. Thus, GMO food labeling may
lead to a lower (higher) price, P∗
al < P ∗
bl (P∗
al > P ∗
bl); and this happens when the majority of the
Uninformed consumers would become Dislike-GM (Like-GM) upon GMO food labeling, i.e., qM L
(qMH ) is large enough. This increases the population of Dislike-GM (Like-GM) consumers and thus
leads to the price reduction (increase).
Proposition 1. GMO food labeling will reduce (increase) the GM food price if it will make most
Uninformed consumers to dislike (like) GM food. Price reduction P∗
al(= L)< P ∗
bl(= M)happens
when c < cl< L,qH+qMH ≤L−cl
H−cl,qML ≥qH+qM−L−cl
M−cl,qH
qM<M−c
H−M,qH+qM≥L−c
M−c. Price
increase P∗
al(= H)> P ∗
bl(= M)happens when L≤c < cl< M,qH
qM<M−c
H−M,qH+qMH
qMM ≥M−cl
H−M.
Another interesting result is that if the firm targets Like-GM consumers only by charging price
Hbefore labeling (P∗
bl =H), he will charge the same price and target the same group after labeling
(P∗
al =H). Intuitively, GMO food labeling will turn some of the Uninformed consumers into Like-
GM and thus increase the population of Like-GM consumers. Therefore, if the firm would find it

:Impact of Consumer Attitude Heterogeneity on Pricing Strategy for GM Food
Article forthcoming in Annals of Operations Research 7
optimal to target Like-GM consumers only before labeling, he would find the same after labeling
with an increased Like-GM consumer population. Despite the population increase, the profit margin
will drop from H−cto H−cland thus the firm’s profit may not increase after labeling.
Proposition 2. GMO food labeling will not affect the GM food price if it was optimal for the
firm to target Like-GM consumers only by charging price Hbefore labeling, i.e., if P∗
bl =H, we
have P∗
al =H.
3.2. Fixed Pricing Model
In this section, we consider the fixed-pricing case where the firm have to maintain a same price
after labeling for practical reasons, e.g., industry tradition, brand image, or market competition.
Let Pdenote this price and the optimal price P∗should maximize the firm’s expected profit during
the before and after labeling periods. Since this price is set before GMO food labeling is enforced,
the firm would not know if labeling will be enforced by the government (or state) and thus would
apply a probability ql∈[0,1] for it.
If P= Expected Profit π(P) := Πbl(P) + qlΠal(P) + (1 −ql)Πbl (P)
H(2 −ql)[(H−c)qH] + ql[(H−cl)(qH+qMH )]
M(2 −ql)[(M−c)(qH+qM)] + ql[(M−cl)(qH+qMH +qM M )]
L(2 −ql)[L−c] + ql[L−cl]
Usually the firm would like to earn a positive profit from both periods, before and after labeling.
We find, however, that it may be optimal to incur a loss after labeling. This happens when c <
M < cland qMis large enough (or when c < L < cland qLis large enough) such that setting price
at P=M(P=L) will generate very high profit without labeling, high enough to not only cover
the profit loss upon labeling, P−cl=M−cl<0, (P−cl=L−cl<0), but also exceeds the profit
earned under P=H(under P=Hor M).
Proposition 3. Under fixed-pricing, it is optimal to set P∗=M(P∗=L) such
that profit loss is incurred upon labeling when c < M < cland qMis large enough
(when c < L < cland qLis large enough). Mathematically, if c < M < cland

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8Article forthcoming in Annals of Operations Research
qM>(2qH+qlqMH )(H−M)+qlqM M (cl−M)
(2−ql)(M−c), we will have P∗=M; if c < L < cland qL>
max{qH(H−L)−(2−ql)qM(L−c)+ql[qMH (H−L)−(qM M +qM L)(L−cl)]
(2−ql)(L−c)+ql(L−cl),2(qH+qM)(M−L)−qlqML (M−cl)
(2−ql)(L−c)+ql(L−cl)}, we will have
P∗=L.
In general, the optimal fixed-price P∗depends on the variable cost and market size of each group
of consumers before and after labeling.
If and if P∗
M≤c<clH
L≤c < M qM≤(2qH+qlqMH )(H−M)+qlqMM (cl−M)
(2−ql)(M−c)H
L≤c < M qM>(2qH+qlqMH )(H−M)+qlqMM (cl−M)
(2−ql)(M−c)M
c < L π(H)≥max{π(M), π(L)}H
c < L π(M)>max{π(H), π(L)}M
c < L π(L)>max{π(H), π(M)}L
4. Competitive Pricing Model
In this section, we study how price competition affects the GM food pricing. We assume the two
competing firms are identical. That is, they have a same cost and brand image (such that customers
are willing to pay a same price for their products). Thus, if both firms are offering a same price for
the GM food product, the consumer demand will be evenly split between the two firms. Similar
to the monopolistic model, we consider the two different pricing schemes - dynamic pricing and
fixed pricing before and after labeling. Specifically, we start by considering the case where the two
competing firms use a same pricing scheme, either dynamic or fixed pricing. This might be due to
the industry tradition. We then consider the general case and allow the two competing firms to
choose their own pricing scheme along with the prices.
4.1. Both Using Dynamic Pricing
When both firms adopt the dynamic pricing scheme, they will enter into a two-stage price compe-
tition, where the first stage is before labeling and the second stage is after labeling. Note that the

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Article forthcoming in Annals of Operations Research 9
competition in different stages is independent. We start by presenting the payoff table in the first
stage: before labeling (bl).
Firm 1’s price P1
Firm 2’s price P2H M L
H(Πbl(H)
2,Πbl(H)
2) (0,Πbl(M)) (0,Πbl (L))
M(Πbl(M),0) ( Πbl(M)
2,Πbl(M)
2) (0,Πbl(L))
L(Πbl(L),0) (Πbl (L),0) ( Πbl(L)
2,Πbl(L)
2)
As defined in Section 3.1, the profit functions at different prices, H,M, or L, are: Πbl(H) =
(H−c)qH; Πbl(M) = (M−c)(qH+qM); Πbl (L) = L−c. Comparing the payoffs, we know that any
firm’s best response, P∗
i(P−i), is:
P∗
i(H) =



















Hif Πbl(H)
2≥max{Πbl(M),Πbl (L)},
Mif Πbl(M)>Πbl (H)
2and Πbl(M)≥Πbl (L),
Lotherwise;
P∗
i(M) =









Mif Πbl(M)
2≥Πbl(L),
Lotherwise;
P∗
i(L) = L. (1)
Let’s consider how one firm sets his best-response price. Given his competitor’s price at Hor M, the
firm’s response decision-making process is the same as that in the monopoly case—comparing his
profit earned under different reasonable prices which are the same as or lower than his competitor’s.
The only difference is that when considering a same price as his competitor’s, his profit becomes
the half of the monopolist’s. When considering a lower price than his competitor’s, however, he
essentially becomes the “monopoly” and earns the monopolist’s profit. Thus, the firm has more
incentive to charge a lower price than his competitor (a form of price differentiation). Given his
competitor’s price at L, the firm’s decision-making is simple: he responds with Lfor sure and earns
half of the monopolist’s profit.

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10 Article forthcoming in Annals of Operations Research
Thus, theoretically speaking, (H, H ),(H, M ),(H, L),(M, M ),(M, L) and (L, L) are all candidates
for a Nash equilibrium. But since every firm has no incentive to out-price his competitor and
thus earning no profit, we know that only symmetric price pairs are possible NEs and they are
(H, H ),(M, M ) and (L, L). We let P∗
bl denote the NE price before labeling, noting that bold letters
are used to denote a vector.
Proposition 4. The NE price P∗
bl is symmetric: (L, L)is a NE; (H, H )and (M, M )may also
be a NE. (H, H)being a NE is less likely than Hbeing the optimal price before labeling for the
monopoly case. If the firm’s individual profit (or profit margin) at different prices, Πbl(H),Πbl(M)
and Πbl(L), are not too far apart, e.g., H−c < 2(M−c)(1 + qM
qH)and M−c < 2(L−c)1
qH+qM,
(L, L)will be the unique NE.
It is interesting to note that it is possible that both firms will be better off at (H, H ) or (M, M )
than at (L, L). But both firms’ incentive of price differentiation—charging a lower price than his
competitor—may prevent them arriving equilibrium at (H, H) or (M , M ). This is especially true
when the firm’s individual profit at different prices, Πbl(H),Πbl(M) and Πbl (L), are close enough,
and thus (L, L) will be the unique NE.
Similarly, we can analyze the NE price for the second stage competition after GMO food labeling
(al) using the payoff table below.
Firm 1’s price P1
Firm 2’s price P2H M L
H(Πal(H)
2,Πal(H)
2) (0,Πal(M)) (0,Πal (L))
M(Πal(M),0) ( Πal (M)
2,Πal(M)
2) (0,Πal(L))
L(Πal(L),0) (Πal (L),0) ( Πal (L)
2,Πal(L)
2)
As defined in Section 3.1, the profit functions at different prices, H, M , or L, after labeling are:
Πal(H) = (H−cl)(qH+qM H ); Πal (M) = (M−c)(qH+qMH +qM M ); Πal(L) = L−c. Comparing the

:Impact of Consumer Attitude Heterogeneity on Pricing Strategy for GM Food
Article forthcoming in Annals of Operations Research 11
payoffs, we know that any firm’s best response P∗
i(P−i) is:
P∗
i(H) =



















Hif Πal(H)
2≥max{Πal(M),Πal (L)},
Mif Πal(M)>Πal (H)
2and Πal(M)≥Πal (L),
Lotherwise;
P∗
i(M) =









Mif Πal(M)
2≥Πal(L),
Lotherwise;
P∗
i(L) = L. (2)
Similarly as in the before labeling case, every firm has more incentive to charge a price lower
than his competitor, and only symmetric price pairs, (H, H ),(M, M ) and (L, L), are feasible Nash
equilibria. We let P∗
al denote the NE price after labeling, noting that bold letters are used to denote
a vector. Our intuition is that competition will reduce the price, making both firms more likely to
charge the lowest price Lafter labeling.
Proposition 5. The NE price P∗
al is symmetric: (L, L)is a NE; (H, H )and (M, M )may
also be a NE. If the firm’s individual profit (or profit margin) at different prices, Πal(H),Πal (M)
and Πal(L), are not too far apart, e.g., H−cl<2(M−cl)(1 + qMM
qH+qMH )and M−cl<2(L−
cl)1
qH+qMH +qM M ,(L, L)will be the unique NE.
4.2. Both Using Fixed Pricing
In this section, we consider the scenario that both firms adopt the fixed-pricing scheme, i.e., both
firms use a same price for both before and after labeling, maybe under industry tradition. Unlike
in the dynamic pricing scenario, the competition in this fixed-pricing scenario is a one-shot game
in which both firms compete on price to maximize their own expected profit. The expected payoff
table is shown below.

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12 Article forthcoming in Annals of Operations Research
Firm 1’s price P1
Firm 2’s price P2H M L
H(π(H)
2,π(H)
2) (0, π(M)) (0, π(L))
M(π(M),0) ( π(M)
2,π(M)
2) (0, π(L))
L(π(L),0) (π(L),0) (π(L)
2,π(L)
2)
As defined in Section 3.2, the profit functions at different prices, H, M , or L, after labeling
are: π(H) = (2 −ql)(H−c)qH+ql(H−cl)(qH+qM H ); π(M) = (2 −ql)(M−c)(qH+qM) + ql(H−
cl)(qH+qMH +qM M ); π(L) = (2 −ql)(L−c) + ql(L−cl).
Comparing the payoffs, we know that any firm’s best response P∗
i(P−i) is:
P∗
i(H) =



















Hif π(H)
2≥max{π(M), π(L)},
Mif π(M)>π(H)
2and π(M)≥π(L),
Lotherwise;
P∗
i(M) =









Mif π(M)
2≥π(L),
Lotherwise;
P∗
i(L) = L. (3)
Let’s consider how one firm sets his best-response price. Given his competitor’s price at Hor M,
the firm’s response decision-making process is the same as that in the monopoly case—comparing
his expected profit earned under different reasonable prices which are the same as or lower than
his competitor’s. The only difference is that when choosing a same price as his competitor’s, his
profit becomes the half of the monopolist’s. When choosing a lower price than his competitor’s,
however, he essentially becomes the “monopoly” and earns the monopolist’s expected profit. Thus,
the firm has more incentive to charge a lower price than his competitor to dominate the market.
Given his competitor’s price at L, the firm’s decision-making is simple: he responds with Las well
and earns half of the monopolist’s expected profit.
Thus, theoretically speaking, (H, H ),(H, M ),(H, L),(M, M ),(M, L) and (L, L) are all candidates
for a Nash equilibrium. But since every firm has no incentive to out-price his competitor and thus

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Article forthcoming in Annals of Operations Research 13
earning no profit, we know that only symmetric price pairs are feasible and they are (H, H),(M , M )
and (L, L). We let P∗denote the NE price under the fixed-pricing scheme, noting that bold letters
are used to denote a vector.
Proposition 6. The NE price P∗is symmetric: (L, L)is a NE; (H, H)and (M , M )may also
be a NE. If the firm’s individual expected profit (or profit margin) at different prices, π(H), π(M)
and π(L), are not too far apart, (L, L)will be the unique NE.
It is intuitive that competition will reduce the price, making both firms more likely to charge
the lowest price L. Although fixed pricing might be the tradition of the industry in which the two
firms are competing, both firms may have an incentive to change the price in the second stage
(after labeling). When this happens, this game with fixed pricing becomes the game with dynamic
pricing.
4.3. Choosing Pricing Schemes
We now allow both firms to decide their pricing schemes freely, Dynamic (D) or Fixed (F) pricing,
together with their prices under this “grand” competition. If one firm chooses D-pricing, he will be
able to set his price twice, one before labeling and one after labeling; if he chooses F-pricing, he will
only set his price once and before labeling. For example, D−Hmeans that the firm decides to use
dynamic pricing and charge Hbefore labeling, and may charge H,Mor L, whichever is optimal,
after labeling; F−Hmeans that the firm decides to use fixed pricing and charge Hbefore and
after labeling. It is possible to consider that adoption of fixed-pricing improves the brand image
and thus may come with some forms of reward, e.g., more customer demand when charging a same
price as the competitor who uses dynamic pricing. Both firms’ expected payoff function under six
different choice combinations of pricing scheme and price (D−H, D−M , D−L, F −H, F −M , F −L)
is shown in the following three tables.

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14 Article forthcoming in Annals of Operations Research
Firm 1
Firm 2
D−H D−M D−L
D−H(2 −ql)( Πbl(H)
2,Πbl(H)
2) + qlΠ∗
al (2 −ql)(0,Πbl(M)) + qlΠ∗
al (2 −ql)(0,Πbl(L)) + qlΠ∗
al
D−M(2 −ql)(Πbl(M),0) + qlΠ∗
al (2 −ql)( Πbl(M)
2,Πbl(M)
2) + qlΠ∗
al (2 −ql)(0,Πbl(L)) + qlΠ∗
al
D−L(2 −ql)(Πbl(L),0) + qlΠ∗
al (2 −ql)(Πbl(L),0) + qlΠ∗
al (2 −ql)( Πbl(L)
2,Πbl(L)
2) + qlΠ∗
al
where Π∗
al := (Πal(P∗
al1)
2,Πal(P∗
al2)
2) is both firms’ payoff after labeling under the NE price P∗
al =
(P∗
al1, P ∗
al2);
1
2
D−H D−M D−L
F−H(2 −ql)( Πbl(H)
2,Πbl(H)
2) + qlΠ∗
al(H) (2 −ql)(0,Πbl (M)) + qlΠ∗
al(H) (2 −ql)(0,Πbl(L)) + qlΠ∗
al(H)
F−M(2 −ql)(Πbl(M),0) + qlΠ∗
al(M) (2 −ql)( Πbl(M)
2,Πbl(M)
2) + qlΠ∗
al(M) (2 −ql)(0,Πbl(L)) + qlΠ∗
al(M)
F−L(2 −ql)(Πbl(L),0) + qlΠ∗
al(L) (2 −ql)(Πbl(L),0) + qlΠ∗
al(L) (2 −ql)( Πbl (L)
2,Πbl(L)
2) + qlΠ∗
al(L)
where Π∗
al(P1) := Π∗
al(P1, P ∗
2(P1)) is both firms’ payoff after labeling at price (P1, P ∗
2(P1)); see their
detailed expression in the payoff table for the after labeling case in Section 4.1;
Firm 1
Firm 2
F−H F −M F −L
F−H(π(H)
2,π(H)
2) (0, π(M)) (0, π(L))
F−M(π(M),0) ( π(M)
2,π(M)
2) (0, π(L))
F−L(π(L),0) (π(L),0) ( π(L)
2,π(L)
2)
We first analyze each firm’s best response strategy given that his competitor chooses to adopt
the dynamic-pricing scheme, including choices of D−H, D−Mand D−L. Comparing the first two
tables above on the first column (given that firm 2 chooses D−H), we note that firm 1 should always
respond with the same pricing scheme—the dynamic scheme—to enjoy the same pricing flexibility
as his competitor in the after labeling competition. This result also applies to the comparison on

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Article forthcoming in Annals of Operations Research 15
the next two columns (given that firm 2 chooses D−Mand D−L, respectively). Mathematically,
we can show that Π∗
al ≥maxP1∈{H,M,L}Π∗
al(P1) for firm 1’s payoff.
What if his competitor chooses the fixed-pricing scheme? To address this question, we compare
the last two tables above on the first row (given that firm 1 chooses F−H), we note that firm 2
should always respond with a different pricing scheme—the dynamic scheme—to take advantage
of the pricing flexibility (that his competitor doesn’t have) in both the before and after labeling
competitions. This result also applies to the comparison on the next two rows (given that firm 1
chooses F−Mand F−L, respectively).
In sum, we learn that regardless of the competitor’s pricing scheme choice, each firm should
always choose the dynamic-pricing scheme. This means that this grand competition game reduces to
the simpler two-stage competition game (before and after labeling) with both firms’ using dynamic
pricing, which is studied in Section 4.1. Using the results shown in Propositions 4and 5, we know
that both firms will choose dynamic-pricing and a same price before and after labeling under NE.
We let SP∗denote the NE scheme-price combination under the grand competition, noting that
bold letters are used to denote a vector.
Proposition 7. The NE price SP∗is symmetric: (D−L, D−L)is a NE; (D−H, D−H)and
(D−M, D −M)may also be a NE. If the firm’s individual profit (or profit margin) before labeling at
different prices, Πbl(H),Πbl (M)and Πbl(L), are not too far apart, (D−L, D−L)will be the unique
NE.
Note that if the NE price in the second stage—after labeling—is the same as that in the first
stage—before labeling, say (H, H ), then both firms’ choosing to fix price at H, i.e., (F−H, F −H),
is also a NE because it renders both firms exactly the same expected payoff as (D−H, D−H).
Moreover, if price guarantee can attract more market share in practice, each firm will have an
incentive to choose the fixed-pricing scheme, although when both offering the same fixed price, no
one can attract more share.

:Impact of Consumer Attitude Heterogeneity on Pricing Strategy for GM Food
16 Article forthcoming in Annals of Operations Research
5. Conclusion
Food pricing is generally an important yet challenging strategy. Facing the unique consumer atti-
tude toward GM food and the upcoming enforcement of the GMO food labelling law (as discussed
above), GM-food pricing is especially challenging. The GM food suppliers and sellers have been
resistant to the GMO food labelling law, fearing the consumers’ negative reaction to the GM food.
Our optimal or equilibrium pricing analysis and results for different practical cases can help them
proactively respond to the GMO food labelling law.
We obtained the following interesting insights. Due to the additional cost incurred for the GMO
food labelling (or the labelling), the GM food seller should expect to raise price after the labelling
to cover the additional cost. But since consumers’ attitude may change and become negative once
the labelling is available, the seller may need to reduce price after labelling. For a monopolist GM
food seller, we found that the labelling would not affect price if it was optimal for the seller to target
Like-GM consumers only before labelling under dynamic-pricing. In this case, the seller will always
charge the high price (H), i.e., charge a premium for the GM-traits, before and after the labelling.
The labeling may reduce price if it was optimal for the seller to target Uninformed consumers and
most of these consumers will dislike GM food upon reading the GMO label. In this case, the seller
will start with the medium price (M) and then drop to the low price (L), i.e., offer a discount for
the GM-traits, upon labelling. When the industry standard requires fixed-pricing, we found that
if the population of Uninformed or Dislike-GM consumers is large enough, it is optimal for the
monopolist seller to charge the high or medium price (i.e., not to offer discount for the GM-traits)
and incur profit loss after the labelling. When (duopoly) competition is considered, we found that
competition hurts both sellers and the Nash Equilibrium (NE) prices are symmetric. Regardless
of dynamic or fixed pricing, both sellers are more likely to charge the low price (L); that is, both
sellers are more likely to offer discount for the GM-traits.
This paper is the first to study the pricing of GM-food facing heterogenous consumer attitudes
towards GM-food (Like, Uninformed, and Dislike). We admit that the current model is simple with

:Impact of Consumer Attitude Heterogeneity on Pricing Strategy for GM Food
Article forthcoming in Annals of Operations Research 17
assumptions of (1) customers of the same type have a constant reservation price, (2) the market
size and selling duration remain the same after the labelling, and (3) identical sellers. Future
research can generalize the model to relax these assumptions. We believe that the managerial
insights obtained in this paper will also hold. The current model focuses on the US food industry
where GMO labelling will be enforced. It can be extended to study whether GMO labelling will
be preferred by the seller(s); the labelling decision is made by the government trading off the pros
and cons for both consumers and relevant businesses (GM seed, food growers and sellers). This
paper provides valuable guidelines and insights to industry and academic on how to price based
on customers’ heterogenous attitude towards GM-food.
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:Impact of Consumer Attitude Heterogeneity on Pricing Strategy for GM Food
Article forthcoming in Annals of Operations Research 1
Online Supplement: Proofs and Technical Details for “Impact of
Customer Attitude Heterogeneity on Pricing Strategy for GM Food”
Proof of Propositions 1-3:The results follow from simple algebra. 
Proof of Propositions 4and 5:As shown by (1) and (3), P∗
i(P−i)≤P−iunder competition. By
contradiction, we know that asymmetric NE (one firm chooses a higher price than the other firm)
won’t exist as otherwise it will contradict to (1) or (3) for the firm who chooses a higher price. A
close examination of (1) or (3) shows that the conditions under which P∗
i(H) = Hand P∗
i(M) = M
hold are similar to those under which P∗
bl =Hand P∗
bl =Mhold in the monopoly case, respectively.
The only difference is that, in the former (when both are choosing Hor M), each firm earns only
half of the monopolist’s profit. Thus, P∗
i(H) = Hand P∗
i(M) = Mare less likely to hold than
P∗
bl =Hand P∗
bl =Min the monopoly case, respectively. Moreover, they are even less likely to hold
if Πj(H),Πj(M) and Πj(L), j=bl, al, are closer. This concludes the proof. 