Why did U.S. food retailers voluntarily pledge to go cage-free with eggs?

Abstract

I develop a model of provision competition between food retailers to examine one potential economic rationale behind voluntary cage-free egg pledges. I show that competition pushes retailers to a prisoners’ dilemma equilibrium where retailers incur fixed costs to offer both non-cage-free and cage-free eggs to steal or prevent the loss of some basket-shopping consumers. In a dynamic setting, retailers can potentially sustain an equilibrium of higher profits by collectively withholding non-cage-free eggs. I show that changing supply conditions and consumer trends could have led to such an equilibrium with pledges acting as a signal to potentially facilitate tacit coordination.

1. Introduction

In 2016, many U.S. food retailers of grocery products made voluntary pledges to only provide eggs from cage-free sources by 2026 or earlier (Graber and Keller, 2020).¹ These pledges to go cage-free with eggs came amongst the trend of increasing public interest in the ban of battery cages for egg laying hens, and 10 U.S. states ultimately either banned the production and/or sale of ‘caged’ eggs (Ufer, 2022). Implications of the cage-free egg transition for consumers and egg producers have been well studied in the literature (Allender and Richards, 2010b; Malone and Lusk, 2016; Mullally and Lusk, 2017; Lusk, 2019; Kotschedoff and Pachali, 2020; Carter, Schaefer and Scheitrum, 2021; Sohae Eve and Vukina, 2022; Caputo et al. 2023b; Xie and Lusk, 2023). However, the question of why food retailers voluntarily decided to only provide cage-free eggs has not been thoroughly explored.

Food retailers compete for consumers with prices, assortments, and other store amenities (Fox, Montgomery and Lodish, 2004; Briesch, Chintagunta and Fox, 2009; Bonanno and Lopez, 2009; Hamilton and Richards, 2009). Eggs are an important product category to draw in grocery shopping consumers, and retailers typically offer multiple variants of eggs to cater to consumers with heterogenous preferences for different egg attributes. Recent work by Allender and Richards (2010a), Lusk (2019), Sohae Eve and Vukina (2022), Caputo et al. (2023a) and Cao et al. (2021) show that a significant segment of consumers still prefer non-cage-free eggs. These studies raise the question of why retailers facing competitive pressure would voluntarily risk losing a large portion of consumers by withholding an egg variety favoured by many.

In this article, I propose one potential reason that retailers made pledges to only offer cage-free eggs was to soften within category assortment competition and save on fixed costs associated with providing non-cage-free eggs. Specifically, retailers will often offer a variety of attractive products to compete for basket-shopping consumers. However, providing many different ‘luring’ products can be costly to the retailer. I develop a theoretical model of strategic retailer interaction that captures the provision strategies used by retailers. In the model, retailers can provide non-cage-free eggs at a cost to steal basket-shopping consumers that favour non-cage-free eggs from a rival store. I show the equilibrium is a classic ‘prisoners’ dilemma’ scenario where retailers provide both cage-free and non-cage-free eggs. I also show that a cooperative equilibrium where retailers only provide cage-free eggs is more profitable for all retailers.²

Intuitively, if gains from stealing consumers outweigh the fixed cost of providing non-cage-free eggs, retailers will always incur the fixed cost. However, since all retailers are providing non-cage-free eggs, retailers do not attract additional consumers but do incur more fixed costs in a competitive equilibrium compared to the cooperative equilibrium.

As the state-level bans shift the supply landscape and cost structure of egg production, the incentives for retailers’ provision decisions can also change. My model shows that increasing sourcing and production costs of non-cage-free eggs increase the incentives for retailers to result in a cage-free eggs-only equilibrium under a dynamic game setting. Intuitively, even though gains from stealing consumers still outweigh the fixed cost of providing non-cage-free eggs, net gains might be reduced to a point where an outcome of not engaging in costly provision competition is sustainable as a result of demand and supply changes in 2016. Similar to price announcements under a pattern of price leadership, these non-binding cage-free pledges can serve as signals and coordination devices to other retailers on their intentions and commitments in terms of egg provision choices with the hope that pledges can start to soften provision competition.

Although theoretical, I hope this article can provide some insights into a seeming puzzle of why profit maximising firms would voluntarily lose a non-trivial amount of consumers with regard to these cage-free egg pledges. These results contribute to the broader literature on food retail competition by modelling and highlighting how retailers can engage in product provision competition. Moreover, evidence of price leadership and follow-the-leader pricing, where public price announcements can facilitate tacit price coordination, has been empirically established in many retail settings such as supermarkets, gasoline and beer (Clark and Houde, 2013; Seaton and Waterson, 2013; Byrne and De Roos, 2019; Miller, Sheu and Weinberg, 2021). I show the possibility of tacit coordination in retail in terms of variety competition.

I also contribute to the public policy literature on voluntary industry pledges, which are common in the food industry with examples such as pledges to reduce sodium, calories and sugar, marketing to children and increasing voluntary food safety standards (Sharma, Teret and Brownell, 2010; Hawkes and Harris, 2011; Philipsborn et al., 2018; Minor et al., 2019). I highlight an alternative profit maximising motive behind voluntary pledges that seemingly inflict self-harm.

I further contribute to the literature on the cage-free egg transition, animal welfare and the supply dimensions of transitioning to animal-friendly products. Consumers have a growing interest in animal welfare along the food supply chain, and retailer decisions have a lot of ramifications both downstream to consumers and upstream to producers. From a welfare perspective, I show that only providing cage-free eggs could be beneficial for retailers but inflict welfare loss on consumers.

The rest of the paper proceeds as follows: Section 2 provides background information on retail competition and the transition to cage-free eggs. Section 3 sets up the model and determines the Nash equilibrium under a one-shot game and the subgame perfect Nash equilibrium (SPNE) under a dynamic game setting. Section 4 examines comparative statics to see how supply factors and consumer trends can change the threshold at which a cooperative equilibrium is possible and sustainable. Section 5 looks at the associated welfare changes. Section 6 concludes and discusses the policy implications.

2. Background and literature review

There is growing consumer interest and concern regarding food safety, health attributes, local sourcing and animal welfare among food and agricultural products. This interest is permeating back upstream into the supply chain as consumers are becoming more interested in where and how their food products are sourced (Lagerkvist and Hess, 2011; Clark et al., 2017; Britwum and Yiannaka, 2019; Ortega and Wolf, 2018; Dong, Klaiber and Plakias, 2023). In particular, humane treatment of egg-producing hens has generated a lot of consumer interest. As such, 10 U.S. states passed bills and/or referendums to require the production of eggs within the state to be cage-free, and 8 of those states also require the sale of eggs to be from cage-free sources (Ufer, 2022). In 2023, cage-free hens make up almost 40 per cent of the U.S. egg-laying flock (USDA-ERS, 2023).

The food retail store is where the majority of eggs for consumers end up as 56.6 per cent of U.S.-produced eggs were distributed to retail (American Egg Board). Food retailers such as Walmart and Kroger are multiproduct firms, and they offer multiple similar versions of a food product for many food categories such as different types of cereal, many flavours of ice cream and numerous varieties of apples. As such, retail stores can easily offer and market differentiated varieties of eggs (organic, local, cage-free, brown, containing omega-3, etc.) to consumers depending on their preferences. Some eggs feature multiple attributes such as eggs that are both organic and cage-free. See Sohae Eve and Vukina (2022) for excellent summary statistics on retail shares of different egg varieties.

For consumer purchase decisions on cage-free products, economic theory suggests consumers with valuation for the cage-free attribute above the additional price premium will purchase cage-free eggs and consumers with little to no valuation for the cage-free attribute will purchase cheaper non-cage-free eggs. Allender and Richards (2010a), Lusk (2019) and Sohae Eve and Vukina (2022) show sales bans of non-cage-free eggs will reduce consumer welfare as consumers with a revealed preference for non-cage-free eggs will have to substitute with different eggs or no longer purchase eggs.³

As some consumers have a high valuation for the cage-free attribute and some consumers have a low valuation for the cage-free attribute, retailers providing both types of differentiated eggs are the likely outcome compared to retailers only providing one type of egg. Competitive pressure pushes retailers to provide multiple egg variants to attract consumers with varying valuations for the different egg attributes.

Even for a monopolist, the retailer profits from offering both types of eggs are typically higher under many theoretical models. If retailers are assumed to profit maximise on eggs alone, a price-discriminating monopolist retailer can extract more rent by using the cage-free attribute to quality price discriminate (Mussa and Rosen, 1978; Tirole, 1988; Dong, 2023).⁴

These studies assume retailers make pricing and provision decisions on eggs as a category independent of other products sold within the store. Modern food retailers are multiproduct firms that offer anywhere from less than 10,000 to more than 100,000 products (measured in stock-keeping units) across many product categories and departments. Consumers also typically make store choice decisions based on purchasing a basket of grocery goods along with other store characteristics (Bliss, 1988; Lal and Matutes, 1994; Chevalier, Kashyap and Rossi, 2003; DeGraba, 2006; Hamilton, Liaukonyte and Richards, 2020). Correspondingly, retailers will engage in competition on price, varieties, services and other amenities to attract consumers (Richards and Hamilton, 2006; Bonanno and Lopez, 2009).

Recent studies have shown that retailers compete across product categories and utilise the consumer complementarity between products to profit maximise (Lal and Matutes, 1994; Richards, Hamilton and Yonezawa, 2018; Thomassen et al., 2017; Hamilton, Liaukonyte and Richards, 2020). Intuitively, retailers can leverage consumer travel cost savings associated with purchasing a bundle of products at one store instead of having to travel to multiple stores. Thomassen et al. (2017) show that actual retail margins are consistent with retailers’ pricing based on one-trip shoppers’ demand complementarity compared to retailers’ pricing categories independently. In addition, consumers will often make unplanned purchases once in store as some studies show that 60 per cent of purchases are unplanned (Kollat and Willett, 1967; Park, Iyer and Daniel, 1989; Heilman, Nakamoto and Rao, 2002; Johnson, 2017).

Correspondingly, a key strategy for retailers is to draw in consumers by offering better product assortments. Shoppers will often shift where they purchase their basket of goods based on prices and availability of select key products (Lal and Matutes, 1994). Messinger and Narasimhan (1997) show that the key reason retailers offer more products is to attract one-trip shoppers.

Eggs are a key product category that draws in consumers as the percentage of U.S. households that purchase eggs is 94 (O’Keefe, 2020). Eggs also comprise roughly 2 per cent of consumer food-at-home expenditures (Bureau of Labor Statistics (BLS), 2025), and consumers also purchase eggs very frequently due to the perishable nature of eggs. With the popularity of eggs among consumers, the price and availability of different eggs can be significant factors in consumers’ store choices. The availability of non-cage-free eggs could possibly result in ‘stealing’ some consumers from a rival store. Most food retailers currently offer multiple varieties of eggs to draw in all consumers with varying preferences for the cage-free attitude to purchase the type of eggs that they like best. The pledges to only provide cage-free eggs could mean the loss of some consumers and profits, which raises the question of why retailers would voluntarily lose profits.

The official pledges of these retailers often cite the alignment of their practices with consumer preferences and expectations on animal welfare as the rationale behind the cage-free commitments. However, Caputo et al. (2023a) show that 56 per cent of consumers did not know that their preferred retailer made such a pledge based on survey data. Studies also show a significant share of consumers have low value for cage-free eggs and retailers can simply offer both types of eggs. Voluntarily providing cage-free eggs only would risk losing a large portion of consumers as providing multiple types of eggs is critical for attracting the entire spectrum of consumers.

While some states banned the sales of non-cage-free eggs in recent cage-free bills, it is unlikely these bills destroyed the ability and incentives of retailers to provide non-cage-free eggs. The total population of states with sales bans comprises less than 25 per cent of the total U.S. population (Ufer, 2022). Some retail chains such as Giant Eagle and Hy-Vee have almost no presence in any of the states with sales bans but still made these pledges. In terms of provision, the production bans are in states that comprise about 13 per cent of the total egg-laying flock (Ufer, 2022). Although the bans could result in higher sourcing costs, they did not eliminate the availability of non-cage-free eggs.

There are fixed costs for a retailer to provide products. In the case of eggs, there are sourcing/shoe leather costs with searching, finding and negotiating for egg suppliers.

Most retailers are also constrained by selling space (a store only has so much selling area before major renovations). Provision of non-cage-free eggs is at the opportunity cost of other more profitable high-margin items such as processed liquid eggs or ready-to-eat eggs. Moreover, reducing the number of products within a category could mean more refrigerator space for other more high-margin categories such as high-end cheeses and deli meats. Finally, consumers typically regard non-cage-free eggs and cage-free eggs as mutually exclusive items in that they usually purchase one or the other.

While retailers would like to save on costs associated with provision, food retailers also face competition with the potential for rivals to incur the costs, provide both types of eggs, and lure away some consumers. The best response for a retailer is likely to follow suit and provide non-cage-free eggs, which results in the zero-sum equilibrium of every retailer providing non-cage-free eggs. Ellickson (2006), Ellickson (2007) and Ellickson (2013) show that product varieties are strategic complements in retail competition where one firm incurring costs to provide more products leads other firms to follow. Hamilton and Richards (2009) also show that retailers increase the assortment depth (number of different varieties) within a product category if competition increases.

However, if all retailers tacitly withhold quality improvements by only providing cage-free eggs, consumers are not stolen away by competition, and retailers can save on provisional costs. The incentives for retailers to tacitly disengage from provision competition depend on the trade-offs between gains from stealing and the provision cost savings. A non-competitive or cooperative outcome among competitive rivals is difficult to sustain in cases where there are incentives to ‘cheat’ and intentions are unclear. One way to sustain cooperative outcomes is information sharing for credible monitoring and enforcement. Even instances where the talk is ‘cheap’ and lacks credibility, communication can still facilitate and help sustain a cooperative outcome (Fonseca and Normann, 2012; Awaya and Krishna, 2016).

Pledges are a great way to announce and signal intentions and commitments publicly. Miller, Sheu and Weinberg (2021) provide evidence of ‘supermarkups’ and extra profits under a price leadership game in the beer industry where one brewer makes public price announcements as signals and coordination devices with other brewers closely following the announced price. Similarly, the cage-free pledges came from almost every major retailer in the country.⁵ The window in which all retailers made the voluntary pledge was also very narrow. Most retailers made the pledge within the 6 months between the end of 2015 and June 2016. The short window highlights the likelihood of these pledges serving as coordination devices and signals.

Similar to the theoretical papers of Bourquard and Wu (2020), Winfree and Watson (2021) and Nuño-Ledesma, Wu and Balagtas (2024), I develop my hypothesis into a formal model where I combine a model of horizontal product differentiation in food retailing with the availability of different egg types as a vertical quality attribute of the store. The assumptions and mechanisms of the model are supported by empirical evidence and by the literature on the cage-free egg transition and retail competition. The implications of the model will hopefully shed light on some of the underlying economic incentives and the decision-making process of retailers surrounding the cage-free transition.

3. Model

3.1. Model set-up

I start the model with two horizontally differentiated and symmetric stores, and the horizontal differentiation is modelled through the linear Hotelling line (Hotelling, 1929; Mérel and Sexton, 2011; McCluskey and Winfree, 2022).⁶ Unlike McCluskey and Winfree (2022) where firms also locate strategically, I assume both stores are fixed in terms of location and are located at the end points of a line with a length of 1 (maximally differentiated). Modelling retail competition via two stores fixed on opposite ends of the line is common in the retail literature (Lal and Matutes, 1994; DeGraba, 2006; Inderst and Valletti, 2011).

Next, I assume consumers have utility |$U$|⁠, and |$U$| is derived from purchasing a basket of grocery goods at a store. The term |$r$| represents the utility that the consumer has for a basket of grocery goods without eggs. Store 1 is located at |${l_1} = 0$|⁠, and store 2 is located at |${l_2} = 1$| where |$l$| indexes store location. |$x$| represents where the consumer is along the line, and |$\left| {{l_i} - x} \right|\,$| is the distance to store |$i$| from the vantage point of a consumer. Finally, |$t$| is travel cost/differentiation preference, and |$t\left| {{l_i} - x} \right|$| is the total disutility from travelling to store |$i$|⁠.

Consumers receive utility |$e$| from a conventional egg and receive utility |$\left( {e - {p_{iNCF}}} \right)$| if the consumer decides to buy non-cage-free eggs at store |$i$|⁠, |$HNC{F_i}$| = 1. If consumers purchase cage-free eggs at store |$i$|⁠, |$HC{F_i}$| = 1, they receive |$\left( {{\theta _c} + e - {p_{iCF}}{\rm{\,}}} \right)$|⁠, where |${\theta _c}$| is the additional consumer valuation for the cage-free attribute of eggs. The value of |${\theta _c}$| depends on the type of consumer, |$c$|⁠. I assume consumers have unit demand for eggs and consumers only buy one type of eggs or no eggs with the choice set as either [|$HNC{F_i}$| = 0, |$HC{F_i}$| = 1], [|$HNC{F_i}$| =  1, |$HC{F_i}$| = 0] or [|$HNC{F_i}$| = 0, |$HC{F_i}$| = 0]. The choices can be modelled through the constraint |$HNC{F_i} + HC{F_i} \le 1$|⁠.

Among the consumers, I assume there are three types of consumers that currently purchase eggs, |$c \in \left[ {l,s,h} \right]$|⁠, and the consumer types are distinguished by their differential preference for the cage-free attribute. Consumers that have low preference are indexed as |$l$|⁠, consumers with ‘switching preference’ are indexed as |$s$| and consumers with high preference are indexed |$h$|⁠. These consumers only differ in their valuation for the cage-free attribute of eggs.

The terms |${c_{NCF}}$| and |${c_{CF}}$| are the marginal cost of non-cage-free and cage-free eggs, respectively. I note that the marginal cost of cage-free eggs is higher than the marginal cost of non-cage-free eggs, |${c_{CF}} \gt {c_{NCF}}$|⁠. Recent studies (Caputo et al., 2023b) show marginal costs for cage-free eggs are higher due to additional production costs, which provide an empirical basis for this claim.

For all consumers, I assume |${c_{CF}} \gt e \gt {c_{NCF}}$|⁠.⁷ For consumers with high preference, I assume that |${\theta _h} \gt \,{c_{CF}} - {c_{NCF}}$|⁠. For consumers with switching preference, I assume that |${c_{CF}} - {c_{NCF}} \gt {\theta _s} \gt \,{c_{CF}} - e$|⁠. Finally, for consumers with low preference, I assume that |${\theta _l} = 0.$| I assume the share of |$s$| consumers is |$\lambda $|⁠, the share of |$l$| consumers is |$\sigma $| and the share of |$h$| consumers is |$1 - \lambda - \sigma $|⁠. I assume each type of consumer is evenly distributed along the horizontal line and the shares of each consumer type are independent of location |$x$|⁠. In other words, for a given location, |$x$|⁠, the shares of |$s$|⁠, |$l$| and |$h$| consumers at that location are |$\lambda ,\,\sigma $| and 1|$ - \lambda - \sigma $|⁠, respectively.⁸

The consumer utility maximisation equation is written below⁹:

Stores make total profit |${\pi _i}$| based on the total profit of eggs and other goods. For eggs, stores make a profit based on quantity demanded of non-cage-free eggs, |${Q_{iNCF}}$|⁠, and cage-free eggs, |${Q_{iCF}}$|⁠, multiplied by their markups |$\left( {{p_{iNCF}} - {c_{NFC}}} \right)\,$|and|$\,\left( {{p_{iCF}} - {c_{CF}}} \right)$|⁠. The store incurs fixed costs of |${F_{NCF}},\,{F_{CF}}$| for providing non-cage-free eggs and cage-free eggs.

The store makes an additional profit based on non-egg products that consumers purchase once in the store, where |${Q_{ib}}$| is the total non-egg products per trip demanded. I assume |$B$| is the per-trip profit from non-egg products. The total profit on non-egg products is the total quantity demanded, |${Q_{ib}}$|⁠, multiplied by the per-trip profit. Quantities demanded, |${Q_{ib}}$|⁠, |${Q_{iCF}}$| and |${Q_{iNCF}}$| are functions of egg prices in both stores, |${p_{iCF}},{p_{ - iCF}},{p_{iNCF}},{p_{ - iNCF}}$|⁠, the availability of eggs, |$NC{F_i},C{F_i}$|⁠, consumer choices |$HNC{F_i},HC{F_i}$|⁠, and consumer preferences and distribution parameters |${\theta _c},t,\lambda ,\sigma $|⁠.¹⁰

where

3.2. Game and strategies

I examine the non-cooperative game where retailers offer only cage-free eggs or both cage-free and non-cage-free eggs.¹¹ I assume both stores will always offer cage-free eggs, which reduces the choice of stores to simply provide or not provide non-cage-free eggs. There are four possible strategies for each store. The strategies for store 1 are |$\left[ {NC{F_1} = 1,\,NC{F_2} = 1} \right]$|⁠, |$\left[ {NC{F_1} = 1,\,NC{F_2} = 0} \right],\,$|  |$\left[ {NC{F_1} = 0,\,NC{F_2} = 1} \right]$| and |$\left[ {NC{F_1} = 0,\,NC{F_2} = 0} \right]$|⁠, and the strategies for store 2 are |$\left[ {NC{F_2} = 1,\,NC{F_1} = 1} \right]$|⁠, |$\left[ {NC{F_2} = 1,\,NC{F_1} = 0} \right]\,$|⁠, |$\left[ {NC{F_2} = 0,\,NC{F_1} = 1} \right]$| and |$\left[ {NC{F_2} = 0,\,NC{F_1} = 0} \right]$|⁠. Table 1 presents the normal form of the game with the strategy profiles of store 1 and store 2 and the associated outcomes. Table 1 is also the pay-off matrix and shows the profit for both store 1 and store 2 in each of the four possible outcomes.

3.3. Solution

Next, I solve for the profits in the two-by-two game in Table 1. To reduce the complexity of the analysis and to make the model analytically tractable, I make two assumptions based on real-world practices of retailers.

3.3.1. Assumptions

Simplifying Assumption 1: Consumers only make one trip for shopping.

I assume |$t \gt e - {c_{NCF}}\,$|⁠. In other words, the value of eggs is not worth the cost of an extra trip to the other store. This assumption eliminates the possibility of consumers buying eggs at store 1 and the rest of goods, B, at store 2, and vice versa. While multistore shopping is common among some consumers, a large portion of consumers are one-trip shoppers and are the focus of retailers. This is also consistent with the modelling assumptions of Lal and Matutes (1994) and Johnson (2017). Moreover, recent studies have shown the one-trip shopper is the consumer that retailers target and set prices on (Thomassen et al., 2017).

Even among multistore shoppers, it is unlikely that these shoppers only purchase eggs during a shopping trip as 60 per cent of purchases are unplanned (Kollat and Willett, 1967; Park, Iyer and Daniel, 1989; Heilman, Nakamoto and Rao, 2002; Johnson, 2017). Even if multistore shoppers do not switch their entire baskets due to changing egg offerings, they can still be profitable for retailers to target.

Simplifying Assumption 2: Retailers price eggs at cost |${p_{iCF}} = {c_{CF}}$| and |${p_{iNCF}} = {c_{NCF}}$|⁠.

This assumption follows from Assumption 1 and is based on the multiproduct nature of food retailing. Lal and Matutes (1994) and Johnson (2017) provide models of loss leading, where some products are priced at cost or at low margins to attract consumers. This practice of loss leading is a well-known strategy in retailing, and eggs are often used as loss leaders. Hosken and Reiffen (2004) extend the Lal and Matutes model to show that more frequently purchased goods are selected as loss leaders, which is consistent with the perishability nature of eggs. Empirically, industry evidence supports the notion that eggs are low-margin items (Kilroy, MacKenzie and Manacek, 2016). Allender and Richards (2010b) also show that egg margins are below what would be expected if retailers were engaged in Nash–Betrand competition on eggs alone. I assume that eggs are a loss-leading good that stores aggressively price compete on by pricing at cost to draw in consumers.

This assumption allows me to abstract from (i) pricing competition on eggs and (ii) factoring in the profits of eggs into store profits. Introducing price competition into the model would be complex and distracts from the main goal of this article. As multiproduct firms, I would have to model egg prices and other background good prices as a bundle. Moreover, Ellickson (2006), Ellickson (2007) and Ellickson (2013) find that a lot of supermarket competition stems from quality competition, so I focus on modelling competition in strategic provisions.

I could potentially assume a small and fixed margin on eggs, but this would not significantly impact the conclusions. As a low-margin product, the profit margins on eggs likely pale in comparison to the profit margins of other goods in the basket.

Next, I define |${Q_{iN}} = {Q_{ib}} - {Q_{iNCF}} - {Q_{iCF}}$| or the total demand for basket goods from consumers who do not buy eggs. Applying the two assumptions, the store profit equation simplifies to:

After applying the two assumptions, stores make no profits on eggs and eggs are utilised as positive store amenities that draw in consumers in the model. Stores make profits from the other goods that consumers purchase once they come into the store, and the total profit depends on how many consumers come into the store.

3.3.2. Solution for Outcome D

I now solve for the profits of each store for each of the four outcomes in Table 1. I start with Outcome D. As consumers will only shop at one store and purchase one egg product (or no eggs), consumers essentially have six choices if both stores offer both cage-free and non-cage-free eggs as shown in Table 2.

Consumers can choose not to purchase any eggs and shop at either store 1 or 2, which results in choices 1 and 2, respectively. Shopping at stores 1 and 2 and purchasing cage-free eggs result in choices 3 and 4. Shopping at stores 1 and 2 and purchasing non-cage-free eggs result in choices 5 and 6.

Consumers with high preference have valuation such that |${\theta _h} \gt \,{c_{CF}} - {c_{NCF}}$|⁠, which implies |${\theta _h} \gt \,{c_{CF}} - e$|⁠.¹² This leads to |${\theta _h} + e \gt \,{c_{CF}}$| and |$\theta_h+e-c_{CF}\gt\,e-c_{NCF}$|¹³, which means that high preference consumers will buy cage-free eggs always if eggs are priced at marginal cost. These consumers are willing to buy cage-free eggs and value the cage-free attribute more than the additional cost of production, so they will always buy cage-free eggs. Since both stores offer identical products and are symmetrical, the consumers’ store choice depends on their location on the line. This is the standard Hotelling model (Hotelling, 1929), and the standard solution method results with an indifferent consumer at point |$\hat x$|⁠. Since the stores offer identical products, the two stores split the consumers with |$\hat x = \frac{1}{2}$| and |${Q_{iCF}} = \frac{1}{2}\,\left( {1 - \lambda - \sigma } \right)$|⁠. The total demand for cage-free eggs is half of the line multiplied by the share of consumers with high preference.

Consumers with switching preference have valuation |${c_{CF}} - {c_{NCF}} \gt {\theta _s} \gt \,{c_{CF}} - e$|⁠. This leads to |${\theta _s} + e \gt \,{c_{CF}}$| and |${\theta _s} + e - {c_{CF}} \lt \,e - {c_{NCF}}$|⁠, which means consumers are willing to buy cage-free eggs but value the cage-free attribute less than the marginal cost difference between cage-free and non-cage-free eggs. They will buy non-cage-free eggs when available and switch to cage-free when non-cage-free eggs are not available. Their store choice depends on their location on the line, and their store choice solution is like above with stores dividing up the line evenly.

Finally, consumers with low preference have valuation |${\theta _l} = 0$|⁠, which leads to |${\theta _l} = 0 \lt \,e - {c_{CF}}$|⁠. These consumers are not willing to buy cage-free eggs, but they will buy non-cage-free eggs. They will not buy eggs if only cage-free eggs are available. Their store choice depends on their location on the line, and their store choice solution is like above with stores dividing up the line evenly.

The total demand for non-cage-free eggs, |${Q_{iNCF}} = \frac{1}{2}\,\left( {\lambda + \sigma } \right)$|⁠, is half of the line multiplied by both the share of consumers with switching preference and the share of consumers with low preference. The profits for store 1 and store 2 are |$\pi _1^D = \pi _2^D = \left( {\frac{1}{2}\,\left( {\lambda + \sigma } \right) + \frac{1}{2}\,\left( {1 - \lambda - \sigma } \right)} \right)B - {F_{NCF}} - {F_{CF}}$|⁠, which simplifies to |$\pi _1^D = \pi _2^D = \left( {\frac{1}{2}\,} \right)B - {F_{NCF}} - {F_{CF}}$|⁠.

3.3.3. Solution for Outcome C

In this scenario, store 1 is no longer offering non-cage-free eggs. Compared to Outcome D, consumers only have five choices now as choice 5 is no longer available. The consumer utilities for each possible choice are listed in Table 3.

Since cage-free eggs are available at both locations, high-preference consumers still have their preferred options available and make the same choice as in Outcome D.

For consumers with switching preference to right of the midpoint, |$x \gt 1/2$|⁠, their preferred choice is not affected since they shop at store 2. Consumers with switching preference to left of the midpoint, |$x \lt 1/2$|⁠, shopped at store 1 when non-cage-free eggs were available at store 1. Some of these consumers are now willing to travel to store 2 since store 2 offers non-cage-free eggs and store 1 no longer does. However, at some point, the distance trade-off for these consumers becomes too great and they stay at store 1. For switching consumers, purchasing cage-free eggs at store 1 dominates the option of purchasing no eggs at store 1 as |${\theta _s} + e - \,{c_{CF}} \gt 0$|⁠. Thus, the best alternative options for these consumers are to either travel to store 2 or to purchase cage-free eggs at store 1 with the indifferent consumer located at:

Intuitively, the indifferent consumer is located at a point at which gains from buying non-cage-free eggs at a further away store are balanced by the additional travel cost. Consumers to the left of the new indifference point will continue shopping at store 1 but switch to cage-free eggs, and the rest will switch to store 2. In other words, for consumers who are relatively indifferent between stores 1 and 2, the additional provision of non-cage-free eggs at store 2 might tip the balance for them to switch their shopping at the other store.

Similar to the consumers above, some low-preference consumers will travel to store 2. Unlike switching consumers, low-preference consumers’ next best alternatives are travelling to store 2 or continuing shopping at store 1 and not purchasing eggs. Not purchasing eggs at store 1 strictly dominates purchasing cage-free eggs at store 1 as |${c_{CF}} \gt 0 + \,e$|⁠. The indifferent consumer is located at:

Similar to switching consumers, the indifferent consumer is located at a point at which gains from buying non-cage-free eggs at a further away store compared to not buying eggs are balanced by the additional travel cost. Consumers to the left of the new indifference point will continue to shop at store 1 but buy no eggs.

The total demand for cage-free eggs becomes |${Q_{1CF}} = \left( {\frac{1}{2} + \frac{{{\theta _s} - {c_{CF}} + {c_{NCF}}}}{{2t}}} \right)\lambda $|⁠, and the demand of shoppers with no egg purchases is |${Q_{1N}} = \left( {\frac{1}{2} + \frac{{{c_{NCF}} - e}}{{2t}}} \right)\sigma $|⁠. For store 2, the demands are |${Q_{2NCF}} = \left( {\frac{1}{2} - \frac{{{\theta _s} - {c_{CF}} + {c_{NCF}}}}{{2t}}} \right)\lambda $| and |${Q_{2N}} = \left( {\frac{1}{2} - \frac{{{c_{NCF}} - e}}{{2t}}} \right)\sigma $|⁠. I note that |${\theta _s} - {c_{CF}} + {c_{NCF}} \lt 0\,$| and |${c_{NCF}} - e \lt 0$|⁠, so store 1 loses consumers to store 2 by not providing non-cage-free eggs. The profit for store 1 is |$\pi _1^C = B\left( {\frac{1}{2} + \frac{{{\theta _s} - {c_{CF}} + {c_{NCF}}}}{{2t}}\lambda + \frac{{{c_{NCF}} - e}}{{2t}}\sigma } \right) - {\rm{\,}}{F_{CF}}$|⁠. The profit for store 2 is |$\pi _2^C = B\left( {\frac{1}{2} - \frac{{{\theta _s} - {c_{CF}} + {c_{NCF}}}}{{2t}}\lambda - \frac{{{c_{NCF}} - e}}{{2t}}\sigma } \right) - {\rm{\,}}{F_{CF}} - {F_{NCF}}$|⁠.

3.3.4. Solution for Outcome B

Outcome B is a mirror situation of Outcome C with profits a mirror of Outcome C. The consumer utilities for each possible choice are listed in Table 4.

The profit for store 1 is |$\pi _1^B = B\left( {\frac{1}{2} - \frac{{{\theta _s} - {c_{CF}} + {c_{NCF}}}}{{2t}}\lambda - \frac{{{c_{NCF}} - e}}{{2t}}\sigma } \right) - {\rm{\,}}{F_{CF}} - {F_{NCF}}$|⁠. The profit for store 2 is |$\pi _2^B = B\left( {\frac{1}{2} + \frac{{{\theta _s} - {c_{CF}} + {c_{NCF}}}}{{2t}}\lambda + \frac{{{c_{NCF}} - e}}{{2t}}\sigma } \right) - {\rm{\,}}{F_{CF}}$|⁠.

3.4.5. Solution for Outcome A

Consumers only have four choices now as choices 5 and 6 are no longer available as seen in Table 5.

Cage-free eggs are available at both locations. High-preference consumers still have their preferred options available and make the same choice as Outcome D.

For consumers with switching preference, the decision for store choice goes back to Outcome D as neither store offers non-cage-free eggs. However, these consumers switch to cage-free eggs. Similarly, low-preference consumers also shop at the same stores as in Outcome D but purchase no eggs. The profits for store 1 and store 2 are |$\pi _1^A = \pi _2^A = \frac{1}{2}B - {F_{CF}}$|⁠.

In Table 6, I plugged in solved profits for each outcome in Table 1.

For ease of reading, I define |$\alpha = - \left( {\frac{{{\theta _s} - {c_{CF}} + {c_{NCF}}}}{{2t}}\lambda + \frac{{{c_{NCF}} - e}}{{2t}}\sigma } \right)$|⁠. Since Outcome D is the status quo, I normalise profits for Outcomes A, B, and C in relationship to Outcome D by setting the Outcome D profits to zero in Table 7. The pay-offs in Table 7 show a straightforward two-by-two game.

3.4. Nash equilibrium

Assumption 3:

|$B\left( { - \frac{{{\theta _s} - {c_{CF}} + {c_{NCF}}}}{{2t}}\lambda - \frac{{{c_{NCF}} - e}}{{2t}}\sigma } \right) \gt {F_{NCF}}$|

The term |$B\left( {\frac{{{\theta _s} - {c_{CF}} + {c_{NCF}}}}{{2t}}\lambda + \frac{{{c_{NCF}} - e}}{{2t}}\sigma } \right)$| represents the sales stealing effect of attracting consumers from a rival store by providing non-cage-free eggs. Stealing also comes at the cost |${F_{NCF}}$|⁠. This assumption implies that the potential profit from stealing consumers to your store by providing non-cage-free eggs is larger than the fixed cost of providing the eggs. If this assumption were not true, then both stores would only ever offer cage-free eggs. However, as most retailers offer non-cage-free eggs (at least before 2016), I assume that this assumption is true.¹⁴

Proposition 1:

The Nash equilibrium outcome is Outcome D, where both stores provide both kinds of eggs and each receives profit, |$\pi _1^D = \pi _2^D = \left( {\frac{1}{2}\,} \right)B - {F_{NCF}} - {F_{CF}}$|⁠.

Proof:

With Assumption 3, the pay-offs in Table 7 show a straightforward two-by-two game. If the game is one shot, both store 1 and store 2’s dominant strategy is to provide both eggs. For store 1, if store 2 only provides cage-free eggs (⁠|$NC{F_2} = 0)$|⁠, then store 1 can gain profits of |$B\alpha - {F_{NCF}}$| by providing cage-free eggs. If store 2 provides both (⁠|$NC{F_2} = 1)$|⁠, then store 1 can again gain profits of |$B\alpha - {F_{NCF}}$| by providing cage-free eggs. A similar analysis is true for store 2. As the dominant strategy for both stores is to provide both types of eggs, the Nash equilibrium outcome is Outcome D, where both stores provide both kinds of eggs.

This is the prisoners’ dilemma result as the Nash Equilibrium outcome in Outcome D is worse for both stores than Outcome A. Both stores gain profits of |${F_{NCF}}$| in Outcome A compared to profits in Outcome D. With higher profits, Outcome A is the likely outcome that would result if the stores could cooperate.¹⁵ However, Outcome A is unsustainable under competition because there are strong economic incentives for stores to deviate and ‘steal’ consumers from each other by offering non-cage-free eggs.

3.5. Dynamic game setting and solution

In the one-shot game above, both stores’ dominant strategy is to provide non-cage-free eggs, which results in an equilibrium that is worse off for both stores. However, the equilibrium outcome could be different in a dynamic setting as first noted by Stigler (1964). Retailers often compete for a long period of time, and provision decisions are often strategic for the long run. I extend the one-shot game of Table 7 into infinite periods where stores play a repeating dynamic game similar to Rotemberg and Saloner (1986).

In terms of equilibrium outcomes, one of the most obvious and easily supported SPNE is Outcome D for infinite periods where retailers aggressively compete by offering both cage-free and non-cage-free eggs every period. However, in an infinitely repeated game, the Folk Theorem shows a variety of strategies that can sustain the cooperative equilibrium depending on the discount rate. I examine a game where both stores are playing a strategy with the harshest punishment, the grim trigger, and I solve for possible SPNEs.¹⁶

Proposition 2:

If both stores are playing grim trigger strategies, cooperative Outcome A is sustainable if the discount rate for each store is as follows:

Each store receives a profit of |$\pi _1^A = \pi _2^A = \frac{1}{2}B - {F_{CF}}$|⁠.

Proof:

I assume that stores have a discount rate of |$\delta $| for profit received in the next period. Following Table 7, both stores receive profits of |${F_{NCF}}$| each period for the cooperative Outcome A. For infinite periods, total profits become |$\frac{{{F_{NCF}}}}{{1 - \delta }}\,$| as shown in the series summation across periods.

With a grim trigger strategy, if store 1 deviates, the grim trigger is applied in the next period, and everything collapses to Outcome D forever. The ‘sales stealing’ strategy of deviating from Outcome B receives a total pay-off of |$\left( { - \frac{{{\theta _s} - {c_{CF}} + {c_{NCF}}}}{{2t}}\lambda - \frac{{{c_{NCF}} - e}}{{2t}}\sigma } \right)$| as store 1 receives 0 normalised profit after period 1.

As such, the cooperative equilibrium is sustainable if |$\frac{{{F_{NCF}}}}{{1 - \delta }}\, \ge \,$||$\left( { - \frac{{{\theta _s} - {c_{CF}} + {c_{NCF}}}}{{2t}}\lambda - \frac{{{c_{NCF}} - e}}{{2t}}\sigma } \right)$|⁠. A symmetric argument can be made for store 2. Setting up the inequalities shows that if the discount rate is high enough, then a cooperative outcome can be sustained and no stores have incentives to cheat.

If I assume the threshold to be |${\delta ^*}$|⁠, I can show that the critical discount rate to sustain a cooperative outcome is a function of the fixed cost of providing non-cage-free eggs, the marginal costs and consumer demand parameters.

4. Comparative Statics

With the discount rate threshold as a function of underlying cost parameters and consumer preferences, I examine some comparative statics. The results of taking the derivative of |${\delta ^*}$| with respect to |${F_{NCF}}$|⁠, |${c_{NCF}}$| and |${c_{CF}}$| are listed below.

4.1. Comparative Static 1

First, I show that |$\frac{{\partial {\delta ^*}{\rm{\,}}}}{{\partial {F_{NCF}}}} \lt 0$| or as the fixed cost of sourcing non-cage-free eggs goes up, the discount rate needed to sustain a cooperative outcome goes down. In the context of recent events, as state bans on non-cage-free egg production were passed, retailers probably expected sourcing of non-cage-free eggs would become harder and more expensive.

4.2. Comparative Static 2

Second, I show that |$\frac{{\partial {\delta ^*}{\rm{\,}}}}{{\partial {C_{NCF}}}} \lt 0$| or as the marginal cost of non-cage-free eggs goes up, the discount rate needed to sustain a cooperative outcome goes down. Intuitively, non-cage-free egg-purchasing consumers (either switchers or low preference) are less likely to switch their stores to purchase non-cage-free eggs if the prices of non-cage-free eggs are higher. As more producers switch to cage-free operations, there are likely lost economies of scale, and the marginal cost of non-cage-free eggs could go up.

4.3. Comparative Static 3

Finally, I show that |$\frac{{\partial {\delta ^*}{\rm{\,}}}}{{{c_{CF}}}} \gt 0$| or as the marginal cost of cage-free eggs goes down, the discount rate needed to sustain a cooperative outcome goes down. Retailers probably also expected the marginal cost of cage-free eggs to go down due to economies of scale with more producers starting to produce cage-free eggs.

Next, I examine how changing consumer preferences changes the threshold needed to reach a cooperative equilibrium.

4.4. Comparative Static 4

As the share of consumers that purchase non-cage-free eggs goes down, the threshold needed to reach a cooperative equilibrium also goes down, |$\frac{{\partial {\delta ^*}{\rm{\,}}}}{{\partial \lambda }} \gt 0$|⁠, |$\frac{{\partial {\delta ^*}{\rm{\,}}}}{{\partial \sigma }} \gt 0$|⁠. Intuitively, as the share of consumers that purchase non-cage-free eggs goes down, the profit gain of stealing those consumers goes down, which reduces the incentive to deviate.

4.5. Comparative Static 5

Similarly, as the valuation for the cage-free attribute of switching consumers goes up, the threshold needed to reach a cooperative equilibrium also goes down, |$\frac{{\partial {\delta ^*}{\rm{\,}}}}{{\partial {\theta _s}}} \lt 0$|⁠. Intuitively, as the valuation for the cage-free attribute goes up, switching consumers are less likely to switch to non-cage-free eggs at a rival store, which reduces the incentive to deviate.

4.6. Comparative static summary

In summary, |$\frac{{\partial {\delta ^*}{\rm{\,}}}}{{\partial {F_{NCF}}}} \lt 0$|⁠, |$\frac{{\partial {\delta ^*}{\rm{\,}}}}{{\partial {C_{NCF}}}} \lt 0$|⁠, |$\frac{{\partial {\delta ^*}{\rm{\,}}}}{{{c_{CF}}}} \gt 0$|⁠, |$\frac{{\partial {\delta ^*}{\rm{\,}}}}{{\partial \lambda }} \gt 0$|⁠, |$\frac{{\partial {\delta ^*}{\rm{\,}}}}{{\partial \sigma }} \gt 0$| and |$\frac{{\partial {\delta ^*}{\rm{\,}}}}{{\partial {\theta _s}}} \lt 0$|⁠. These comparative statics all predict that recent consumer trends and supply-side changes surrounding cage-free eggs are conducive for a cooperative outcome to emerge. On the supply side, the state bans will likely make the fixed cost and marginal cost of non-cage-free eggs to go up and the marginal cost of cage-free eggs to go down. On the consumer side, as both the share of consumers that value cage-free goes up and consumers increase their valuation of the cage-free attribute, the incentives for retailers to offer non-cage-free eggs go down even though a significant number of consumers still value non-cage-free eggs.

With supply and demand conditions reaching a point where a cooperative equilibrium is sustainable, the pledges made by retailers served as an easy and costless form of communication of their intent to transition to an equilibrium where only cage-free eggs are offered.

I also note that there is the possibility that the changes in supply and demand around 2016 could make |$B\left( { - \frac{{{\theta _s} - {c_{CF}} + {c_{NCF}}}}{{2t}}\lambda - \frac{{{c_{NCF}} - e}}{{2t}}\sigma } \right) \lt {F_{NCF}}$| (see Assumption 3), which would mean that Outcome A is a sustainable equilibrium even in a one-shot game with no tacit coordination required.¹⁷

5. Welfare

While the cooperative equilibrium in Outcome A is better off for retailers, sole provision of cage-free eggs leads to welfare loss for consumers. I show that non-cage-free egg-purchasing consumers are forced to substitute to a less preferred option under the cooperative equilibrium, which is the mechanism captured by recent empirical studies that show consumer welfare loss due to the cage-free transition (Allender and Richards, 2010a; Lusk, 2019; Sohae Eve and Vukina, 2022). For switching consumers in my model, the utility loss is the utility difference between the more preferred non-cage-free eggs compared to cage-free eggs, which is |${\theta _s} - {c_{CF}} + {c_{NCF}}$|⁠. For low preference consumers, the utility loss is the utility of eggs |${c_{NCF}} - e$| as these consumers stop buying. The total consumer welfare loss is |$CS = \,\left( {{\theta _s} - {c_{CF}} + {c_{NCF}}} \right){\rm{\,}}\lambda + \left( {{c_{NCF}} - e} \right)\sigma $| if retailers only offer cage-free eggs. Retailers do gain |${F_{NCF}}$| individually in terms of provision cost savings with total retailer surplus gains at |$2{F_{NCF}}$|⁠.

My model assumes consumers have unit demand for egg products, which assumes consumers do not vary the quantity of eggs purchased or mix and match between egg products. While the unit demand functional form is not well suited for robust welfare estimation, it can provide a general sense of which groups of consumers and retailers are relatively better off or worse off in different outcomes. I show that the cooperative equilibrium of pledges increases retailer profits at the expense of consumer welfare.

6. Conclusion and discussion

With the growth of food retail concentration at the national and local levels, retailers have become more important in dictating supply chain standards upstream (MacDonald, Dong and Fuglie, 2023; Saitone and Sexton, 2017). As Caputo et al. (2023b) discusses, much of the producer transition to cage-free eggs has been a result of retailers’ decision to source only cage-free eggs. With the influence that retailers can have on producers and consumers, examination of retailer decision-making is critical for understanding the supply chain impacts of changing consumer perception surrounding animal welfare and associated changes in policy.

Modern food retailers are multiproduct firms that employ complex competitive strategies including competition among price and variety across many product categories. Any examination of store egg provision decisions needs to be considered in the context of overall store profits.

I provide a simple theoretical model of retail competition that examines one potential reason of why retailers voluntarily pledged to only provide cage-free eggs at potential detriment to their profits. I abstract from price competition but include variety competition as a key strategy of drawing consumers to stores. I show that retailers are better off only providing cage-free eggs to save on sourcing costs but defaulted to providing both non-cage-free and cage-free eggs in equilibrium due to competitive pressure. However, in a dynamic setting, I show the outcome of retailers only providing cage-free eggs is possible even under competitive pressure. The sustainability of such an outcome becomes more likely as sourcing costs and marginal cost of non-cage-free eggs increase and marginal cost of cage-free eggs decreases. My model shows that the recent state bans and changing consumer trends around eggs likely facilitated the only cage-free eggs outcome.

My model is much more abstract and simpler than the actual complexities of food retail competition, which features numerous retailers disparate in size competing against each other. Moreover, food retail competition is typically local with some national retailers choosing to have stores in many local areas across the country and some regional retailers only placing stores in select areas. Furthermore, retailers often negotiate with egg suppliers, which complicates the exogenous constant marginal cost assumption. Nash bargaining frameworks and other cooperative game theory models are often used to analyse how costs are set between retailers and suppliers. Many of these factors along with other considerations such as brand image can undoubtedly influence retailers’ decision-making surrounding cage-free eggs.

While my model looks at the case of two competing symmetric stores under simplifying assumptions, it attempts to examine how provision considerations and tacit coordination can potentially enter into retailers’ decision-making processes under imperfect oligopolistic competition conditions. The outcomes predicted by the model could vary once more complex factors are incorporated. However, the insight of pledges could be due to tacit coordination under imperfect competition in retail, and the insights on the resulting positive or negative welfare impacts to consumers and retailers are likely to hold true. Hopefully, the economic incentives distilled from this simple model can provide some insights on one potential economic motive on why retailers engaged in these cage-free pledges.

This model can potentially be extended into examining the firm level motives behind other voluntary pledges in the food industry surrounding animal welfare products and other products in general as variety provisions also play an important role for competition among food manufacturers (Schmalensee, 1978). Moreover, I show that the importance of examining and modelling tacit coordination in retail competition.

Footnotes

References

Author notes