Consumer-owned retail cooperative in duopoly with horizontally differentiated goods: a Finnish experience

Abstract

In this thesis I analyze the prevailing market structure and a peculiarity of the Finnish grocery retail trade. The market structure resembles duopoly. The two biggest retailers, S-group and K-group, have market shares of 43 and 34 per cent, respectively. Grocery retail trade is exceptionally concentrated in Finland although other Nordic countries also have a concentrated market. The peculiarity of the Finnish market is that the market leader, S-group, is not a profit-maximizing firm but a consumer-owned cooperative. Instead of shareholders the group has 1.8 million member-owners. I formulate and analyze the Nash equilibrium of a duopoly with a cooperative and a profit-maximizing firm (mixed duopoly). I also compare the resulting equilibrium to the Nash equilibrium of a duopoly with two profit-maximizing firms (normal duopoly).

I perform the analysis by constructing a duopoly model with horizontally differentiated goods using a framework developed by Singh and Vives (1984). I also build on the work of Anderson et al (1979) and Ireland and Law (1983). In the basic model employed in this thesis, firms are assumed to compete in price (Bertrand competition) and all consumers are assumed to be homogenous members of the cooperative. However, after analyzing this basic model I separately consider how equilibrium changes if the cooperative were a Stackelberg leader and if an exogenous part of consumers were not part of the cooperative.

The cooperative chooses to price at marginal cost in the Nash equilibrium of mixed duopoly. This is significant because in normal duopoly firms use market power to sustain above marginal cost pricing. The cooperative’s competitor, a profit-maximizing firm, can still sustain above marginal cost pricing in mixed duopoly but less so than would be possible in normal duopoly. In Stackelberg competition the cooperative chooses to price below marginal cost. If some consumers are not members of the cooperative the firms charge different prices due to different reaction curves with the cooperative having the higher price.

The willingness of consumers to substitute one good for the other and their value for variety is measured in the model by parameter gamma. A high level of gamma means that consumers are ready to substitute one good with the other and that they do not value consuming variety. In normal duopoly consumer utility is the higher the higher gamma is. In mixed duopoly utility is highest if gamma is low. The difference is explained by the effect of gamma on pricing power, which is not important in mixed duopoly where the cooperative already restricts the use of pricing power.

If consumers are faced with a choice between normal and mixed duopoly, they are better off choosing mixed duopoly since the cooperative reduces the adverse effects of duopoly. This result has implications on how one should approach the current market structure in Finland since the model’s theoretical cooperative has much in common with actual S-group behavior.