Finally, the behavior of the government, through the Food Reserve Agency (FRA), strongly affects market outcomes. In shortage years the FRA imports maize in competition with the private sector. It can thus be interpreted as an additional big trader on the market. In contrast to the private traders, the government is not a profit-maximizer, but is assumed to pursue a political agenda aimed at re-election. To gain popular support from consumers the government prefers to keep consumer prices low. On the other hand, since many households in Zambia are small maize farmers, the government also has an interest in high producer prices. This set of goals essentially conflicts with that of traders as discussed later.

# **3.2 The consumer market**

The core model is a Cournot oligopoly game. In this model suppliers choose their quantities and the price is determined by the market. The model is appropriate for a basic agricultural product with a high degree of product homogeneity. Further, it has very natural predictions for the market outcome. It reacts smoothly to small changes in the traders’ behavior, and changes in the competitive environment leads to the expected change in market outcome (e.g. an increase in the number of firms results in lower prices and profits). These desirable properties have been reproduced empirically in a plethora of experimental studies (Huck, Normann and Oechssler 1999, 2004, Huck, Müller, and Normann 2001, Offerman, Potters, and Sonnemans 2002).

Traders face a downward-sloping demand function, where the consumer price, _P_<sup>_C_</sup> , is a decreasing function of the total quantity supplied by the market. For simplicity, a linear demand function is assumed with the inverse form:<sup>7</sup> where _Q=Σqi_ is the total quantity supplied by the _n_ traders, _G_ is the government quantity and _S_ is the baseline supply offered by small traders. Exogenous parameters _a_ and _b_ specify intercept and slope of the demand function, respectively. As mentioned, the suppliers on the consumer market consist of four big traders and a large number of small traders. The small traders are price takers with a capacity constraint (i.e. they do not import). They jointly supply a fixed quantity _S_ , which they sell irrespective of the market price, without strategic considerations.

Each trader faces constant marginal costs, _c_ . For simplicity, marginal costs are assumed identical to the producer price (the price that the farmers receive), assuming other costs (notably transport costs) to be constant and thus not affecting optimal choices. Note that this assumption implies that traders have the same cost structure, since the producer price is the same for all.<sup>8</sup>

> 7 Empirical estimates often yield a relatively constant demand elasticity over the relevant range of market outcomes. This invites the use of a constant elasticity demand function of the form _p=Q_<sup>η</sup> .  Estimations of such demand functions turned out to have very undesirable properties in a strategic market model.  In extreme cases they lead to corner equilibria, in which firms would optimally sell one grain of maize at an infinite price.  The reason is that one cannot expect the constant elasticity assumption to hold over the entire price range, including those prices not empirically observed.  In a strategic model, however, the unobserved range can affect the equilibria dramatically and this augers against the use of this functional form in the present context.

> 8 Note that, although intuitive, this model of price determination of the maize market is an approximation.  In reality, the government announces consumer and producer prices at the start of the season and is at liberty to change this price later in the season or cease purchasing at any time depending on its rate of intake and in light of changes in market conditions.

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