Bertrand and Cournot Competition Under Asymmetric Costs: Number of Active Firms in Equilibrium

Abstract

We compare the number of active firms, i.e. the number of firms producing a positive quantity, in equilibrium across four different models of oligopoly. The two main models are Cournot where quantity is the strategic variable and prices are determined by the market, and Bertrand where price is the strategic variable and demands are determined by the market. Within each of these models, we also have two types of goods: homogeneous and differentiated. We concentrate on the linear demand structure with constant marginal costs. We find that within a fixed class of good, either homogeneous or differentiated, Cournot always results in more active firms in equilibrium than Bertrand. Moreover, we find that within a fixed type of market, Cournot or Bertrand, differentiated goods result in more active firms in equilibrium than homogeneous goods. These results depend crucially on cost asymmetries between the firms, as with symmetric costs the results trivialize to all firms active or all firms inactive. Many studies have shown that consumer welfare is generally higher under Bertrand than Cournot. Our result can be seen as explaining this as consumers have more choice in Cournot markets at the expense of lower welfare, whereas they have less choice in Bertrand markets (as the number of firms in equilibrium is less) but they are compensated for this fact by reduced prices and therefore higher welfare.