Technical Appendix to “A Gap for Me: Entrepreneurs and Entry” Volker Nocke University of Pennsylvania October 1, 2005 The Cournot Model with Heterogeneous Firms. Here, we show that our assumptions on the reduced-form profit function SΠ(c; h(µ)) are satisfied in a homogenous goods Cournot model, where firms differ in their (constant) marginal costs. We will be interested in the properties of extremal Cournot equilibria (i.e., of the equilibria with the smallest and largest industry output); see Vives (1999). There is a population of N active firms. Firm i’s (constant) marginal cost is denoted by c i . An increase in market size means a replication of the population of consumers (leaving the dis- tribution of consumers’ tastes and incomes unchanged), so that inverse demand P (X) depends only on the ratio X = Q/S between aggregate output Q and market size S. Throughout, we make the following smoothness assumption: (A) P (·) is twice differentiable and P 0 (·) < 0. We claim that, in any extremal Cournot equilibrium, each firm’s output and profit are proportional to market size S. Consequently, equilibrium price is independent of market size. To see this, note that firm i’s first-order condition for profit maximization is given by P µ P j q j S ¶ − c + q i S P 0 µ P j q j S ¶ =0, (1) where q j is firm j ’s quantity. Since output and market size enter only through the ratio q j /S, this ratio must be independent of market size in any (extremal) equilibrium. Hence, the equilibrium gross profit of a firm with marginal cost c can be written as SΠ(c; Q/S), where equilibrium industry output Q is a function of the vector of marginal costs c ≡ (c 1 ,c 2 , ..., c N ), and is proportional to market size, Q = S · h(c). Any change in the underly- ing distribution of marginal costs that increases equilibrium industry output Q can be thought of representing an increase in the intensity of competition h(c). (Below, we will verify that an increase in Q does indeed reduce the gross profit of any firm with positive output.) To simplify notation, we will henceforth set S =1, and analyze the properties of Π(c; Q). The assumptions on the reduced-form profit function in the main text involve two types of profit comparisons: (i) holding fixed the distribution of marginal costs (i.e., for any given equilibrium), we compare the profit of firms with different marginal costs; and (ii) we compare the profit of different firms with variations in the distribution of marginal costs (i.e., across 1