Consider an industry with a homogeneous product where firms set output (or capacity) levels and price is determined by total output (or capacity). Suppose there is a large number of potential entrants and that each firm can choose one of two possible technologies, with cost functions Ci = Fi + ci qi (i = 1, 2).

(a) Derive the conditions for a free-entry equilibrium.

(b) Show, by means of a numerical example, that there can be more than one equilibrium, with different numbers of large and small firms.

10.13. ALTERNATIVE PRODUCTION TECHNOLOGIES. Consider an industry with a homogeneous product where firms set output (or capacity) levels and price is determined by total output (or capacity). Suppose there is a large number of potential entrants and that each firm can choose one of two possible technologies, with cost functions C; = F; + c; q; (i = 1, 2). (a) Derive the conditions for a free-entry equilib rium. (b) Show, by means of a numerical example, that there can be more than one equilibrium, with different numbers of large and small firms