《工业组织》（英文版）monopoly power 2

Proposition: The H index emerges within an oligopoly odel as an endogenously determined,by the degree of collusion the number f firms and the distribution of costs, iable Clarke, Davies (1982)model From last lecture the profit maximizing condition was written (1+λ,) Set dQ a o. for all j=1 and for all 1 0≤αs1.Asα( the degree of implicit collusion) tends to1 we tend to perfect collusion (joint profit maximization)and as it tends to o we tend to the Cournot case. So, d (1/S;) Substitutiting (2)into (1) 3) Summing over the N firms in the industry and solving for price gives

P=DMC, nIN(m-a)-(1-a)] Substituting this into (3),which is then squared and summed gives /N)+1-N where Cv is the coefficient of variation of marginal costs across firms So the level of concentration depends on the degree 'of collusion within the industry (conduct), the number of firms and the distribution of costs. The intuition behind this result is that for a given set of demand and cost curves, the largest firms tend to benefit more from the collusive restriction of output, and thereby size inequalities are further increased (provided N is constant)