put and industry output, both at the long-run Cournot-Nash equilibrium are denoted, respectively, by $ q^{N}(n_{e}) $ and $ Q^{N}(n_{e}) $ , where $ n_{e} $ denotes the number of firms in the long-run Cournot-Nash equilibrium. It is clear that $ Q^{N}(n_{e}) = n_{e}q^{N}(n_{e}) $ . To verify these facts, we have only to notice that the marginal cost curve crosses the marginal revenue curve, derived from the residual demand curve $ R^{N}R^{N} $ , at $ q^{N}(n_{e}) $ and profits at $ q^{N}(n_{e}) $ are exactly zero.

Suppose that the number of competing firms is lowered marginally from $ n_{e} $ to n. Since fewer firms are now sharing the same market demand curve, the residual demand curve for an individual firm must shift up to $ R^{S}R^{S} $ , so that the new Cournot-Nash equilibrium, denoted by $ q^{N}(n) $ and $ Q^{N}(n):=n q^{N}(n) $ , must satisfy $ q^{N}(n_{e})Q^{N}(n) $ . It is clear that this decrease in the number of firms from $ n_{e} $ to n must exert two conflicting effects on welfare, which is measured in terms of the net market surplus, viz. the sum of consumer's surplus and the producer's surplus. The first is its effect on the allocative efficiency due to the concomitant decrease in consumer's surplus, which results from the increase in equilibrium price from $ p^{N}(n_{e}) $ to $ p^{N}(n) $ . In Figure I, this negative effect is measured by the area $ Ap^{N}(n)p^{N}(n_{e})B $ . The second is its effect on the production efficiency due to the further exploitation of residual scale economies, which results from the induced increase in individual equilibrium output from $ q^{N}(n_{e}) $ to $ q^{N}(n) $ . In Figure I, this positive effect is measured by the area $ Ap^{N}(n)c^{N}(n)D $ . The net effect on social welfare is given by the difference between these two effects, viz., the area $ Cp^{N}(n_{e})c^{N}(n)D $ less the area ABC. Because the latter area must be a higher order infinitesimal than the former area, the net effect turns out to be positive, vindicating that a marginal decrease in the number of firms increases welfare. In other words, the long-run Cournot-Nash equilibrium number of firms, $ n_{e} $ , is socially excessive at the margin. Although this theorem is verified in this paper by means of a simple geometric device, a full analytical proof is available, e.g., in Kotaro Suzumura and Kazuharu Kiyono (1987), whereas several generalizations of the excess entry theorem are presented in Masahiro Okuno-Fujiwara and Kotaro Suzumura (1993), and Kotaro Suzumura (1995).

Contrary to the first conventional belief widely held among orthodox economists, we have thus demonstrated that there is a clear welfare-theoretic sense in which competition can be socially excessive. As a corollary to this proposition, we must be ready to admit in principle that the “regulation by enlightened, but not omnipotent, regulators could in principle achieve greater efficiency than deregulation [Panzer (1980, p.313)].” Note, however, that this observation, which is valid in itself, does not offhandedly justify that the second conventional belief should be supported in rejection of the first conventional belief. In other words, the excess entry theorem at the margin does not necessarily provide a rationalization of the actual interven-