Economic growth and economic development 561

Introduction to Modern Economic Growth that the equilibrium price will be pN = ψ, where the superscript N denotes “no innovation” Total quantity demanded will be D (ψ) > and can be distributed among the N firms in any arbitrary fashion Since price is equal to marginal cost, the profits of firm in this equilibrium will be = πN ¡ N ¢ p − ψ q1N = 0, where q1N denotes the amount supplied by this firm Now imagine that firm innovates, but because of non-excludability, the innovation can be used by all the other firms in the industry The same reasoning implies that the equilibrium price will be pI = λ−1 ψ, and total quantity supplied by all the ¢ ¡ firms will equal D λ−1 ψ > D (ψ) Then, the net profits from will be π I1 = ¡ I ¢ p − λ−1 ψ q1I − µ = −µ < Therefore, if it undertakes the innovation, firm will lose money The reason for this is simple The firm incurs the cost of innovation, η, but because the knowledge generated by the innovation is non-excludable, it is unable to appropriate any of the gains from innovation This simple example underlies a claim dating back to Schumpeter that pure competition will not generate innovation Clearly, this outcome is potentially very inefficient For example, µ could be arbitrarily small (but still positive), while λ, the gain from innovation, can be arbitrarily large, and the equilibrium would still involve no innovation For future reference, let us calculate the social value of innovation, which is the additional gain resulting from innovation A natural measure of social value is in the sum of the consumer and producer surpluses generated from the innovation Presuming that after innovation, the good will be priced at marginal cost, this social value is Z ψ I (12.1) D (p) dp − µ S = λ−1 ψ ψ = Z λ−1 ψ [D (p) − D (ψ)] dp + D (ψ) ψ 547 λ−1 − µ λ