References and Literature

The literature on R&D in industrial organization is vast, and our purpose in this chapter has not been to review this literature, but to highlight the salient features that will be used in the remainder of the book.

which we will encounter in Section 14.4 in Chapter 14. A more up-to-date reference that surveys the recent developments in the economics of innovation is Scotchmer (2005).

The classic reference on the private and social values of innovation is Arrow (1962). Schumpeter (1943) was the first to emphasize the role of monopoly in R&D and innovation. The importance of monopoly power for innovation and the indications of the non-rival nature of ideas are discussed in Romer (1990, 1993) and Jones (2006). Most of the industrial or­ganization literature also emphasizes the importance of ex post monopoly power and patent systems in providing incentives for innovation. See, for example, Scotchmer (2005). This perspective has recently been criticized by Boldrin and Levine (2003).

The idea of creative destruction was also originally developed by Schumpeter. Models of creative destruction in the industrial organization literature include Reinganum (1983, 1985). Similar models in the growth literature are developed in Aghion and Howitt (1992, 1998).

Chamberlin (1933) is the classic reference on monopolistic competition. The Dixit-Stiglitz model is developed in Dixit and Stiglitz (1977) and is also closely related to Spence (1976). This model was first used for an analysis of R&D in Dasgupta and Stiglitz (1979). An excellent exposition of the Dixit-Stiglitz model is provided in Matsuyama (1995).

An excellent general discussion of issues of innovation and the importance of market size and profit incentives is provided in Schmookler (1966). Recent evidence on the effect of market size and profit incentives on innovation is discussed in Popp (2002), Finkelstein (2003) and Acemoglu and Linn (2004).

Mokyr (1990) contains an excellent history of innovation. Freeman (1982) also provides a survey of the qualitative literature on innovation and discusses the different types of inno­vations.

In this chapter and the rest of this part of the book, we will deal with monopolistic environments, where the appropriate equilibrium concept is not the competitive equilibrium, but one that incorporates game-theoretic interactions. Throughout the games we will study in this book will have complete information, thus the appropriate notion of equilibrium is the standard Nash equilibrium concept or when the game is multi-stage or dynamic, it is the subgame perfect Nash equilibrium. In these situations, equilibrium always refers to a Nash equilibrium or a subgame perfect Nash equilibrium, and we typically do not add the additional “Nash” qualification. We presume that the reader is familiar with these concepts. A quick introduction to the necessary game theory is provided in the Appendix of Tirole (1990), and a more detailed treatment can be found in Fudenberg and Tirole (1994), Myerson (1995) and Osborne on Rubinstein (1994).

policy is licensing, where firms that have made an innovation can license the rights to use this innovation to others. This exercise asks you to work through the implications of this type of licensing. Throughout, we think of the licensing stage as follows: the innovator can make a take-it-or-leave-it-offer to one or many firms so that they can buy the rights to use the innovation (and produce as many units of the output as they like) in return for some licensing fee ν.

(1) Consider the competitive environment we started with and show that if firm 1 is allowed to license its innovation to others, this can never raise its profits and it can never increase its incentives to undertake the innovation. Provide an intuition for this result.

(2) Now modify the model, so that each firm has a strictly convex and increasing cost of producing,, and also has to pay a fixed cost ofto be active (so that the average costs take the familiar inverse U shape). Show that licensing can be beneficial for firm 1 in this case and therefore increase incentives to undertake the innovation. Explain why the results differ between the two cases.

Exercise 12.10. Derive the expression for the ideal price index, (12.11), from (12.10) and the definition of the consumption index C.

Exercise 12.11. Consider the maximization problem in (12.13) and write down the first- order conditions taking into account the impact of pi on P and C. Show that as N → ∞, the solution to this problem converges to (12.14).

Exercise 12.12. In the Dixit-Stiglitz model, determine the conditions on the function v (∙) such that an increase in N raises the profits of a monopolist.

Exercise 12.13. Suppose thatwith α ∈

(0,1). Suppose also that new varieties can be introduced at the fixed cost μ.

(1) Consider the allocation determined by a social planner also controlling prices. Char­acterize the number of varieties that a social planner would choose in order to max­imize the utility of the representative household in this case.

(2) Suppose that prices are given by (12.14). Characterize the number of varieties that the social planner would choose in order to maximize utility of the representative household in this case.

(3) Characterize the equilibrium number of varieties (at which all monopolistically com­petitive variety producers makes zero profits) and compare this with the answers to the previous two parts. Explain the sources of differences between the equilibrium and the social planner’s solution in each case.

Exercise 12.14. This exercise asks you to work through the Salop (1979) model of product differentiation, which differs from the Dixit-Stiglitz model in that equilibrium markups are 471

declining in the number of firms. Imagine that consumers are located uniformly around a circle with perimeter equal to 1. The circle indexes both the preferences of heterogeneous consumers and the types of goods. The point where the consumer is located along the circle corresponds to the type of product that he most prefers. When a consumer at point x around the circle consumes a good of type z, his utility is

while if he chooses not to consume, his utility is 0. Here R can be thought of as the reservation utility of the individual, while t parameterizes the “transport” costs that the individual has to pay in order to consume a good that is away from his ideal point along the circle. Suppose that each firm has a marginal cost of ψ per unit of production

(1) Imagine a consumer at point x, with the two neighboring firms at points

As long as the prices of these firms are not much higher than those further a far, the consumer will buy from one of these two firms. Denote the prices of these two firms by pi and p₂. Show that the price difference that would make the consumer indifferent between purchasing from the two firms satisfies

with

(2) Suppose that pi and p₂ satisfy the above inequality.

strictly prefer to buy from firm 2 and allstrictly prefer to buy from firm

1.

(3) Now assume that there are three firms along the circle at locations

Show that firm 2's profits are given by

and calculate its profit maximizing price.

(4) Now look at the location choice of firm 2. Suppose that pi = p3. Show that it would like to locate half way between zi and z3.

(5) Prove that in a symmetric equilibrium with N firms, the distance between any two firms will be 1/N.

(6) Show that the symmetric equilibrium price with N equity-distant firms is

(7) Explain why the markup here is a decreasing function of the number of firms, whereas it was independent of the number of firms in the Dixit-Stiglitz model.