CHAPTER 13 Expanding Variety Models As emphasized in the previous chapter, the key to endogenous technological progress is that the R&D is a purposeful activity, undertaken for profits, and the knowledge (machines, blueprints, or new technologies) that it generates increases the productivity of existing factors The first endogenous technological change models were formulated by Romer (1987 and 1990) Different versions have been analyzed by Segerstrom, Anant and Dinopoulos (1990), Grossman and Helpman (1991a,b), Aghion and Howitt (1992) Some of those will be discussed in the next chapter The simplest models of endogenous technological change are those in which the variety of inputs used by firms increases (expands) over time as a result of R&D undertaken by research firms In this chapter, we focus on these expanding input (machine) variety models In this model, research (R&D) leads to the creation of new varieties of machines (inputs), and a greater variety of machines leads to greater “division of labor,” increasing the productivity of final good firms This can therefore be viewed as a form of process innovation An alternative, formulated and studied by Grossman and Helpman (1991a,b), focuses on product innovation In this model, research leads to the invention of new goods, and because individuals have love-forvariety, they derive greater utility when they consume a greater variety of products Consequently “real” income increases as a result of these product innovations Since this variant of the model is slightly more difficult, we postpone its discussion to the end of this chapter In all of these models, and also in the models of quality competition we will see below, we will use the Dixit-Stiglitz constant elasticity structure introduced in the previous chapter 571