Introduction to Modern Economic Growth firm i ∈ [0, 1] is (11.34) Yi (t) = F (Ki (t) , A (t) Li (t)) , where Ki (t) and Li (t) are capital and labor rented by a firm i Notice that A (t) is not indexed by i, since it is technology common to all firms Let us normalize the measure of final good producers to 1, so that we have the following market clearing conditions: Z Ki (t) di = K (t) and Z Li (t) di = L, where L is the constant level of labor (supplied inelastically) in this economy Firms are competitive in all markets, which implies that they will all hire the same capital to effective labor ratio, and moreover, factor prices will be given by their marginal products, thus ∂F (K (t) , A (t) L) ∂L ∂F (K (t) , A (t) L) R (t) = ∂K (t) The key assumption of Romer (1986) is that although firms take A (t) as given, w (t) = this stock of technology (knowledge) advances endogenously for the economy as a whole In particular, Romer assumes that this takes place because of spillovers across firms, and attributes spillovers to physical capital Lucas (1988) develops a similar model in which the structure is identical, but spillovers work through human capital (i.e., while Romer has physical capital externalities, Lucas has human capital externalities) The idea of externalities is not uncommon to economists, but both Romer and Lucas make an extreme assumption of sufficiently strong externalities such that A (t) can grow continuously at the economy level In particular, Romer assumes (11.35) A (t) = BK (t) , i.e., the knowledge stock of the economy is proportional to the capital stock of the economy This can be motivated by “learning-by-doing” whereby, greater investments in certain sectors increases the experience (of firms, workers, managers) 522