Economic growth and economic development 678

Introduction to Modern Economic Growth where, as usual, ρ > The supply side is represented by an aggregate production function combining the outputs of two intermediate sectors: i ε h ε−1 ε−1 ε−1 , (15.3) Y (t) = γYL (t) ε + (1 − γ)YH (t) ε where YL (t) and YH (t) denote the outputs of two intermediate goods As the indices indicate, the first is L-intensive, while the second is H-intensive The parameter ε ∈ [0, ∞) is the elasticity of substitution between these two intermediate goods, while γ is again a distribution parameter determining the importance of the two intermediate goods for aggregate output The resource constraint of the economy at time t takes the form C (t) + X (t) + Z (t) ≤ Y (t) , (15.4) where, as before, X (t) denotes total spending on machines and Z (t) is aggregate R&D spending The two intermediate goods are produced competitively with the following production functions: (15.5) YL (t) = 1−β and (15.6) YH (t) = 1−β ÃZ NL (t) xL (ν, t)1−β dν ! Lβ xH (ν, t)1−β dν ! Hβ, ÃZ NH (t) where xL (ν, t) and xH (ν, t) denote the quantities of the different types of machines (used in the production of one or the other intermediate good) and β ∈ (0, 1).1 These machines are again assumed to depreciate after use The parallel between these production functions and the aggregate production function of the economy in the baseline expanding product varieties model of Chapter 13 is obvious There are two important differences, however First, these are now production functions for intermediate goods rather than the final good Second, the two production functions (15.5) and (15.6) use different types of machines The range of machines complementing labor, L, is [0, NL (t)], while the range of machines complementing factor H is [0, NH (t)] 1Note that the range of machines used in the two sectors are different (there are two disjoint sets of machines); we use the index ν to denote either set of machines for notational simplicity 664