Introduction to Modern Economic Growth already seen in Chapter 12 that if the cost of R&D are identical for incumbents and new firms, Arrow’s replacement effect will imply that it will be the new entrants that undertake the R&D The same applies in this model The incumbent has weaker incentives to innovate, since it would be replacing its own machine, and thus destroying the profits that it is already making In contrast, a new entrant does not have this replacement calculation in mind As a result, with the same technology of innovation, it will always be the entrants that undertake the R&D investments in this model (see Exercise 14.1) This is an attractive implication, since it creates a real sense of creative destruction or churning Of course in practice we observe established and leading firms undertaking innovations This might be because the technology of innovation differs between incumbents and new potential entrants, or there is only a limited number of new entrants as in the model studied in Section 14.3 below (though in the current model this will not be sufficient, see Exercise 14.1) 14.1.2 Equilibrium An allocation in this economy is similar to that in the previous chapter It consists of time paths of consumption levels, aggregate spending on machines, and aggregate R&D expenditure [C (t) , X (t) , Z (t)]∞ t=0 , time paths of machine qualities denoted by, [q (ν, t)]∞ ν∈[0,1],t=0 , time paths of prices and quantities of each machine and the net present discounted value of profits from that machine, [χ (ν, t | q) , x (ν, t) , V (ν, t | q)]∞ ν∈[0,1],t=0 , and time paths of interest rates and wage rates, [r (t) , w (t)]∞ t=0 We will now characterize the equilibrium in this economy Let us start with the aggregate production function for the final good producers A similar analysis to that in the previous chapter implies that the demand for machines is given by (14.4) x(ν, t | q) = µ q (ν, t) χ (ν, t | q) ¶1/β L for all ν ∈ [0, 1] and all t, where χ (ν, t | q) refers to the price of machine type ν of quality q (ν, t) at time t This expression stands for χ (ν, t | q (ν, t)), but there should be no confusion in this notation since it is clear that q here refers to q (ν, t), and we will use this notation for other variables as well The price χ (ν, t | q) will be determined by the profit- maximizing calculations of the monopolist holding the patent for machine of type ν 613