Exercise 19.29. Consider the model in Section 19.6, but assume that new products are created with the innovation possibilities frontier as in Section 13.2 in Chapter 13. Assume that before trade knowledge spillovers are created by the entire set of available inputs in the world economy, that is, the innovation possibilities frontier is similar to (13.24) in Section 13.2, except that N˙ j (t) = ηN (t)Lj R (t)

for country j, where N (t) = N1 (t) + N2 (t) and Lj R (t) is the number workers working in R&D in country j. Consequently, trade opening does not change the structure of knowledge spillovers. (1) Show that in this model, trade opening has no effect on the equilibrium growth rate. Provide a precise intuition for this result. (2) Next assume that before trade opening the innovation possibly the frontier takes the form N˙ j (t) = ηNj (t)Lj R (t). Show that in this case, trade opening leads to an increase in the equilibrium growth rate as in Proposition 19.14. Explain why the results are different. (3) Which of the specifications in 1 and 2 is more plausible? In light of your answer to this question, how do you think trade opening should affect economic growth.