(This follows Kurgan, 1979; see also Grossman and Help man, 1991b.) Suppose the world consists of two regions, the “North” and the “South.” Output and capital accumulation in region i (i = N,S) are given by Yi(t) = Ki(t) α[Ai(t) (1 − aL_i)Li] 1−α and K˙i(t) = s_iY_i(t). New technologies are developed in the North. Specifically, A˙N (t) = BaLN L NA N (t). Improvements in Southern technology, on the other hand, are made by learning from Northern technology: A˙S (t) = μaLSLS [A N (t) − AS (t)] if A N (t) > AS (t); otherwise A˙S (t) = 0. Here aLN is the fraction of the Northern labor force engaged in R&D, and aLS is the fraction of the Southern labor force engaged in learning Northern technology; the rest of the notation is standard. Note that L_N and L_S are assumed constant.

(c) Assume aL_N = aL_S and s_N = s_S. What is the ratio of output per worker in the South to output per worker in the North when both economies have converged to their balanced growth paths?