Exercise 20.7. * Consider a generalization of the model of Section 20.1, where the sectoral production functions are given by the following Cobb-Douglas forms Y A (t) = KA (t) αA ¡ BA (t)LA (t) ¢1−αA Y M (t) = KM (t) αM ¡ BM (t)LM (t) ¢1−αM Y S (t) = KS (t) αS ¡ BS (t)LS (t) ¢1−αS and assume that BA (t), BM (t) and BS (t) grow respectively at the rates gA, gM and gS. (1) Derive the equivalent of Propositions 20.1 and 20.2. (2) Show that as long as preferences are given by (20.3) and γA > 0 and/or γS > 0, balanced growth is impossible. (3) Show that there exists a generalization of condition (20.21) such that this model will have a CGP as defined in Section 20.1. [Hint: the generalization includes two separate conditions that depend on technology growth rates as well as preference parameters].