Exercise 20.20. Consider an open economy version of the model of Section 20.3. In particular, suppose that the economy trades with the rest of the world taking product prices as given. The rest of the world is characterized by the same technology, except that it has an initial level of productivity in the manufacturing sector equal to XF (0) and an agricultural productivity given by AF . Suppose that there are no spillovers in learning-by-doing, so that equation (20.74) applies to the “home” economy and the law of motion of manufacturing productivity in the rest of the world is given by X˙ F (t) = δY M,F (t), where Y M,F (t) is total foreign manufacturing production at time t. (1) Show that comparative advantage in this economy is determined by the comparison of X (0) /BA versus XF (0) /AF . Interpret this. (2) Suppose that X (0) /BA < XF (0) /BF , so that the home economy has a comparative advantage in agricultural production. Show that the initial share of employment in manufacturing in the home economy, n∗ (0), must satisfy X (0) F0 (n∗ (0)) BAG0 (1 − n∗ (0)) = XF (0) F0 ¡ nF∗ (0)¢ BFG0 (1 − nF∗ (0)), where nF∗ (0) is the share of manufacturing employment in the rest of the world. Show that n∗ (0) given by this equation is strictly less than n∗ as given by (20.79). (3) What happens to manufacturing employment in the home economy starting as in part 2 of this exercise? [Hint: derive an equivalent of the equation in part 2 for any t, differentiate this with respect to time and then use the laws of motion of X and XF ]. (4) Explain why agricultural productivity, which was conducive to faster industrialization in the closed economy, may lead to delayed industrialization or to deindustrialization in the open economy. (5) Consider an economy specializing in agriculture as in the earlier parts of this exercise. Is welfare at time t = 0 necessarily lower when this economy is open to trade than when it is closed to trade? Relate your answer to the analysis in Section 19.7 of Chapter 19.