This question goes through an example of a model with a pure exchange economy. there are two countries, home and foreign, and two goods, cloth (c) and food (f). we focus on economies that feature homothetic preferences, so that we can assume that in each country there is a single consumer who owns the aggregate endowments e = (ec, ef ), and e∗ = (e∗ c , e∗ f ), respectively. the aggregate endowments are given as follows: e = (100, 70), and e∗ = (50, 80). the two countries are characterized by the following preferences. home coutry’s aggregate utility function is: