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:

Along 8-cm diameter steam pipe whose external surface temperature is 900c connects two buildings. the pipe is exposed to ambient air at 70c with a wind speed of 50 km/hr blowing across the pipe. determine the heat loss from the pipe per unit length. (b) air at 500c enters a section of a rectangular duct (15 cm x 20 cm) at an average velocity of 7 m/s. if the walls of the duct are maintained at 100c. a) the length of the tube for an exit temperature of the air to be 40 0c. b)the rate of heat transfer from the air. c) the fan power needed to overcome the pressure drop in this section of the duct.