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:

Acommercial grade cubical freezer, 4 m on a side, has a composite wall consisting of an exterior sheet of 5.0-mm thick plain carbon steel (kst= 60.5 w/m k), an intermediate layer of 100-mm thick polyurethane insulation (kins 0.02 w/m k), and an inner sheet of 5.0- mm thick aluminium alloy (kal polyurethane insulation and both metallic sheets are each characterized by a thermal contact resistance of r 2.5 x 104 m2 k/w. (a) what is the steady-state cooling load that must be maintained by the refrigerator under conditions for which the outer and inner surface temperatures are 25°c and -5°c, respectively? (b) for power saving purpose, which wall material should be increased/reduced in. thickness in order to reduce 50% of the cooling load found in part (a)? redesign the thickness of the proposed material. 177 w/m-k). adhesive interfaces between the q=575.93 w