1. Pure Exchange Economy In this problem we will go through the model seen in class using an example with specific assumptions about tastes and endowments. Home and Foreign are endowed with different amounts of two goods, Apples and Bananas. The two countries are characterized by the following preferences. Home country's aggregate utility function is: i U: xjx while Foreign country's aggregate utility function is: The two countries\" endowments are the following: Home has 100 Apples and 70 Bananas while Foreign has 50 Apples and SCI Bananas. Let's start by looking at what happens if the two countries are in autarky and then we will analyze what happens if the two countries are allowed to trade. As for all general equilibrium problems you have to think in terms of relative prices, therefore from now on we are interested only in the relative price of Apples relative to Bananas p = iii' which is equivalent to assuming that we are taking Bananas as our numeraire, p3 = 1. 1. For the Home country draw a graph with the quantity of the two goods on the two axes and explain why at the consumption point the MRS must be equal to the autarky relative price. 'What is the meaning of autarky relative price since there is no exchange allowed with other countries? The autarky prices are in fact determined by two factors: what are these factors? Find the autarky price p in the Home country. 2. For the Foreign country do the same analysis and draw a graph showing what determines relative prices in autarky. Find the autarky price pl\" in the Foreign country. 3. Now compare autarky prices in the two countries. In which country is the price of Apples higher relative to the price of Bananas? What factors determine the different autarky \"ulna"?!- T... nnnLin..l._... .'-- 4L1" \"unmnin -"l.-. I\" 1.. 2|- \"*0