Consider a two-period, two- country, endowment economy. Let one of the countries be the United States, denoted by U, and the other Europe, E. These are the only two countries in the world and they are both large open economies. Households in the United States have preferences described by the utility function: U"(CY, Cy) = In(CP) + In(Cy). where C and C2 denote consumption of U.S. households in periods 1 and 2, respectively. Europeans have identical preferences, given by: UE(CF, CE) = In(CF) + In(CF). where C and C2 denote consumption of European households in periods 1 and 2, respectively. Let Q1 and Q2 denote the U.S. endowments of goods in periods 1 and 2, respectively. Similarly, let Of and Q2 denote the European endowments of goods in periods 1 and 2, respectively. Assume further that the endowments are nonstorable, that the U.S. and Europe are of equal size, and that there is free capital mobility between the two economies. The United States starts period 1 with a zero net foreign asset position. (a) Assume that Europe and the United States have identical endowments, which are also constant over time. Specifically, assume that Q1=09=Q1=Q5 = 10. Compute the equilibrium world interest rate, the equilibrium current account for the US and the current account for Europe. In two lines, provide an intuition to interpret your results. (7 marks) b) Suppose now that period 1 in the model coincides with 2008, when a crisis hit the US but not Europe. In addition, agents expect the crisis to be temporary. This means that you should assume that Q, drops from 10 to 8. All other endowments remain unchanged at 10. This contraction in output has two characteristics: first, it originates in the United States (the European endowments are unchanged); second, it is temporary (the U.S. endowment is expected to return to its normal value of 10 after one period). Calculate the equilibrium interest rate and the current accounts of the United States and Europe in period 1. In two lines, provide an intuition to interpret your results. (7 marks)(c) Again, suppose that period 1 in the model coincides with 2008, when a crisis hits the US but not Europe. However, now agents expect the crisis to be long-lasting and to be even more severe in the future. This means that you should assume that the U.S. endowment falls from 10 to 8 in the first period and is expected to continue to fall to 6 in the second period (Q!' = 8 and Q!= 6). The endowments in Europe remain unchanged at 10 each period. Like the one described in the previous item, this contraction originates in the United States. However, it differs from the one described in the previous item in that it is more protracted. Calculate again the equilibrium interest rate and the two current accounts in period 1. In two lines point out differences in the effects of the two types of contraction and provide intuition to interpret your results. (7 marks) (d) At the beginning of the Great Contraction of the US, interest rates fell sharply around the world. In light of the models studied above, how can you explain this interest rate decline? (3 marks) (e) Now assume that in addition to the decline in expected period-2 endowment (as in part (c)), there is also an increase in US agents' uncertainty about the future realization of output in their country. Explain in words how the Current Account of the US and the world interest rate would change with respect to part (c). (3 marks) (f) Finally, assume that a similar crisis as described in part (c) happened in a small open economy, such as New Zealand, instead of the United States. Explain in words how the world interest rate would be affected in this case, and how the Current Account of New Zealand would compare to the one of the United States if facing a long-lasting crisis as the one described in part (c)