4 A Large Open Economy Consider a two-period, two-country, endowment economy. Let one of the countries be the United States {U} and the other lChina {C}. Households in the United States have preferences described by the utility function so? + may where Cf; and 0%\" denote consumption of US. households in periods 1 and 2, respectively. Chinese people have identical preferences, given by acFanf where CF and CEO denote consumption of Chinese households in periods 1 and 2, respectively. Let Q? and CE denote the U.S. endowments of goods in periods 1 and 2, respectively. Similarly, let Q? and Q? denote the Chinese endowments of goods in periods 1 and 2, respectively. Assume further that the endowments are nonstorable, that the U5. and China are of equal size, and that there is free capital mobility between the two economies. The United States and the China start period 1 with a zero net foreign asset position. 1. {1Upts} Assume the U.S.'s endowments are Q? = 15 and CE = 15, and China's endowments are Q? = If.. and Q? = 2|]. Calculate the equilibrium world interest rate and the current accounts of the United States and China in period 1. 2. {15pm} Consider the same situation as in Part 1. Suppose now that the Ufi. economy is hit by a recession in period 1 and the endowment Q? is reduced by diff}. U.S.'s endowment in period 2 {GE} and China's endowments in each period [13? and Q?) are unchanged from those in Part 1. In this new situation, it turns out that the world interest rate 1*} is 1.1\") [So 1 + \"cf = EDD}. Based on this observed world interest rate, how severe is the recession that hits the U.S. in period 1? Calculate the 9'6 reduction in the U.S.'s period-1 endowment, d