Goods Market in an Open Economy [10 points] Consider the following open economy. The real exchange rate is xed and equal to 1. Consumption is given by C = 50 + 0.5(Y T), investment is I = 20, taxes are T = 10, and the government's budget is balanced. Imports and exports are given by IM = 0.2Y and X = 0.02Y* where Y* is foreign GDP. (a) [2 points] Solve for the equilibrium Y in the domestic economy for any given Y*. (b) [3 points] What is the government purchases multiplier in this economy? If we were to close the economy -- so exports and imports were identically zero -- what would the multiplier be? Explain the differences (if any) between the open and closed economy multipliers. (c) [3 points] Suppose that foreign GDP is 10 times as large as domestic GDP. What is equilibrium domestic GDP? What is equilibrium foreign GDP? lf foreign economy is hit by an adverse demand shock and its GDP decreases by 10%, by how much does domestic GDP fall? (d) [2 points] Assume that the government in the domestic economy wants to restore the level of domestic GDP to its level before foreign economy is hit by the adverse demand shock. How much should G increase to achieve this target output