Problem_Set_6_Solutions - Economics W3213 Spring 2010 Bruce...

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Economics W3213 Spring 2010 Bruce Preston Problem Set 6 Solutions Review Questions 1. Chapter 14: Exercises 1 and 2; Chapter 16: 4, 5 and 7; and Chapter 17: 4, 5 and 8 Short Answer Questions Indicate whether you think the following statements are true, false or uncertain. Support your answer by giving all necessary reasoning and calculations. 1. In its most recent monetary policy decision, the European Central Bank lowered interest rates for the Euro area. In the open economy IS/AS/MP model, this policy action will reduce aggregate demand in the U.S. Solution: True A fall in interest rates in the Euro area leads to higher demand for US assets as the relative return is now higher. To purchase those assets, foreigners have to convert Euros into Dollars which leads to an appreciation in the US dollar, as the supply of currency is °xed by central bank policy. Because of the currency appreciation, US goods are now more expensive for Europeans, and European goods cheaper for Americans. This leads to a fall in net exports. This serves to weaken demand in the US. In terms of our short-run model, aggregate demand is determined by ~ Y t = ° a ° ° b ( R t ° ° r ) where ° a = ° a c + ° a i + ° a g + ° a nx ° 1 + ° b nx ° ° R w ° ° r ± ° b = ° b i + ° b nx : Hence, a fall in ° R w is equivalent to a fall in ° a . 2. In the short-run model, a speci°cation for government expenditures of the form G t ° Y t = ° a g + ° ~ Y t 1
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is consistent with an exogenous change in government expenditures having an impact on the output gap that is greater than one-for-one. That is @ ~ Y t @ ° a g > 1 . Solution: True/Uncertain To answer this, consider re-deriving the IS curve given this assumption in the case of a closed economy for simplicity. Output equals the sum of consumption, investment and government expenditures which is: Y t = C t + I t + G t = ° a c ° Y t + ° a i ° Y t ° ° b ( R t ° ° r ) ° Y t + ° a g ° Y t + ° ~ Y t ° Y t : Hence ~ Y t = Y t ° Y t ° 1 = ° a c + ° a i ° ° b ( R t ° ° r ) + ° a g + ° ~ Y t ° 1 = 1 1 ° ° h ° a c + ° a i ° ° b ( R t ° ° r ) + ° a g + ° ~ Y t ° 1 i = 1 1 ° ° ² ° a ° ° b ( R t ° ° r ) ³ : For 0 < ° < 1 changes in ° a g will have an e/ect equal to 1 1 ° ° for constant real interest rates. Of course, Problem Set 5, short-answer question 3, showed that the more activist is monetary policy the smaller will be the multiplier. (This is because the endogenous response of monetary policy to the resulting higher in±ation will dampen the output increase somewhat.) What is interesting here, in contrast to that earlier problem, is that at least in principle the multiplier can be greater than one. Long Answer Question 1. Consider the following version of the Barro-Gordon model based on the AD/AS model developed in class. The Phillips curve is given by ± t = ± e t + v ~ Y t + ° o t (1) where v > 0 and ± t is in±ation, ± e t in±ation expectations, ~ Y t the output gap and ° o t a supply shock. The government is interested in minimizing ±uctuations in output and in±ation. Suppose that it has a loss function, which represents the publics²preferences,
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