exam1-fall2008-sols - Econ407 Advanced Macroeconomics Exam...

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Econ407 Advanced Macroeconomics Exam # 1 Suggested Solutions October 21, 2008 Instructor: Jos´ e Tessada Instructions : The exam consists of three questions, each one with five parts for a total of fifteen parts. Each part is worth two points , thus the exam has thirty points total . Please read carefully the instructions for question 3. Be concise, go straight to the point unless explicitly required to link different arguments. Write less than 10 lines per question. Writing long answers makes it harder for the grader to find the right arguments, thus restrain yourself from using too many words. Question 1 The Ramsey Model (a) Draw the equilibrium path (saddle path) and the ˙ c = 0 and ˙ k = 0 lines for the Ramsey model in the c - k space. Define c and k for this purpose. Answer. See question 1.a, Practice Exercises 2. (b) In the Ramsey model with infinitely lived agents, show in the graph the golden-rule level of capital per capita? Will the economy ever achieve that level? Can the equilibrium in this economy be “dynamically inefficient”? Explain intuitively. Answer. For the first half of the question see the answer to question 1.d, Practice Exercises 2. The equilibrium cannot be dynamically inefficient because there is a “single agent”. Remember that the equilibrium is dynamically inefficient when starting from it we can improve welfare (increase consumption in this particular case) without having to decrease it at any other point. With a single agent choosing the optimal path of consumption it is not possible for the equilibrium to have this characteristic: if there was such a possibility it implies the agent was not maximizing intertemporal utility, hence the equilibrium could not have been a solution to the original problem. (c) What happens with the steady state level of consumption and capital per capita if the government decides to finance a stream of government expenditures using “lump-sum” taxes (i.e., it charges a fixed amount of dollars as taxes to each household). Suppose this announcement is a surprise and it is believed to be permanent and that government budget is balanced all the time. What is the effect of this policy change on consumption, investment and capital stock? Answer. See lecture notes 4, slides 37-39. (d) What happens with the steady state level of consumption and capital per capita if the government decides to tax capital at a rate τ to finance a stream of government expenditures. Suppose this announcement is a surprise and it is believed to be permanent and that government budget is balanced all the time. What is the effect of this policy change on consumption, investment and capital stock? Answer. See solutions to question 1.e, Practice Exercises 2. (e) Why do your answers for parts (c) and (d) differ? Explain intuitively. What does this imply for the government’s choice of tax instruments?
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