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Unformatted text preview: Ph.D. Preliminary Examination MACROECONOMIC THEORY 1 Majors : Answer two (2) questions in Part I and two (2) questions in Part II. Points for each question in Part I are twenty (20), and points for each question in Part II are thirty (30). Minors: Answer all three (3) questions in Part I and one (1) question in Part II OR answer one (1) question in Part I and two (2) questions in Part II. Points for each question in Part I are twenty (20), and points for each question in Part II are forty (40). PLEASE MAKE YOUR ANSWERS NEAT AND CONCISE Make whatever assumptions you need to answer the questions. BE SURE TO STATE THEM CLEARLY. Macroeconomic Theory Fall 2007 Part I Short Questions 2 Macroeconomic Theory Fall 2007 Question I.1 Taxation Consider an economy where the representative consumer has preferences ∑ ∞ t =0 β t u ( c t ). The technology is available to the representative firm is AK and the budget constraint faced by the representative consumer is: ∞ X t =0 p t ( c t + x t ) ≤ ∞ X t =0 ( r t (1 − τ kt ) k t ) + T where T is a lumpsum transfer in period zero. Consider two different fiscal policies: FP1: τ 1 k > , τ 1 kt = τ 1 k < ∀ t > , T 1 = 0. FP2: τ 2 k > , τ 2 kt = 0 ∀ t > , T 2 = τ 2 k r k . Under fiscal policy 1, the government taxes capital income in the first period in such way that is possible to subsidize capital income in all subsequent periods. Under fiscal policy 2, the government taxes capital income only in period zero and the consumer gets the revenue back through a lumpsum transfer. (a) Prove that under FP2, the TDCE allocation is Pareto optimal. Be sure to state the assumptions that you need. Also prove the result from scratch, that is, do not apply any lemma, such as, lumpsum taxation yields a Pareto optimal allocation. (b) Assume that the utility function is u ( c t ) = c 1 − σ t 1 − σ . Consider { c i t , k i t , x i t } ∞ t =0 the TDCE allocation under FPi . Compare the growth rate of consumption under the two different fiscal policies. In particular, calculate the ratio c 1 t c 2 t . (c) Show that c 2 > c 1 . 3 Macroeconomic Theory Fall 2007 Question I.2 Consider a closed economy inhabited by a continuum of infinitely lived agents with common expected utility given by: E ∞ X t =0 β t u ( c t ) u ( c ) = 1 1 − γ c 1 − γ , γ > where β < 1 is the discount factor and c is consumption. Each agent can trade a non contingent bond and faces the following budget constraint and borrowing constraint a t +1 + c t = a t (1 + r ) + y t a t +1 ≥ Where r is the equilibrium interest rate and y t is a stochastic endowment Assume that y t can take the values 1 + ε and 1 − ε with probability 1 / 2 and is i.i.d across time and across people. Bonds are in 0 net supply and each agent starts with initial bond position equal to 0....
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 Spring '08
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 Economics, representative, Preliminary Examination MACROECONOMIC THEORY

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