macro F08

macro F08 - at 15:38 Ph.D Preliminary Examination...

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Unformatted text preview: August 22, 2008 at 15:38 Ph.D. Preliminary Examination MACROECONOMIC THEORY 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 THREE (3) of the five 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 2008 Part I Short Questions 2 Macroeconomic Theory Fall 2008 Question I.1 Consider the Planner’s Problem version of the single sector growth model with labor augmenting technological change: max { c t ,` t ,n t ,x t ,k t } X t β t u ( c t , ` t ) subject to: (i) c t + x t ≤ F ( k t , A t n t ); (ii) n t + ` t ≤ 1; (iii) k t +1 ≤ (1 − δ ) k t + x t ; (iv) k given, all variables non-negative. Assume that A t = γ t A . (a) Give a set of conditions under which the solution to this problem can be obtained by solving a stationary DP. (b) Explicitly add enough conditions to your answer in (a) for you to show that k t +1 k t → γ , and actually show it. 3 Macroeconomic Theory Fall 2008 Question I.2 Search and R&D Consider the problem faced by each of a large number of inventors. An inventor can either choose to invent a new product at a cost of b or not. If the inventor chooses to invent, the quality of the invention is random. Let z denote the quality of an invention where z is drawn independently across inventors and time from a distribution F ( z ) . The quality of the invention is also the per period profits from the invention. Once an invention is produced, the inventor must manage the product if he wants to sell it. While managing, an inventor has no time to invent. With probability p , an invention becomes worthless, and the inventor can go back to his first love, inventing new products. Assume investors are risk neutral and discount future profits. (a) Set up a typical inventor’s problem. (b) Define a stationary equilibrium for the economy. (c) Suppose the costs b fall. What happens to the fraction of those engaged in invention in a stationary equilibrium? (d) Suppose the distribution F changes in a mean-preserving fashion. What happens to the fraction of those engaged in invention in a stationary equilibrium? 4 Macroeconomic Theory Fall 2008 Question I.3 Imagine a three period economy with a continuum of workers of measure 1 and a continuum of firms of measure .5. Matches of firms and workers produce one unit of output which is not storable. Workers preferences are given by the expected sum of consumption in all three periods discounted by rate β . There is no homeproduction....
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macro F08 - at 15:38 Ph.D Preliminary Examination...

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