Economics Exam: Lucas Tree Model, Stockman CIA Model, and Macroeconomic Puzzles, Exams of Introduction to Macroeconomics

Download Economics Exam: Lucas Tree Model, Stockman CIA Model, and Macroeconomic Puzzles and more Exams Introduction to Macroeconomics in PDF only on Docsity! K. Salyer, Economics 200E, Spring 2007 1 Final Exam Directions: Answer all questions - they are equally weighted. Good luck and enjoy your summer — after the prelims. 1. Consider a two-state version of the Lucas tree model; that is, the endowment is assumed to follow a two-stateMarkov process with possible realizations x1 < x2 and symmetric transition probability matrix with diagonal elements  = 1=2. Suppose agents in this economy trade one- and two period bonds that cost p1t and p2t units of consumption, respectively, and return one unit of consumption upon maturity. Dene the term premium as the difference between the expected return from selling a two-period bond after holding it for one-period and the certain return from a one-period bond. What is the sign of this term premium? Provide an explanation for your answer. 2. Consider the following version of the Stockman CIA model: The economy is populated by identical agents that have preferences given by: 1X t=0 t [U (ct) +W (1 ht)] where ct is consumption and ht is labor. Each period, agents produce output via a concave production function with labor as the only input (there is no cap- ital): yt = f (ht). The revenue from the sale of this output is combined with money carried over from the previous period, the monetary transfer, and returns from both one-period nominal and real bonds purchased in period t in order to acquire new money holdings and new bonds. The monetary transfer from the government is proportional to their initial money holdings; i.e. they receive an interest payment on their money holdings. This interest payment is equal to the (constant) monetary growth rate, :To be precise, if their money choice at period t is Mt then they receive a transfer of Mt at the beginning of period t + 1: Consumption purchases in period t must be nanced by cash acquired in period t 1 and augmented by the monetary transfer. (a) Set up the problem as a dynamic programming problem, derive and inter- pret the rst-order conditions. (b) Solve for the steady-state in this economy. Does the monetary growth rate inuence the level of steady-state output? Explain. (c) Does the Fisher relation hold in this economy? (d) Is the equilibrium in this economy Pareto optimal? 3. Consider a simple stochastic production economy in which agents have log util- ity and the production function is yt = ztk t where y is output, z is an i.i.d. technology shock, and kt is beginning of period capital. Depreciation is 100%. Answer the following 1