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PS1-ans_key

# PS1-ans_key - University of Minnesota Department of...

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University of Minnesota Department of Economics Econ 4301/4331W: Development Economics Problem Set 1 (Last revised: June 20th) This problem set (PS) is due on Monday, June 30 at the beginning of class. The maximum score is 50 points. Be sure to review the Syllabus for details about PS and their grading! Feel free to contact me via e-mail if you have specific questions about the HW assignment. Note that some Exercises have several parts, and each part may conceal more than one task for you. Be sure to answer every question thoroughly for full credit! 1 Problems (50) Exercise 1 - Solving the Solow Model (15 points) Consider an economy where there are L t identical consumers, each of them having one unit of available time. Aggregate consumption and savings policies are given by C t = (1 - s ) Y t and S t = sY t . There is a representative firm that has a Cobb-Douglas production technology of the form Y t = F ( K t , L t ). There is no government and the economy is closed. (a) Suppose F ( K t , L t ) = K α t L 1 - α t , where 0 < α < 1. Using the law of motion for the capital stock and population, determine the future capital per worker ˆ k t +1 as a function of ˆ k t , i.e. ˆ k t +1 ( ˆ k t ). Show all work. (b) Using your answer from part (a), impose the steady state condition ˆ k t +1 = ˆ k t = ˆ k * and solve for the steady state capital per worker ˆ k * and output per worker ˆ y * . Show all work. (c) Use the Solow diagram to discuss the transition dynamics of the economy. I.e. Consider two cases, 1. ˆ k 0 < ˆ k * and 2. ˆ k 0 > ˆ k * . Discuss what happens to both the levels and growth rates of ˆ k t and ˆ y t over time.

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PS1-ans_key - University of Minnesota Department of...

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