F2010_MT3_P_VersionA

# F2010_MT3_P_VersionA - first initial of last name: ECO 320L...

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first initial of last name: ECO 320L Fall 2010 Professor Beatrix Paal Midterm 3 Problems name: 11/22/2010 3 questions, 26 points total "The core values of The University of Texas at Austin are learning, discovery, freedom, leadership, individual opportunity, and responsibility. Each member of the University is expected to uphold these values through integrity, honesty, trust, fairness, and respect towards peers and community." Version A Page 1

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Points summary: Question 1 Question 2 Question 3 Question 4 Question 5 Question 6 TOTAL Version A Page 2
1. (_____ of 10 points) An economy is described by the Solow growth model. The aggregate production function is 2 (,) 0 . 3 800 K FKN K N  . The population growth rate is n = 0.15 and the depreciation rate is = 0.05. Let the savings rate be denoted by s . a. (_____ of 2 points) Derive that the per worker production function can be written as 2 () 0 . 3 800 k fk k , where k is the capital labor ratio. b. (_____ of 3 points) Let the savings rate be denoted by s . Derive that the steady state capital labor ratio, as a function of the saving rate, is 160 240 SS k s . Version A Page 3

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c. (_____ of 3 points) Prove that the Golden Rule capital labor ratio is 40 GR k . d. (_____ of 2 points) What is the Golden Rule savings rate? Version A Page 4
2. (_____ of 6 points + 3 points extra credit) Assume that the aggregate production function is of the following form: 1 () tt t YA K N h  where t h stands for average human capital per worker, and the other symbols have the usual meaning. In the presence of human capital accumulation the growth accounting relationship needs to be slightly modified.

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## This note was uploaded on 06/09/2011 for the course ECON 320 taught by Professor Azzamonti during the Spring '08 term at University of Texas at Austin.

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F2010_MT3_P_VersionA - first initial of last name: ECO 320L...

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