HomeAs2 - Fall 2010 - Answer Key

HomeAs2 - Fall 2010 - Answer Key - has the highest output...

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Econ 3T03 Fall 2010 Home Assignment #2: Due to October 1, 2010, at the end of class. 1. (10 points) Consider 2 countries, Avataria and Pandora, which can be described by Solow model. Avataria has a capital-labor ratio that is initially 10 times smaller than that of Pandora, but neither country is yet in a steady state. Both countries produce unobtainium according to the same production function, y( k ) = 2 k 1/3 . People of Avataria save 10% of their income, while thrifty Pandorians save 20% of their income. In both countries the depreciation rate is 5%. Finally, people of Avataria live forever, and to keep their country from overpopulation, they have decided not have any children, so there is no population growth there, while in Pandora the population growth rate is 35%. (a) Calculate the steady-state capital-labor ratio for each country. (b) Calculate output per worker and consumption per worker for each country. Which country
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Unformatted text preview: has the highest output per worker? The highest consumption per worker? (c) Based on Solow model, does the initial capital-labor ratio serve as a good indicator of what happens with a country in a steady state? Answers: (a) Using the formula s/(n+ δ ) = k/y(k) , or s y(k) = (n+ δ ) k , We get: Avataria: 0.1 × 2 k 1/3 = 0.05 k , or k 2/3 = 4, so k = 8; Pandora: 0.2 × 2 k 1/3 = 0.4 k , or k 2/3 = 1, so k = 1. The initial capital-labor ratios have no effect on the steady-state capital-labor ratios. (b) y = 2 k 1/3 , so in Avataria y = 4, in Pandora y = 2. c = (1 – s ) y , so Avataria has c = 0.9 y = 3.6, while Pandora has c = 0.8 y = 1.6. Avataria has higher levels of both output per capita and consumption per capita. (c) Initial capital-labor ratio does not affect a country’s steady state levels in Solow model. (It only affects the time and speed with which the country reaches the steady state.)...
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