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Solow Model (66 points)
(6 points) In what follows, assume an aggregate production function Y=K^a ?(AN)?^(1-a), with a=1/3. Also assume a depreciation rate of 10%, or d=0.1. Assume that technology in each country grows at a rate of 1.5% each year. Solve for steady state output per effective worker in terms of the level of technology A, the population growth rate n, and the savings rate s. Now solve for steady state output per worker.
(24 points) Use your formula from part (a), and the data from the table below, to predict the ratio of output per worker in each country relative to that of the United States in the steady state, assuming that for each country A=1.
Country    Per worker GDP, 2010    Ratio of per worker GDP, relative to United States    Savings rate, s (%)    Population growth rate, n (%)    A (level of technology)
United States    67319    1    20.6    1    1.000
Ireland    55068    0.818016    19.7    0    0.967
France    52331    0.777359    23.8    1    0.691
Japan    44702    0.664032    31.6    0    0.679
South Korea    44251    0.657333    34    0    0.563
Spain    41679    0.619127    23.4    0    0.614
Argentina    27871    0.414014    15.8    1    0.486
Mexico    19892    0.295489    18.1    1    0.427
China    13045    0.193779    19.2    0    0.266
India    8496    0.126205    11.9    1    0.227
Zimbabwe    1711    0.025416    13.1    1    0.182
Uganda    2612    0.0388    2.8    3    0.192

(24 points) Now repeat the same exercise assuming A is given by the levels in the last column of the table. Discuss briefly the differences you find in these two approaches.
(12 points) Rank the countries in the order of expected growth rate over the coming decades, from the fastest to the slowest. Use the data on the ratio of steady state output per worker to that for U.S., along with the actual ratio of per worker GDP compared to U.S. for each country to rank the countries.

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