Solve for steady state output per effective worker in terms of the level of technology

Solow Model

Order type: Math/Physics/Economics/Statistics Problems

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 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 found 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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