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Unformatted text preview: Ecn 110B - World Economic History University of California - Davis October 9, 2009 John Parman Growth Accounting Problems - Solutions This is a set of problems to give you practice working with the various growth accounting equations. You can safely assume that the growth rate of land is always zero unless a problem states otherwise. Solutions will be posted on Smartsite later this weekend. 1. Suppose that the shares of capital, labor and land in output are .6, .35 and .05 respec- tively. The current growth rate of the capital stock is 6 percent a year, the current population growth rate is 4 percent a year and the current growth rate of output is 8 percent a year. (a) What is the current growth rate of output per worker? To get the growth rate of output per worker we just need to subtract the population growth rate from the growth rate of total output: g y = g Y- g L = 8- 4 = 4 (b) What is the current growth rate of technology? Since we have all of growth rates in terms of total amounts, not amount per capita, it makes sense to use the growth accounting equation with Y , K , L and Z (rather than y , k and z ): g Y = g A + a · g K + b · g L + c · g Z 8 = g A + . 6 · 6 + . 35 · 4 + . 05 · 8 = g A + 3 . 6 + 1 . 4 g A = 3 (c) What fraction of the growth in output per worker is explained by growth in technology? What fraction is explained by growth in capital per worker? We already found that the growth rate of output per worker is 4. The growth rate of capital per worker will be g K minus g L which is 2. Now we have all of the information we need to answer the question: g A g y = 3 4 = . 75 a · g k g y = . 6 · 2 4 = . 3 2 Growth Accounting Problems - Solutions So growth in technology accounts for 75% of the growth in output per worker while growth in capital per worker accounts for 30% of the growth in output per worket. (They do not add up to 100% because there is a negative effect on growth in output per work of the negative growth in...
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