Growth Accounting 1865-1929 Problem Set

Growth Accounting Problem Set, 1865-1929: The Great Traverse Due in lecture on October 6, 2008 1. Begin with our rule-of-thumb for industrial-era economic growth:

1 1 g(Y ) =  g(K ) +  (g(L) + g(E)) 2 2

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with g(Y) is the proportional growth rate of total output, g(L) the growth rate of the population or labor force, and g(E) the growth rate of the efficiency of labor. Remember that g(y), g(k), and d = g(k) - g(y) are the growth rates of output per capita, the capital stock per capita, and the rate of capital deepening, respectively. Solve for the growth rate of output per capita as a function of the growth rate of the efficiency of labor and of the rate of capital deepening. Show your work. 2. Begin with our equation for the growth rate of the capital stock per capita:

 s  Y  g(k) =    − δ − g(L)  p k  K 

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where δ is the rate of depreciation, s is the economy’s savings rate, and pκ Assume also that—at the moment—there is no capital deepening going on, so that the value of d in your answer to (1) is zero. Solve for the capital-output ratio K/Y as a function of the other parameters and variables. Show your work. 3. In 1865 the rate of population growth is 3% per year, the rate of growth of the efficiency of labor is this 0.9% per year we got from the British Industrial Revolution, the rate of depreciation δ is some 4% per year, the rate of national savings s is some 20% per year and the price of capital goods pk we set at 1. Assuming there is no capital deepening going on, what is the capital-output ratio (in 1865 prices) in 1865? 4. In 1929 our rate of population growth has dropped to 2% per year. The price of capital goods has dropped to 2/3 (in 1865 prices). And the national savings rate has increased by one-quarter to some 25%. Assuming there is no capital deepening going on, what is the capital-output ratio (in 1865 prices) in 1865? 5. What is the rate of capital deepening between 1865 and 1929? Assuming no change in g(E), what is the predicted rate of growth of output per worker between 1865 and 1929? 6. Suppose there had been no immigration—that population growth dropped to 1% per year after 1865. What would the rate of economic growth in output per capita have been between 1865 and 1929? 7. Suppose that there had been no reduction in the price of capital goods—no industrial revolution proper. What would the rate of economic growth in output per capita have been between 1865 and 1929? 8. Suppose that there had bee no increase in the U.S. savings rate s. What would the rate of economic growth in output per capita have been between 1865 and 1929?

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