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Unformatted text preview: 3 G ROWTH AND A CCUMULATION FOCUS OF THE CHAPTER • In this chapter we study how potential output the output that would be produced if all factors were fully employed grows over time. • To better accomplish this, we learn growth accounting and the fundamentals of neoclassical growth theory. Together, they tell us that output growth results both from improvements in technology and from increases in one or more of the inputs to the production process capital, labor, and natural resources. Neoclassical growth theory also tells us that in the long run, growth in potential output results entirely from technological improvement. * Note: The authors in this chapter and the next use the term “long run” in a way that is inconsistent with the rest of the textbook. They should be saying “very long run.” SECTION SUMMARIES 1. Growth Accounting Output grows because of increases in factors of production like capital and labor, and because of improvements in technology. The production function provides a link between the level of technology ( A ), the amount of capital ( K ), labor ( N ), and other inputs used, and the amount of output ( Y ) created. The generic formula for the production function is: Y = AF(K,N) The Cobb-Douglas production function , a more specific formula, is frequently used as well, as it provides a good approximation of production in the actual economy. The formula for the Cobb- Douglas production function is: Y = AK θ N 1 - θ 21 22 C HAPTER 3 θ pronounced “theta”, represents capital’s share of income total payments to capital, as a fraction of output, or (iK)/Y . (1 - θ ) i s labor’s share of income , given by (wN)/Y . To derive these results algebraically, you need one more fact: When the markets for capital and labor are in equilibrium (i.e., when the supply of capital equals the demand for capital, and the supply of labor equals the demand for labor), capital and labor are each paid their marginal product . For the Cobb-Douglas function, the marginal product of capital (MPK) is θ AK θ N θ . The marginal product of labor (MPL) is (1 - θ )AK θ N 1 - θ We can express our production function in terms of growth rates rather than levels: ∆ Y/Y = [(1 - θ )x ∆ N/N] + [ θ x ∆ K/K] + ∆ A/A The symbol ∆ pronounced “delta” means “change in”. The term ∆ Y/Y , then, should be interpreted as the growth rate of output. The terms interpreted as the growth rate of output....
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