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The production 1. 1—are described in Summers and Heston (1991) and Heston, Summers, and Aten (2002). We discuss these data in chapter 12. 1) where Y (t) is the flow of output produced at time t. Capital, K (t), represents the durable physical inputs, such as machines, buildings, pencils, and so on. 1). It is important to notice that these inputs cannot be used by multiple producers simultaneously. This last characteristic is known as rivalry—a good is rival if it cannot be used by several users at the same time.

10. Note that, in the previous section and here, we assumed that each person saved a constant fraction of his or her gross income. We could have assumed instead that each person saved a constant fraction of his or her net income, f (k) − δk, which in the market setup equals ra + w. In this case, the fundamental equation of the Solow–Swan model would be k˙ = s · f (k) − (sδ + n) · k. Again, the same equation applies to the household-producer and market setups. 13 The corresponding value of k is denoted k ∗ .

Cass (1965) and Koopmans (1965) brought Ramsey’s analysis of consumer optimization back into the neoclassical growth model and thereby provided for an endogenous determination of the saving rate. This extension allows for richer transitional dynamics but tends to preserve the hypothesis of conditional convergence. The endogeneity of saving also does not eliminate the dependence of the long-run per capita growth rate on exogenous technological progress. The equilibrium of the Cass–Koopmans version of the neoclassical growth model can be supported by a decentralized, competitive framework in which the productive factors, labor and capital, are paid their marginal products.

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