# Effects of a declining population in a model of economic growth with endogenous human capital - Lucas (1988)

Part of the Contributions to Economics book series (CE)

## Keywords

Human Capital Capital Stock Population Growth Rate Physical Capital Hamiltonian Function
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## References

1. 1.
See Chiang (1992) for a detailed description of problems of dynamic optimization. An introduction to dynamic optimization in continuous time and how it can be used in economic growth theory is given by Barro and Sala-i-Martin (2004), 604f. The behaviour of the household which maximizes its utility over time is based on Ramsey (1928).Google Scholar
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3. 3.
See Chiang (1992), 261, Solow (2000), 129.Google Scholar
4. 4.
In infinite horizon problems the transversality condition needed to provide a boundary condition is typically replaced by the assumption that the optimal solution approaches a steady state; see Kamien and Schwartz (1991), 174.Google Scholar
5. 5.
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7. 7.
See Barro and Sala-i-Martin (2004), 615.Google Scholar
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9. 9.
Barro and Sala-Martin (2003), 617.Google Scholar
10. 10.
In the literature, the model is called “Uzawa-Lucas” model as Lucas (1988) is based on Uzawa (1965). Lucas (1988) includes several models. In this thesis, Lucas (1988) refers to chapter 4 of his paper.Google Scholar
11. 11.
The production of human capital involves no physical capital. Rebelo (1991) applies a Cobb-Douglas function which employs both human and physical capital in the production function.Google Scholar
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13. 13.
If the accumulation of human capital would follow a rule such as $$\dot h = E\left( {1 - u} \right)h^\zeta$$ and ζ < 1 there are diminishing returns to human capital accumulation. This means that the growth rate of human capital is $$\frac{{\dot h}} {h} \leqslant E\left( 1 \right)h^{\zeta - 1}$$ so that $$\frac{{\dot h}} {h}$$ goes to zero as h grows (see Lucas (1988), 18). See Solow’s criticism of (4.12) in Solow (2000), 126.Google Scholar
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Lucas (1988), 17. See criticism by Nerlove and Raut (1997), 1140, “... so 10 men who can read are better than 100 who cannot no matter what the size of the labour force?”Google Scholar
15. 15.
In Lucas (1988) the production function is Y = A · Kα(uhL)1−αhαγ with technology level A. The term hαγ captures the external effects of human capital. As we are not concerned with externalities of human capital, we can simplify the function to (4.15), i.e. we set γ = 0. In addition we neglect the technology A as it is exogenous in this model.Google Scholar
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17. 17.
Blanchard and Fischer (1989), 38.Google Scholar
18. 18.
For example, Barro and Sala-i-Martin (1995), chapter 5.Google Scholar
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20. 20.