【正文】 lem, if the arguments in the previous section are valid. It will also worsen inequality if population growth among the poor is disproportionately larger.Effect on environment (2) Positive effectsThe effect of population growth on technical progress can in turn be divided into two parts. First, population growth may spur。The adjustment of birth rates: Macro and microinertiaMacro: The distribution of the population by age plays an important role. The fact that both birth and death rates are initially high in a poor country makes the net population growth rate low, just as in rich countries, but there is a second implication that is quite different: the populations of the former type of countries will be very young, on average. This feature tends to keep overall birth rates high even if fertility rates are reduced at different age groups.Micro: Fertility choice and missing marketsOffspring are generally a substitute for various missing institutions and markets, notably the institution of social security in old age.Children as “consumption good” and “investment good”, on top of this “consumptiongood” aspect of children is their role as an “investment good”。 To illustrate Figure in Ray (1998). (24) The steady stateTo illustrate Figure in Ray (1998). Steady state is level of per capita capital stock, to which per capita capital stock, starting from any initial level, must converge. (25) How the parameters affect the steady state k*/y* = s /(n+δ) 210 (26) Level effect and growth effect of population growth To illustrate Figure in Ray (1998) (27) Technical progress Two growth sources: technical progress and accumulation of capital inputs. The basic Solow model can be adapted easily to include technical progress. Suppose working population P(t), amount of labor in efficient units L(t), so L(t) = E (t) P(t) 211 E (t) is efficiency index. If efficiency grows at π, so E (t+1) = (1+π) E (t). 212 Even if there is technical progress, steady state is still existing as the outputcapital ratio tends to fall. The longrun increase in per capita ine takes place precisely at the rate of technical progress. （3） The convergence and divergence (31) What means convergence? (32) Unconditional convergence In the face of similar parameters governing evolution, the different initial conditions does not matter. To illustrate Figure in Ray (1998).Convergence is indicated by a strong negative relationship between growth rate of per capita ine and the initial value of per capita ine. log(yt+1) – log (yt) = a + b log(yt) +ε 213 Illustrate the figures below (next pages) Parente and Prescott (1993) studies 102 countries over the period of 196085 and finds standard deviation increasing over time. Does it mean the Solow model is wrong and HarrodDomar model is right? (33) Conditional convergence Unconditional convergence has the assumption that across all countries the level of technical progress, the rate of savings, the rate of population growth and the rate of depreciation are all the same. If these conditions are changed, the steady state should be different for different countries. This leads to conditional convergence. If the rate of savings and population growth rates are different, the ine level would differ and growth rate would be the same. (4) The new growth theories ( endogenous growth theories): Introduction (1) While the Solow model gets some of the predicted correlations correct, how do we reconcile the huge observed differences in per capita ine with the more modest predictions of the model? (2) Can we be satisfied with a theory that only assumes differences in key parameters without explaining these differences? (3) Longrun per capita growth may well be driven by technical progress alone, but this does not mean that technical progress falls on societies like manna from heaven. Human beings, through their conscious actions (and some luck), determine the rate of technical progress, and if this is so, such actions should be part of an explanatory theory, and not simply blackboxed.(4) Finally, do capital and labor, along with the smooth unimpeded flow of technical knowledge, tell the whole story of economic production? (41) Model of human capital and growthContributors: Uzawa [1965], Lucas (1988), Barro [1991], Mankiw, Romer, and Weil [1992].Labor is skilled in production, labor that can operate so phisticated machinery, labor that can create new ideas and new methods in economic activity. It is important to contrast this form of labor with unskilled labor. Augment the Solow model by permitting individuals to “save” in two distinct forms: physical capital and human capital. y = kahla (214)where h stands for human capital and unskilled labor has been omitted for now. First, a fraction s of output is saved, permitting the accumulation of physical capital: k(t + 1) k(t) = sy(t). (215)Another fraction q is saved in a different way: it is used to augment the quality of human capital, so that h(t+1)h(t)=qy(t). (216) Let r denote the ratio of human to physical capital in the long run. Divide both sides of (215) by k(t) and use (214) to note that Likewise, divide both sides of () by h(t) and use () once again to see the growth rate of human capital.Because these two growth rates are the same in the long run (so that the ratio of human to physical capital also stays constant), we must have