By Klaus F. Zimmermann (auth.), PD Dr. Klaus F. Zimmermann (eds.)

The concept of optimal inhabitants has attracted the eye of economists ever considering that economics used to be made a technology. Roots may be traced again to old Greece. the subject has lately stumbled on emerging curiosity between inhabitants economists and demographers. the industrial proposal of optimal inhabitants seeks to outline the inhabitants measurement, which maximizes a welfare criterion of the society. the aim of this publication is to stipulate this idea from a micro and macro point of view and to hyperlink it with problems with technical development, social defense, constrained assets and migration. It treats fertility endogenously and reports its welfare and coverage implications. The emphasis is on a rigorous theoretical therapy of the topic utilizing the trendy progress and welfare idea in addition to the hot classical micro version of the kin.

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The assumption that fertility is endogenous enables us to consider noncoercive policies aimed at moving the economy from the LFA to either the BOA or the MOA by changing the incentives (prices) which parents face. We consider all possible direct and indirect taxes and subsidies as candidates for the optimal policy. Notice that, in our case, children themselves are a commodity and may be subject to a tax or a subsidy. Such a tax, which is a head tax, is not a lump-sum nondistortionary tax as in the traditional economic literature with exogenous population.

The product which is to be maximized is thus b . p(i') and the production function is defined as: cp(b) = max lb· p( i') e I e~ bJ The outcome is obvious: if b :s f* we choose e = f*, hence cp(b) = b . p(t'*); if 1* we choose f = band cp(b) = b . pCb). ) are compatible with those imposed on f(·) so that cp(b) has the same shape as f(b). Suppose that the functional forms p and f are such that p(x) = f(x)/x so that p is some average product. Since p reaches a maximum we have: b ~ p'(x) = f'(x) . x - f(x) x 2 > 0 below the maximum and negative above it.

In the discrete case (and when the optimal value of n is less than unity) we can duplicate the level of utility by choosing n = 1 and b accordingly but we cannot do it with n = o. Therefore the latter is never chosen and if income is positive, families have at least one child. We can summarize the above results in the following proposition. Proposition 1 The imposition of the integer restriction with a competitive capital market leads to larger and poorer families, although childless families are ruled out.