of period 1 (see below). Recalling the discussion of mortality and morbidity in Section 3.2, we also have _qt_ = 0 _._ 053 and **d** _t_ = (0 _._ 015 _,_ 0 _._ 03 _,_ 0 _._ 06) _∀t ≥_ 2.

The final step is to choose the productivity parameters _zt_ and _α_ and the intertemporal taste parameters _b_ 1 and _b_ 2 so as to yield _e_<sup>0</sup> 2<sup>= 0</sup><sup>_._95(1</sup><sup>_−_0</sup><sup>_._015)</sup><sup>_/_1</sup><sup>_._08 = 0</sup><sup>_._866 with as little</sup> to spare as possible. With the exception of _zt_ , this must be accomplished by trial and error as part of the process of computation. The only prior restriction is that with pure impatience for consumption, _b_ 1 _> b_ 2. Since premature mortality already appears in connection with preferences over dated consumption, the pure discount rate arguably should not greatly exceed 15 percent per generation of 20 years. One can arrive at an appropriate value of _z_ by imposing the assumption that individual productivity, _λt_ , will grow without limit if, after some point, all generations are fully educated. As noted in Section 2.1, by choosing a sufficiently productive technology _f_ ( _et_ ) and otherwise setting up the system so that _e_<sup>0</sup> _t_<sup>=</sup><sup>_e_ ̄</sup><sup>_t∀t ≥_2,where</sup><sup>_e_0</sup> _t_<sup>=</sup><sup>_e_ ̄</sup><sup>_t_issuf-</sup> ficiently close to 1, we ensure that _λ_<sup>2</sup> _t_<sup>willindeedgrowwithoutbound.Recallfrom (3)</sup> that the relevant characteristic root when the upper limit on _et_ is unity is 1+ _g_<sup>_∗_</sup> . Reduc ̄ ing this upper limit to _e_ = 0 _._ 866 yields the root _a_ 2[1+ �(1+2 _a_ 3 _/a_<sup>2</sup> 2<sup>_f_(0</sup><sup>_._866))]</sup><sup>_f_(0</sup><sup>_._866),</sup> where _f_ ( _et_ ) = _ztet, a_ 2 = 2 _/_ 3 _._ 5 and _a_ 3 = 1 _._ 5 _/_ 3 _._ 5. Let _zt_ = 0 _._ 85 _∀t_ , which implies that output per head will grow at the rate of 41.3 percent per generation, or 1.74 percent a year. This seems defensible for an horizon many generations off.

# **4 A New Road: Exact Welfare Measures**

Imagine two islands, each inhabited by a representative extended family. The first is characterized by the constellation of numerical values set out in Section 3. The second is identical, except for the happy event that a road is provided free of charge at the very start of period 1. As a result, unit transport costs, travel-times, morbidity and mortality all become lower than those on island 1. In this more benign environment, it is not only certain that _e_<sup>0</sup> _t_<sup>_>_0</sup><sup>_._866</sup><sup>_∀t ≥_2,butalsohighlylikelythat</sup><sup>_e_0</sup> 1<sup>willbehigher</sup> than on island 1. The latter being so, the path _{λ_<sup>2</sup> _t_<sup>_}∞_</sup> _t_ =2<sup>willlieeverywhereaboveits</sup> counterpart on island 1. The two paths will, moreover, exhibit different asymptotic rates of growth, even though they share the common value of _zt_ . This ‘growth-effect’ stems from lower morbidity, reduced round-trip times to school and fewer involuntary absences, all of which bring the upper limit _e_ ̄ _t_ closer to unity – as long as the road does not fall into utter disrepair. If it were to do so at the end of period 1, for example, _e_<sup>0</sup> _t_<sup>= 0</sup><sup>_._866</sup><sup>_∀t ≥_2wouldstillbeensuredthereafter,underthehypothesisthatitholds</sup> 16