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                                             Mf
                   Figure 1. Preferences, Constraints and
                          Income Expansion Path


Time spend
raising children
                        Subsistence
                        Consumption




     1−γ



       γ


                            ~
                            c                               ct
     Figure 2. The Effect of the Rate of Technological
             Progress on the Average Quality

et

                                     e a ( gt )

                                    e( g t ; q ) = qea ( g t ) + (1 − q )eb ( g t )



                                      eb (gt )




                   b
               g                                    gt
                  Figure 3(a). The Evolution of Education
                        and Technological Progress
    et                                 q=0                  g t +1 = ψ (et )



                                                             et +1 = e( g t +1 ; q )

  e H (q)




e L (q)
            L
          g (q)                g
                                   b
                                        g U (q)   g H (q)        gt
           Figure 3(b). The Evolution of Education
                   and Technological Progress.
  et                         q ∈ (0, q )
                                     ˆ                   g t +1 = ψ (et )


                                                           et +1 = e( g t +1 ; q )
e H (q)




 e L (q)


                  g L (q )   g
                                 b
                                     g U (q)   g H (q)         gt
          Figure 3(c). The evolution of education
                and technological progress.
                              q>q
                                ˆ                        g t +1 = ψ (et )
 et
e H (q)                                                    et +1 = e( g t +1 ; q )




                              b
                          g                    g H (q)        gt
              Figure 4. Fertility Rates Across Types

nti
                                                                                        n b ( g t , g t +1 , xt )




                                                                                       n a ( g t , g t +1 , xt )




       ~ 
                1/ α
                        ~ 
                                  1 /α   (           ~ 
                                                              1/ α
                                                                      ~ 
                                                                                1 /α

       a
          c                c             x ( gt )       z                z
                                                                                       xt
       h (g ) 
                       b
                        h (g ) 
                                                    a
                                                     h (g ) 
                                                                     b
                                                                      h (g ) 
                                                                              
           t              t                          t              t 
                Figure 5(a). The Evolution of Technological
                     Progress and Effective Resources
                                  q=0
                                                            H
                                                       GG
           GG   L                            XX
                                     GG U                            CC
  xt




x L (q )




                              b
     g L (q)              g       g U (q )   ˆ
                                             g (q)   g H (q )   gt
          Figure 5(b). The Evolution of Technological
               Progress and Effective Resources
                             q ∈ (0 , q )
                                      ˆ

                         L                                         H
                    GG         GG U         XX               GG             CC
  xt




x L (q)




               g L (q) g b   g U (q )       ˆ
                                            g (q)   g   H
                                                            (q )       gt
     Figure 5(c). The Evolution of Technological
          Progress and Effective Resources
                       q > q ˆ

                              XX                   GG   H

xt                                                               CC




                  b
              g             ˆ
                            g (q)       g H (q )            gt