Consider an OLG economy. Every period, a constant mass (normalised to 1) of young

individuals is born and live for two periods. Individuals have preferences over leisure,

t

l

, when

young and consumption,

1t

c

, when old. These preferences are represented by the lifetime utility

function

1

ln (1 )ln

tt t

Uml mc

, where (0,1)m . When young, individuals have a unit of

time which they can devote to either leisure or to activities that promote the formation of human

capital. These are denoted by

t

e while human capital evolves according to

1

ttt

hAeh

( 0A ,

01). When old, individuals supply their human capital to perfectly competitive firms, who

employ a technology that is linear in effective labour in order to produce final goods, i.e.,

11tt

y h

( 0 ), and use their labour income to purchase consumption goods.

Question 1

Solve an individual's maximisation problem and find the optimal allocation of time between

leisure and learning activities. Provide intuition for your result.

Question 2

Analyse the dynamics of human capital. What are the parameter conditions necessary for the

economy to sustain a positive growth rate in the long-run?