Consider an overlapping generations economy in which, every period, a constant mass (normalised to 1) of two-period lived individuals is born. These individuals have preferences over leisure, lt , when young and consumption, ct+1, when old, according to the lifetime utility function Ut = lnlt +(1-)lnct+1 , where (0,1). 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 activities are denoted by e while human capital evolves according to ht+1 = Bethtb(B>0, 00). Their labour income is used to purchase consumption goods.a) Solve an individual's maximisation problem and find the optimal allocation of time between leisure and learning activities. Provide detailed intuition for your results.b) Analyse the dynamics of human capital and illustrate them on a phase diagram. What are the parameter conditions necessary for the economy to sustain a positive growth rate in the long- run? Explain why.