In this exercise, we will explore what happens when we include taxes and government spending (public investment) in the Becker-Tomes model that you learnt in class. In this economy, there exists I family dynasties; denote by i = 1, 2, ..., I. In each family, there is only one parent and one child; i.e., there is no population growth and reproduction is asexual. Finally, each individual lives for just 2 periods: (i) childhood (c), and (ii) adulthood (a). The index t denotes the time of birth; i.e., denotes the "birth cohort" that each individual belongs to. 1(a) Suppose that the parent pays taxes that are proportional to her income. The tax rate is given by . The taxes are used to fund public investment in children's human capital. From the point of view of the parent, the level of public investment that accrues to her child is taken as exogenously given. Write down and explain the parent's budget constraint