'2. {50 points} Consider an enriched version of the two-period consumptionsavings framework from Chapter 3 and 4, in which the representative individual not only makes decisions about consumption and savings but also housing purchases. For this particular application, it is useful to interpret period 1 as the \"young period\" of the individual's life, and interpret period '2 as the \"old period\" of the individual's life. In the young period of an individual's life, utility depends only on period-1 consumption c1. In the old period of an individual's life, utility depends both on period2 consumption 03 , as well as histh \"quantity\" of housing [denoted h }. From the perspective of the beginning of period 1, the individual's lifetime utility function is lnc1+lncg + Ink, where ln{r} stands for the natural log function; the term lnh indicates that people directly obtain happiness from their housing. Due to the \"timetobuild\" nature of housing [i.e., it talaes time to build a housing unit], the representative individual has to incur expenses in histh young period to purchase housing for histh old period. The real price in period 1 [i.e., measured in terms of periodl consumption} cfa \"unit\" of housing (again, think of a unit of housing as square footage} is pi\