Let us consider John, who lives for three periods (t = 0, 1, 2) and likes consume both non-durable goods (c) and housing (H). In period 0, the young (and poor) John lives with his strict parents and has no choice whatsoever on his consumption bundle. For simplicity, let us assume that he receives a fixed utility of Vo = 0 in this period. At the end of period 0 (i.e. when John is about to graduate from a college and start living on his own), John receives an endowment of An from his parents deposited in his saving account as well as a house of size Ho. Between period f and { + 1, each dollar deposited in the saving account receives an interest of r dollars. In period f = 1,2, John splits his budget between non-durable consumption, ", and investment in housing , hy. Each unit of non-durable goods cost p dollars and each unit of housing investment cost of dollars (think about this cost as how much John has to pay to expand his house by a square feet). Housing depreciates at rate 6. That is, if John lives in a house of size H-1 and decides to invest he units into housing in period t, he will end up, in period t, with a house of size He =(1-6)Hi-1+ h Suppose John receives wage of y1 dollars in period 1 as a young worker and wage of yz dollars in period 2 as he advances through his career (assume that he works for his entire life time, again poor John :(.) Let John's life-time utility function be U(c, C2, H1, H2) =u(c), H1) + Bu(c2, H2) where, for t = 1, 2, we have u(c, H.) = log(c) + (1 -a) log( H.) Let us denote by A, John's balance in the saving account at the end of period 1 and suppose the balance at the end of period 2 is As = 0 (the bank shuts down John's account after he dies and he is not allowed to hold negative balance right before that happens). Assume for now that John can both freely invest and disinvest (i.e. sell away some fraction of his house) in housing in each period as well as freely borrow and save. That means it is possible that John choose to have Aj