This problem substitutes financial health with housing in a 2 period consumption savings model. The representative consumer has the utility function u(c1, c2) = lnc1 + lnc2 with each period budget constraint as : 1) P1c1 + H1h1 = H1h0 + Y1...2) P2c2 + H2h2 = H2h1 + Y2...where P is the price level of consumption good, H is the unit value (price) of housing, h1 is the level of housing decided to be owned at the end of period 1 and h2 is the level of housing decided to be owned at the end of period 2. h0 is the level of housing in the beginning of period 1 and it is assumed to be equal to 0. a) What is the optimal choice of h2? Explain. b) Let H2 / H1 = 1 + v, where v is the nominal valuation rate of the house (rate of increase in the nominal value-price of housing from period 1 to period 2). Using the period by period budget constraint, show that the Lifetime Budget Constraint is P1c1 + ((P2c2) / (1+v)) = Y1 + (Y2 / (1+v)). c) Use the Lifetime Budget Constraint and write down the Lagrangian of the consumer and the first order conditions.