The Show more 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)
The Show more 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 + Y12) P2c2 + H2h2 = H2h1 + Y2where 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. Show less
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