4. (20 points) With all the talk in the news the past few years of soaring and then crashing house prices, let's see how our simple multi-period model can be used to think of how house prices are determined. Suppose the instantaneous utility function is u(c,5, ht), where 0,; as usual stands for consumption in period t, and now ht stands for the level of housing services an individual enjoys in period t (i.e., the \"quantity\" of house an individual owns). Denote by Ht the nominal price of a house in period t. The quantity of house owned at the beginning of period t is htil, and the quantity of house owned at the end of period t is ht, and assume that the quantity of house can be changed every period (think of this loosely as making additions, repairs, etc to your house on a regular basis). Thus, we can write the ow budget constraint in period t as PtCt + cht = chtil + Y}: where Yt is nominal income over which the consumer has no control. Note for simplicity we have omitted other assets from the model, houses are the only assets in this model. Solve for the nominal price of a house in period 15, Ht. Discuss qualitatively why the marginal rate of substitution between housing services and consumption appears in the pricing equation