4. (30 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 multiperiod model can be used to think of how house prices are determined. Suppose the instantaneous utility function is \"((215,313) 2 111(61) + 1.11014), where c; as usual stands for consumption in period t, and now h; stands for the level of housing services an individual enjoys in period t (i.e., the \"quantity\" of house an individual owns). Denote by H; the nominal price of a house in period t. The quantity of house owned at the beginning of period t is ht-\" and the quantity of house owned at the end of period t is h,, 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 flow budget constraint in period t as 1310: + (1 + \"Eta\" htl) = YE, where K is nominal income over which the consumer has no control and t is an AdValorem tax collected on housing service transaction. Note for simplicity we have omitted other assets from the model, houses are the only assets in this model. a. Solve for the nominal price of a house in period t, Ht. b. How does the consumer's optimal choice of each good is affected by a policy shift from t = 0 to t > 0