(c) (5 points) Now we introduce one more good, the houses, into the economy. As in question(b), an agent endows

 units of consumption goods at the beginning of period t = 0, 1, 2.Moreover, an agent also owns e units of houses in the beginning of period 0. Houses are divisible,and houses provide living services to their holders: let h, denote an agent's holding of houses atthe beginning of each period, then holding ht unit of houses generates ou(h.) units of utility tothe agent. Where a ＞ O represents the relative importance of housing utility to consumptionutility. We assume that houses are perfectly durable, and that means houses do not vanish ordepreciate over time or after they provide the living service.
 Let an agent's consumption be ct, and let her house holdings at the beginning of a period beha, then the agent's lifetime utility

After agents receive the living service in each period, the housing market opens. The housingmarket allows agents to exchange between houses and consumption goods. Let pt denote theprice of houses in terms of consumption goods at period t. Solve for po and p1.