申論題

(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 at the beginning of each period, then holding ht unit of houses generates ou(h.) units of utility to the agent. Where a ＞ O represents the relative importance of housing utility to consumption utility. We assume that houses are perfectly durable, and that means houses do not vanish or depreciate 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 be ha, then the agent's lifetime utility
After agents receive the living service in each period, the housing market opens. The housing market allows agents to exchange between houses and consumption goods. Let p_t denote the price of houses in terms of consumption goods at period t. Solve for po and p₁.