申論題

3. Asset Pricing (25 points)
Consider an endowment economy with two periods, t = 0, 1. There are agents with mass one, and an agent endows units of consumption goods at the beginning of period t = 0, 1. The consumption good is nondurable and will vanish after it is consumed. The agent's lifetime utility is
where c_t is the consumption at period t, andis the time discount factor. There is a bond market that opens at period O, and agents can purchase or issue one-period real bonds at the market. A one-period real bond issued at period O matures at period 1, and the issuer of the bond must pay 1 unit of consumption goods to the bond holder when the bond matures.
 The bond market is competitive, Let bo denote an agent's net purchases of the bond, and let q_o denote the equilibrium price of the one-period real bond in terrns of period O consumption goods. Then the agent's period O and period 1 budget constraints are
  
 Note that the agents are the only participants in the bond market, but there is no government or any other people outside the economy engaging in the market. (a) (10 points) Solve for the equilibrium price of the one-period real bond, qo.