3. Asset Pricing (25 points)
Consider an endowment economy with two periods, t = 0, 1. There are agents with mass one, and anagent endows

units of consumption goods at the beginning of period t = 0, 1. The consumptiongood is nondurable and will vanish after it is consumed. The agent's lifetime utility is

where ct is the consumption at period t, and

is the time discount factor. There is a bondmarket 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 pay1 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 qodenote 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 orany other people outside the economy engaging in the market.(a) (10 points) Solve for the equilibrium price of the one-period real bond, qo.