Question 2 [24 points] Consider the following economy. Agent B owns w=100 at t=0 but wants to consume at t=1. In order to store his wealth, agent B wants to buy a security from agent A who owns an asset x that is used as collateral to backed that security. The payoff x of the asset is uniformly distributed between [100, 200] and realizes at t=2. Note, f(x)=1/100. Agent A is willing to sell the security if the price is equal expected payoff of the security. a) Suppose agent B buys a bond from agent A. What is the face value of the bond that agent B can buy for a price of 100? [3 Points) b) Suppose agent B buys equity from agent A. What is the fraction Bx that agent B can buy for a price of 100? [2 Points] At t=1, agent B wants to consume and sells the security (that he has bought from agent A) to agent C. Suppose agent C can learn about x by paying information cost y=3. If agent C does not acquire information, he is willing to buy the security for a price equals expected payoff. Suppose there is no new public information and x is still between [100, 200) at t=1. c) Agent B owns the bond. How much can he consume at t=1 by trading with agent C such that agent C buys with probability 1? [2 Points] d) Agent B owns equity. How much can he consume at t=1 by trading with agent C such that agent C buys with probability 1? [6 Points] e) In question (d) what is agent B exactly selling to agent C? A verbal description is enough. [2 Points] f) Compare the amount agent B can consume in (c) and (d) and provide an intuition for the result. [2 Points] Agent B owns the bond as in question (a). Now suppose after buying the bond at t=0, at t=1 there is a change in macroeconomic conditions and x is uniformly distributed between [0,200]. Note, f(x)=1/200. What is the value of the bond? [2 Points] h) How much can agent B consume at t=1 by trading with agent C such that agent C buys with probability 1? [3 Points] i) In question (h) what is agent B exactly selling to agent C? A verbal description is enough. [2 Points] Question 2 [24 points] Consider the following economy. Agent B owns w=100 at t=0 but wants to consume at t=1. In order to store his wealth, agent B wants to buy a security from agent A who owns an asset x that is used as collateral to backed that security. The payoff x of the asset is uniformly distributed between [100, 200] and realizes at t=2. Note, f(x)=1/100. Agent A is willing to sell the security if the price is equal expected payoff of the security. a) Suppose agent B buys a bond from agent A. What is the face value of the bond that agent B can buy for a price of 100? [3 Points) b) Suppose agent B buys equity from agent A. What is the fraction Bx that agent B can buy for a price of 100? [2 Points] At t=1, agent B wants to consume and sells the security (that he has bought from agent A) to agent C. Suppose agent C can learn about x by paying information cost y=3. If agent C does not acquire information, he is willing to buy the security for a price equals expected payoff. Suppose there is no new public information and x is still between [100, 200) at t=1. c) Agent B owns the bond. How much can he consume at t=1 by trading with agent C such that agent C buys with probability 1? [2 Points] d) Agent B owns equity. How much can he consume at t=1 by trading with agent C such that agent C buys with probability 1? [6 Points] e) In question (d) what is agent B exactly selling to agent C? A verbal description is enough. [2 Points] f) Compare the amount agent B can consume in (c) and (d) and provide an intuition for the result. [2 Points] Agent B owns the bond as in question (a). Now suppose after buying the bond at t=0, at t=1 there is a change in macroeconomic conditions and x is uniformly distributed between [0,200]. Note, f(x)=1/200. What is the value of the bond? [2 Points] h) How much can agent B consume at t=1 by trading with agent C such that agent C buys with probability 1? [3 Points] i) In question (h) what is agent B exactly selling to agent C? A verbal description is enough. [2 Points]
