Consider an exchange economy with three dates {t=0, 1, 2} and three agents {A, B, C} with utility functions: UA CAO + (1-1A)(CAI+ CA2) UB CBO+CB1+ (1-/B)CB2 Uc Cco+ Cc1+ Cc₂ The agents have the following endowments. Agent A owns a bond at t=0 and obtains w at t=1 with probability (1-PA). Agent B owns w at t=0 and obtains w at t-2 with probability (1-QB). Agent C owns w at t=1 and nothing at the other dates. Furthermore, the bond pays off x at t=2. The risk free rate and repo rate are zero. Suppose x is either 0 or 100 with equal probability and w-50.
Consider an exchange economy with three dates {t=0, 1, 2} and three agents {A, B, C} with utility functions: UA CAO + (1-1A)(CAI+ CA2) UB CBO+CB1+ (1-/B)CB2 Uc Cco+ Cc1+ Cc₂ The agents have the following endowments. Agent A owns a bond at t=0 and obtains w at t=1 with probability (1-PA). Agent B owns w at t=0 and obtains w at t-2 with probability (1-QB). Agent C owns w at t=1 and nothing at the other dates. Furthermore, the bond pays off x at t=2. The risk free rate and repo rate are zero. Suppose x is either 0 or 100 with equal probability and w-50.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Now suppose agent C can produce private information
about the true realization x at t=1 at the cost γ. Suppose lA=lB=φA=φB=1.
γ=23.
- What is the maximum amount LB that agent B can borrow with probability 1? What is the haircut?
- At t=0, what amount LA can agent A borrow from agent B in a repo trade at t=0 and what is the haircut?
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