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.

ENGR.ECONOMIC ANALYSIS
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Chapter1: Making Economics Decisions
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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?

Consider an exchange economy with three dates {t=0, 1, 2} and three agents {A, B, C} with
utility functions:
UA=CA0 + (1-lA)( CAi+ CA2)
UB=CB0+CB1+ (1-/B)CB2
Uc=Ccot Cci+ Cc2
The agents have the following endowments. Agent A owns a bond at t=0 and obtains w at t=1
with probability (1-QA). 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.
Suppose la=lg=QA=QB=1 for questions (a) to (c).
Transcribed Image Text:Consider an exchange economy with three dates {t=0, 1, 2} and three agents {A, B, C} with utility functions: UA=CA0 + (1-lA)( CAi+ CA2) UB=CB0+CB1+ (1-/B)CB2 Uc=Ccot Cci+ Cc2 The agents have the following endowments. Agent A owns a bond at t=0 and obtains w at t=1 with probability (1-QA). 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. Suppose la=lg=QA=QB=1 for questions (a) to (c).
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