In Diamond Dybvig (DD) model of bank run, each person is either an early type, or a late type, with probability 1/2 and 1/2. Utility function is u(c)=1-1/c. If an agent doesn't know their type, then their utility is Eu=1/2*(1-1/c1)+1/2*(1-1/c2), where c1 is how many potatos they eat in period 1, c2 is how many potatos they eat in period 2. If an agent is promised 2 potatos in period 1 and 4 potatos in period 2, their lifetime utility =______.

Microeconomic Theory
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ISBN:9781337517942
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Chapter18: Asymmetric Information
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Problem 18.8P
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In Diamond Dybvig (DD) model of bank run, each person is either an early type, or a late type, with probability 1/2 and 1/2.
Utility function is u(c)=1-1/c.
If an agent doesn't know their type, then their utility is Eu=1/2*(1-1/c1)+1/2*(1-1/c2), where c1 is how many potatos they eat in period 1, c2 is how many potatos they eat in period 2.
If an agent is promised 2 potatos in period 1 and 4 potatos in period 2, their lifetime utility =______.

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