Two investors have each deposited D with a bank. The bank has invested these deposits in a long-term project. If the bank is forced to liquidate its investment before the project matures, a total of 2r can be recovered, where D > r > D/2. If the bank allows the investment to reach maturity, however, the project will pay out a total of 2R, where R > D. There are two dates at which the investors can make with- drawals from the bank: date 1 is before the bank's investment matures; date 2 is after. For simplicity, assume that there is no discounting. If both investors make withdrawals at date 1 then each receives and the game ends. If only one investor makes a withdrawal at date 1 then that investor receives D, the other receives 2r – D, and the game ends. Finally, if neither investor makes a withdrawal at date 1 then the project matures and the investors make withdrawal decisions at date 2. If both investors make withdrawals at date 2 then each receives R and the game ends. If only one investor makes a withdrawal at date 2 then that investor receives 2R-D, the other receives D, and the game ends. Finally, if neither investor makes a withdrawal at date 2 then the bank returns R to each investor and the game ends.

Two investors have each deposited D with a bank. The bank has invested these deposits in a long-term project. If the bank is forced to liquidate its investment before the project matures, a total of 2r can be recovered, where D > r > D/2. If the bank allows the investment to reach maturity, however, the project will pay out a total of 2R, where R > D. There are two dates at which the investors can make with- drawals from the bank: date 1 is before the bank's investment matures; date 2 is after. For simplicity, assume that there is no discounting. If both investors make withdrawals at date 1 then each receives and the game ends. If only one investor makes a withdrawal at date 1 then that investor receives D, the other receives 2r – D, and the game ends. Finally, if neither investor makes a withdrawal at date 1 then the project matures and the investors make withdrawal decisions at date 2. If both investors make withdrawals at date 2 then each receives R and the game ends. If only one investor makes a withdrawal at date 2 then that investor receives 2R-D, the other receives D, and the game ends. Finally, if neither investor makes a withdrawal at date 2 then the bank returns R to each investor and the game ends.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

### 2.2.B Bank Runs

Two investors have each deposited $ D $ with a bank. The bank has invested these deposits in a long-term project. If the bank is forced to liquidate its investment before the project matures, a total of $ 2r $ can be recovered, where $ D > r > D/2 $. If the bank allows the investment to reach maturity, however, the project will pay out a total of $ 2R $, where $ R > D $.

There are two dates at which the investors can make withdrawals from the bank: date 1 is before the bank's investment matures; date 2 is after. For simplicity, assume that there is no discounting. If both investors make withdrawals at date 1 then each receives $ r $ and the game ends. If only one investor makes a withdrawal at date 1 then that investor receives $ D $, the other receives $ 2r - D $, and the game ends. Finally, if neither investor makes a withdrawal at date 1 then the project matures and the investors make withdrawal decisions at date 2. If both investors make withdrawals at date 2 then each receives $ R $ and the game ends. If only one investor makes a withdrawal at date 2 then that investor receives $ 2R - D $, the other receives $ D $, and the game ends. Finally, if neither investor makes a withdrawal at date 2 then the bank returns $ R $ to each investor and the game ends.

**2.22.** Provide the extensive- and normal-form representations of the bank-runs game discussed in Section 2.2.B. What are the pure-strategy subgame-perfect Nash equilibria?

(Note: The text prompts the reader to refer to a specific section of a source discussing the bank-runs game, and queries about its strategic representations and equilibria.)

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