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equilibrium

equilibrium

Microeconomic Theory
Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter2: Mathematics For Microeconomics
Section: Chapter Questions
Problem 2.16P
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Each student in Econ 99 is either above the average, the average or below the average, and there is an equal proportion of each type. Regardless of one's type, being thought to be above the average is worth 12; being thought to be the average is worth 9; and being thought to be below the average is worth 0. One way in which a student can try to indicate their type to others is by choosing 'to signal. This signal is a crude `yes-or-no' choice; that is, each student can only choose whether to signal or not. The cost of the signal is 20 for below-the-average types; 1 for the average types; and O for above-the-average types. Whether or not a student chooses to signal, after he or she has made that decision, he or she must take a compulsory test. The outcome of the test is completely independent of whether or not a student has signaled. Above-the-average types always pass the test; below- the-average types never pass; and the average types pass with probability .5. i) Suppose there were an equilibrium in which only the average types signaled. In such an equilibrium, what must the class of Econ 99 believe when it sees a student signaling and passing the test; signaling and failing; not signaling and passing; or not signaling and failing? ii) Explain that there is indeed an equilibrium in which only the average types signal.
Transcribed Image Text:Each student in Econ 99 is either above the average, the average or below the average, and there is an equal proportion of each type. Regardless of one's type, being thought to be above the average is worth 12; being thought to be the average is worth 9; and being thought to be below the average is worth 0. One way in which a student can try to indicate their type to others is by choosing 'to signal. This signal is a crude `yes-or-no' choice; that is, each student can only choose whether to signal or not. The cost of the signal is 20 for below-the-average types; 1 for the average types; and O for above-the-average types. Whether or not a student chooses to signal, after he or she has made that decision, he or she must take a compulsory test. The outcome of the test is completely independent of whether or not a student has signaled. Above-the-average types always pass the test; below- the-average types never pass; and the average types pass with probability .5. i) Suppose there were an equilibrium in which only the average types signaled. In such an equilibrium, what must the class of Econ 99 believe when it sees a student signaling and passing the test; signaling and failing; not signaling and passing; or not signaling and failing? ii) Explain that there is indeed an equilibrium in which only the average types signal.
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