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Note that CARA utility is <math>u(c)=1-e^{-\rho c}</math>. An employee i's utility from working (if others work) is <math>1-\exp[-\rho(\frac{1}{N}\sum_{i\neq j} z(e_{j})+\frac{1}{N}z(e_{i})-1)]</math>.
An employee i's utility from working <i>if others are not working</i> is: <math>\frac{1}{N}(1-\exp[-\rho(\sum_{i\neq j} z(e_{j}...)])</math>.
An employee i's utility from NOT working if others are not working is: <math>1-\exp[\frac{1}{N}\sum_{i\neq j} z(e_{j})+\frac{1}{N}z(e_{i})-1]</math>
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