Changes

First, note that <math>B>C</math>. Within the algebra, note that the utilities are identical except for the exponents. Because Note that <math>\sum_{i\neq j} z(e_{j})+z-1>\sum_{i\neq j} z(e_{j})</math>because <math>z-1>0</math>. As such, we know that the inequality always holds. As for the intuition: Note that the lotteries are identical except for the payoff in <math>\frac{1}{N}</math> of the time. If he works, this value is higher, so he prefers to work.