Changes

If some shares can be different, then the optimal contract is where some number $<math>M<N$ </math> workers get $<math>s_{i}=\frac{1}{z}$</math>, and the remainder get $<math>s_{i}=0$</math>. $<math>M$ </math> is the largest number such that $<math>\frac{M}{Z}\leq 1$</math>. $<math>M$ </math> workers will provide effort, and $<math>N-M$ </math> workers will shirk.