Is it permissible to hire a shepherd for a specified period in exchange for a known fraction of the flock?

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It is valid to hire a shepherd for a known duration in exchange for half or a known fraction of the flock. This arrangement is valid because the labor (work), the wage (the share of the flock), and the duration are all specified and known. The resulting increase (offspring) is considered to be shared between the parties based on ownership, because the share designated to the worker is deemed to be his property from the moment of the contract, thus entitling him to its increase, similar to a purchase.