This question is with regards to principal agent problem.

Consider the following principal agent problem with adverse selection. A rm faces a worker who may be one of two types, with equal probabilities. The rm's prots from a. type t worker are given by 7T1- : e 53-, z' = 1,2, where 63' is the effort supplied by a type 2' worker and 31- is the payment to a type 2' worker. The cost function of the more productive w0rker (type 1) is given by (:1 = 6% and the cost function of the less productive worker (type 2) is given by 02 = 263. The utility function of a. worker of type i is given by: m = sz Cz- and his opportunity cost utility is a? = 0. Find the solution to the rm's problem (assuming that effort is observable and contractible)