Consider the following team-production model in which there are two workers and team output 32e1 + 20e2, where e1 and e2

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Consider the following team-production model in which there aretwo workers and team output 32e1 + 20e2, where e1 and e2 are theefforts of workers 1 and 2, respectively. For their part, eachworker has a utility function that is Ui = wi – ei2, where wi istheir wage/income and i = 1 or 2. a. What are the first-best levelsof effort for both workers? b. Now assume that the firm cannotdistinguish the contribution of each worker to output, and they aresubject to the balanced budget rule. Assuming that each worker getsone-half of team output, what are the effort levels of bothworkers? Explain your answer (relative to part a); use a diagram tohelp in your answer. c. Now assume that worker 2 is actually amanager. As a manager worker 2 puts in e2 = 0. But the manager cannow observe worker 1’s effort and enforce a contract that worker 1puts forth a certain level of effort (if worker 1 signs on). Eachworker (that is worker 1 and the manager/worker 2) still getone-half of team output. What level of effort does the managerrequire of worker 1? Explain your answer. Compare your answer topart b.