The wage the worker will receive will be The profits for the firm will be π=(10④4)-12=$12， With this principal-agent relationship,the wage that the individual worker receives is related to the revenue of the firm.Therefore,we see greate effort on the part of the worker and,as a result,greater profits for the firm w=R-12.5 Again,the worker will attempt to maximize the wage net of the effort required to obtain that wage:that is.the worker will attempt to maximize: w-e=10e-e)-12.50-e.or9e-e2-12.50. To find the maximum effort that the worker is willing to put forth.take the first derivative with respect ee-d2-129-2e=0.ore=45 de The wage the worker will receive will be w=R-12.50=(0)4.5)-4.52)-12.5=12.25 The profits for the firm will be π=(104.5)-4.52)-12.25=$12.50. With this principal-agent relationship,we find that the wage of the worker is more directly related to the performance of the firm than in either a or b. We find that the worker is willing to supply even even higher profits for the firm. The wage the worker will receive will be The profits for the firm will be  = ((10)(4) - 4 2 ) - 12 = $12. With this principal-agent relationship, the wage that the individual worker receives is related to the revenue of the firm. Therefore, we see greater effort on the part of the worker and, as a result, greater profits for the firm. c. w = R - 12.5. Again, the worker will attempt to maximize the wage net of the effort required to obtain that wage; that is, the worker will attempt to maximize: w − e = 10e − e 2 ( )−12.50− e, or 9e− e 2 −12.50. To find the maximum effort that the worker is willing to put forth, take the first derivative with respect to effort, set it equal to zero, and solve for effort: d 9e − e 2 ( −12.5) de = 9 − 2e = 0, or e = 4.5. The wage the worker will receive will be w = R− 12.50 = (10)(4.5)− 4.5 2 ( )−12.5 =12.25. The profits for the firm will be  = ((10)(4.5) - 4.52 ) - 12.25 = $12.50. With this principal-agent relationship, we find that the wage of the worker is more directly related to the performance of the firm than in either a or b. We find that the worker is willing to supply even more effort resulting in even higher profits for the firm