Two entrepreneurs (1 and 2) own two separate firms. The output of the i-th firm is given by Yi = Bie, i=1,2 Where Yi is the i-th entrepreneur revenue Bi is the marginal productivity of the effort of the i-th entrepreneur e; is the effort exerted by the i-th entrepreneur. The cost of exerting effort for the i-th entrepreneur is . 1) Compute the optimal effort exerted by the i-th entrepreneur [5 points] Assume now that the entrepreneurs decide to join forces and split equally the combined revenues of the two firms. The combined revenues are y + y2. The cost of exerting effort is the same as before for both entrepreneurs. 2) Write the optimization problem of the i-th entrepreneur and compute the optimal effort of the i-th entrepreneur in the combined case. [5 points] 3) Are the two entrepreneurs better off or worse off when joining the two firms? Explain why. [5 points] Two entrepreneurs (1 and 2) own two separate firms. The output of the i-th firm is given by Yi = Bie, i=1,2 Where Yi is the i-th entrepreneur revenue Bi is the marginal productivity of the effort of the i-th entrepreneur e; is the effort exerted by the i-th entrepreneur. The cost of exerting effort for the i-th entrepreneur is . 1) Compute the optimal effort exerted by the i-th entrepreneur [5 points] Assume now that the entrepreneurs decide to join forces and split equally the combined revenues of the two firms. The combined revenues are y + y2. The cost of exerting effort is the same as before for both entrepreneurs. 2) Write the optimization problem of the i-th entrepreneur and compute the optimal effort of the i-th entrepreneur in the combined case. [5 points] 3) Are the two entrepreneurs better off or worse off when joining the two firms? Explain why. [5 points]