5. (20 points total) Suppose a firm employs a worker in a job that requires effort devoted to two tasks - tasks 1 and 2, which get effort E1 and E2. The cost of effort function is C(E1,E2) = (Er?)/10 + (E2) /2. The firm pays each worker a + bi.E1 + b2.E2. The worker's utility is income (that is, a + b1.E1 + b2.E2 - C(E1,E2)). The firm's production function is y = E1 + E2, and the output price is fixed at 1. a. (10) Show that the optimal contract has b1 = 1 and b2 = 1. b. (5) Suppose instead that the firm's production function is y = 2.min(E1, E2). What are the optimal values of the contract parameters b, and b2 in this case? [Note: The production function above is the same as y = min(2E1, 2E2).] c. (5) Why, in part b., is the optimal b2 higher than in part a.? And can you explain the exact difference between the optimal value of b2 in parts a. and b