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) = (E12)/10 + (E2)2/2. The firm pays each worker a + b1E1 + b2E2. The workers utility is income (that is, a + b1E1 + b2E2 C(E1,E2)). The firms production function is y = E1 + E2, and the output price is fixed at 1.

a)Show that the optimal contract has b1 = 1 and b2 = 1.

b)suppose instead that the firms production function is y = 2min(E1, E2). What are the optimal values of the contract parameters b1 and b2 in this case? [Note: The production function above is the same as y = min(2E1, 2E2).]

c) 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.?