A firm employs two workers, labelled by j and k. The output of the two workers are denoted by q j, qk respectively. They are determined by: q ,- = m J- + E} 4k = mk + 6k where m j, mk are the effort levels of the two workers; 5}, 5k are mean zero noises. The firm designs a tournament such that the workers compete by output---an amount of 2 is rewarded to a worker j if qj > qk and vice versa; the loser gets 1, which is smaller than 2. Suppose that the difference in the noise term 71 = 5k 51- has a standard normal density 42(1)). The corresponding cumulative density function is (1)01). The effort cost of the two workers are Cj(mj) = "1%, Ck(mk) = mi ** Part a (5 marks) State the first-order condition for m j. ** Part b (5 marks) Find the equilibrium effort in this tournament (hint: mj = mk due to symmetry). ** Part c (10 marks) Fid the total expected output of the firm in this tournament