d} a) Two agents are competing for a promotion. The winner gets 8, the loser gets zero. The probability worker 1 wins the prize is given by: Prob(1 wins}=.9 + U.1(E1-E2), where agent 1's effort is given by E1 and agent 2's by E2. Each agent's disutility 2 of effort is given by E f2. If both agents work equally hard, which one is more likely to win the promotion? Write down the formula for the expected utility of agent 1. Find hisfher optimal effort as a function of the prize spread, 8. Write down the formula for the expected utility of agent 2. Find hisfher optimal effort as a function of the prize spread, 8. Explain why, in this (trample, both agents work eqaafhr hard for any given prize spread. 1n the blank spreadsheet that is provided for this question, think of the various values of S as different possible prize spreads the rm is considering. In column 2, ll in the (common) effort level both agents will choose. Assume neither agent is paid to show up for work (51:13). Using the definition of utility (and the fact that both agents work equally hard) ll in both agents' utility in columns 3 and 4. Suppose that, to get agent 1 to take the job, she must attain an expected utility level of 212}. To get agent 2 to take the job, he must get an expected utility of 5. In columns 5 and 6, compute the level of a for each agent that just induces them to take thejob (Le. that gives them expected utilities of exactly 20 and 5 respectively}. Suppose the rm chooses the levels of a given by part f. Let the expected value of each agent's output be given by 10E (where E is the agent's effort). Now compute the nn's output in column T, and its prots in column 8. What is the prot- maximizing prize spread? Comment on the different levels of a for the two workers at this point