Consider a setting similar to that in our string of examples. Let H = 900 and L = 200. Also, cH =…

Consider a setting similar to that in our string of examples. Let H = 900 and L = 200. Also, cH = 100 and the manager’s risk aversion measure is ρ = .1. (Low input cost and the outside certainty equivalent are, as usual, normalized to zero.) The primary evaluation measure is, as usual, biased toward the first task, with x = a1+.5a2+ ε. The noise term, ε, is a normal random variable with zero mean and a variance of σ 2 = 10, 000. A second evaluation measure is also available, as described in (15.8), and the noise term is a zero mean random variable with variance denoted σ 2 .

(a) Initially suppose the firm wants input H allocated entirely to the first task and that the weighting coefficient on the second performance measure is γ = .9. Determine an optimal linear contract and cost to the firm for σ 2 ∈ {0, 100, 1,000, 10,000}. Interpret your findings, paying special attention to the notion of good versus bad information.

(b) Next assume the firm seeks a balanced supply of input to each task. Repeat (a) above. Explain your finding.

(c) Continuing with the balanced case in (b) above, now let σ 2 = 10, 000. Determine an optimal arrangement for balanced supply of input for γ ∈ {.7, .9, 1, 1.2}. Interpret you findings, again paying special attention to the notion of good versus bad information.

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