10. balanced allocation Consider a setting as specified immediately above, except the noise term variances for the two measures are identical: σ2 =
σ2 = 15, 000.

Also recall α denotes the weighting on the second task in the first measure (x) and γ denotes its counterpart in the second measure. A balanced supply of input H is sought.

(a) Determine an (α, γ), such that the two measures are equally weighted in the optimal contract. Provide an intuitive explanation.

(b) Repeat

(a) above, but for the case where the first measure is more heavily weighted.

(c) Repeat

(a) above, but for the case where the second measure is more heavily weighted.

(d) Write a short paragraph on the virtues of a balanced approach to such evaluation, one where the measures are, well, equally weighted.