2. A risk neutral worker engages in two different tasks, task 1 and task 2. Let r 1 and (.2 denote the effort he exerts in each, respectively, and assume r1 -I- f’2 I. Effort is privately known only to the worker and also costly to exert. The agent’s cost of effort is defined by the following function , (•I —et
I1r i • r2)
where o .o. The firm’s valuation depends on the amount of effort the worker puts into task 1, only. It is repre-sented by the strictly increasing and concave function 1*((.1). The firm possesses a monitoring technology that allows it to observe a noisy signal of the worker’s total effort. This monitoring technology emits the signal — I if it thinks effort is high and .s — 0 if it thinks effort is low. The probability I is
l’Is — 1 k l'( 21 -(1 I 2.
In addition to paying the worker the fixed wage b’ > 0, the Principal has implemented a bonus scheme, whereby the worker is paid > 0 if and only if .s — I.
(a) (15 points) Set the Principal’s problem and intuitively explain it. How would you interpret f ?
(b) (15 points) What is the optimum F? Intuitively discuss your result.
(c) (20 points) What is the Principal’s cost of implementing effort at the optimum? Discuss your result.
Total for Question 2: 50
