B.1.2 A worker produces a product that is subject to two separate tests. If the worker puts in effort there is: probabil

[answerhappygod]

B 1 2 A Worker Produces A Product That Is Subject To Two Separate Tests If The Worker Puts In Effort There Is Probabil 1 (464.85 KiB) Viewed 27 times

B.1.2 A worker produces a product that is subject to two separate tests. If the worker puts in effort there is: probability p2 that the product passes both tests, probability 2p(1 – p) that it passes one test, and probability (1–p)2 that it passes no tests. If the worker does not put in effort these probabilities are: q?, 2q(1 – 9), (1 – 9)2; where q <p. The manager decides to pay the worker the wage u if both tests are passed, v if only one test, and w if no tests are passed. The worker has the utility Væ- c if she receives the wage x e {w, v, u} and puts in effort. If she does not put in effort she has the utility Vx. The worker can earn the utility U from working elsewhere. (a) What conditions must the wage contract (u, v, w) satisfy if the worker is willing to work at the firm? (b) What conditions must the wage contract (u, v, w) satisfy if the worker prefers high effort to low effort? Write the condition you find in the simplest possible form and explain why the firm would not want v = w in this case? (c) The firm decides that it is content with low effort from the worker. Write down and solve a constrained optimization that describes the cheapest way for the firm to achieve this. Interpret what (d) The firm decides it wants high effort from the worker, but ignores the possibility that the worker might leave the firm and go elsewhere. The firm also decides to pay a wage of zero if both tests are failed. Write down the constrained optimization that describes the firm's cost minimization in this case. (e) Solve this constrained optimization and explain what economic effects it captures. you find.