Question

A worker can exert two effort levels, good or bad, which induce a production error with probabilities 0.25 and 0.75 respectively. His utility function is U(w, e) = 100 - (10 * e) - c, where w is the wage received and c takes the value of 2 if effort e is good and 0 if effort is bad. Production errors are observable and can be introduced into the worker's contract, but effort cannot. The production obtained is worth 20 if there are no errors and 0 otherwise. The principal is risk-neutral with a utility function Up(x, w) = x - w. Assume the worker has a reservation utility equal to 0. a. Let the wage offered be ws if the production is successful, and wf if the production fails. a. What is the optimal contract (ws, wf) if the principal wants to induce a good effort level from the worker? b. Should the principal try to induce a high effort level from the worker?

          A worker can exert two effort levels, good or bad, which induce a production error with probabilities 0.25 and 0.75 respectively. His utility function is U(w, e) = 100 - (10 * e) - c, where w is the wage received and c takes the value of 2 if effort e is good and 0 if effort is bad. Production errors are observable and can be introduced into the worker's contract, but effort cannot. The production obtained is worth 20 if there are no errors and 0 otherwise. The principal is risk-neutral with a utility function Up(x, w) = x - w. Assume the worker has a reservation utility equal to 0.

a. Let the wage offered be ws if the production is successful, and wf if the production fails.

a. What is the optimal contract (ws, wf) if the principal wants to induce a good effort level from the worker?
b. Should the principal try to induce a high effort level from the worker?

Added by Mitchell E.

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