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Homework answers / question archive / Consider the following example
Consider the following example. A risk-neutral worker can choose Low or High effort. The manager cannot observe the worker's action, but the manager can observe the realized revenue for the firm (either $200 or $1100). Low Effort Cost for worker=$0 Probability Low Revenue ($200)=60% Probability High Revenue ($1100)=40% High Effort Cost for worker=$50 Probability Low Revenue ($200)=40% Probability High Revenue ($1100)=60% Instead of offering a flat wage, the manager is trying a new payment scheme. The manager is currently offering to the worker a payment equal to 30% of the revenue of the firm. Given this payment, the firm's expected profit will be:
Answer:
Expected profit = $518.
Expected revenue in case of low effort =
60%($200) + 40%($1100) = $560
Wage (expected) = 30%($560) = $168
Cost to worker = $0
So, net benefit for worker = $168 - $0 = $168
Expected revenue in case of high effort =
40%($200) + 60%($1100) = $740
Wage = 30%($740) = $222
Cost to worker = $50
Net benefit of worker = $222-$50 = $172
The net benefit (wage minus cost) to worker is higher if she chooses to put high effort. So, the worker will choose to put high effort.
Expected revenue in case of high effort is $740
Wage paid to worker is 30%($740) = $222.
Expected Profit = $740-$222 = $518.
Therefore, expected Profit in case of the given payment scheme is $518.
