Shimadzu, a manufacturer of precise scientific instruments, relies heavily on th

Question

Shimadzu, a manufacturer of precise scientific instruments, relies heavily on the efforts of its local salespeople. Selling an instrument requires either luck, high effort, or some combination of the two. A salesperson who chooses to work hard has a 40 percent chance of selling an instrument in a given year while a salesperson who chooses to slack off has a 20 percent chance. Practically no one manages to sell more than one instrument in a single year. Contracts for salespeople are designed on a year-by-year basis. Sales staff members do not mind risk; they choose employers based only on expected wage and the disutility of effort. Disutility of effort is equivalent to $20,000 per year if they work hard and $0 if they slack off. Even if a salesperson slacks off, he or she requires an average salary of at least $50,000 not to seek alternate employment.

Answer the following questions considering only the three mechanisms discussed in class: Fixed (Pure) wage, Pure Franchise, Wage - plus - bonus

a. What is the optimal compensation scheme if Shimadzu only wants slack effort, that is the company is only trying to hire workers but is not interested in whether the workers slack off or not? Find the corresponding equilibrium levels of: i. base wage (Wb) ii. bonus (B) iii. payoff to Shimadzu iv. payoff to the worker

b. Say the workers get a bonus (B) when they sell an instrument: they get paid the base wage, (Wb) if they do not sell an instrument, and get paid the base wage and the bonus (Wb+B) if they sell. What is the minimum level of bonus (B) that will achieve inducing high effort?

c. Consider the case Shimadzu has only one worker. Assume that Shimadzu receives a profit of $300,000 from each sale, and 0 profit otherwise. What is the maximum level of bonus (B) Shimadzu would be willing to pay to induce high effort from the worker?

d. Consider the case Shimadzu has only one worker. According to your analysis for the previous parts, in equilibrium, will Shimadzu choose to provide additional incentives (in this case, the bonus payment) to make sure that the worker chooses to work hard, or will the company choose to go with the mechanism you identified in part (a)? Find the corresponding equilibrium levels of: v. base wage (Wb) vi. bonus (B) vii. payoff to Shimadzu viii. payoff to the worker

Please show work clearly

Explanation / Answer

a. If it hires only slack workers, the chance of success is only 20%.

So, the company should ideally offer 20% as fixed wage and the rest as bonus.

A slack worker wants to earn at least $50,000, including fixed wage plus bonus.

i. the base wage (Wb) = 20% of 50,000 = $10,000

ii. Bonus (B) = 50,000 - 10,000 = $40,000

iii. payoff to Shimadzu = total profit - ns (50,000) - nf (10,000)

where ns is the number of successful sales persons (who sold at least 1 instrument)

and nf is the number of failed sales person (with no sale)

iv. payoff to the worker = 50,000

b. Wage in case they do not sell at all = Wb

Wage in case they make at least 1 sale = Wb + B

The difference is the bonus B.

B should be at least equal to the disutility of effort (i.e. perceived benefit of slacking off)

B = $20,000

c. For a high effort worker, the effective fixed income requirement = base wage + disutility

thus, effective wage for high effort (Whe) = 50,000 + 20,000 = $70,000

the average profit of the company = probability of success in sales . profit in sale

= 40% * 300,000 = $ 120,000

So, the maximum bonus that Shimadzu can give is 120,000 - 70,000 = $50,000

d. Assume the company makes $300,000 profit on every sale and it makes only 1 sale.

The employee must earn at least $50,000 per year.

If the employee chooses to slack off, the probabilistic profit is Ps = 20% * 300,000 = $60,000

If the employee chooses high effort, the probabilistic profit is Phe = 40% * 300,000 = $120,000

In the first case, after paying the employee $50,000, Shimadzu is left with 60,000 - 50,000 = $10,000

In the second case, after paying the employee, Shimadzu is left with 120,000 - 70,000 = $50,000

Since the profit is higher in the second case, it will give incentives to induce high effort.

v. Base wage = Previous fixed wage + disutility = 10,000 + 20,000 = $30,000

vi. Bonus = $40,000

vii. Payoff to Shimadzu = Average profit - sales person cost = 120,000 - 70,000 = $50,000

viii. Payoff to the worker = $70,000

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