6.(20 pointa) Shimadzu, a manufacturer of precise scientific instruments, relies

Question

6.(20 pointa) 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 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 (W,+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 $300,000from each sale, and 0 profit otherwise. What is the maximum level of bonus (B) Shimadzuu 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 wil you identified in part (a)? Find the corresponding equilibrium levels of 1 the company choose to go with the mechanism v. base wage (W) vi. bonus (B) vii. payoff to Shimadzu viii. payoff to the worker

Explanation / Answer

a) The firm just wants to hire sales people and do not care whether they work hard or not. So the firm should offer only base wage of 50,000 and no bonus.

i) So, Base Wage Wb = 50,000

ii) Bonus B = 0

iii) Let revenue to Shimadzu on selling of each equipment be x.

Then Payoff to Shimadzu per sales person = 0.2(x) - 50,000

iv) Payoff to worker = Wb + B = 50,000 + 0 = 50,000

b) Now the company wants to hire only hard working sales people. Let us say base wage is Wb and bonus is B.

The probability that the hard working guy makes a successful sale is 0.4, which means the probability of getting a bonus is also 0.4.

The probability of not making a sale is 0.6, which means the probability of having a disutility of effort is 0.6.

Based on the above two cases, the expected payout of a hard working sales guy is:

Ph = Wb + 0.4*B - 0.6*20,000 >=50,000 ---------------------- Equation 1

Clearly Ph should be more than 50,000 which is the minimum wage for retaining the sales people.

At the same time company wants to discourage lazy sales people. Payout for a lazy sales people would be:

PL = Wb + 0.2*B < 50,000 --------------------------------- Equation 2

We want PL < 50,000 to discouraage lazy sales people.

After solving equation 1 and 2, we get: B>60,000 and Wb<38,000.

So the minimum bonus for inducing hard work is 60,000.

c) Suppose Shimadzu has only one worker and he is hard working. Then there are two cases:

- Case 1: Successful sale (probability 0.4)

Payout to Shimadzu = 300,000 - (Wb+B)

- Case 2: No sale (probability 0.6)

Payout to Shimadzu = 0 - (Wb)

Expexted Payout to Shimadzu = 0.4*(300,000 - Wb -B) - 0.6*(Wb) >=0

Expecte payout to Shimadzu has to be positive in order for company to remain profitable and sustainable.

which gives 120,000 - 1.6(Wb) > B ---------------------------Equation 3

We also know that in order to retain hard working sales people their expected payout has to be more than 50,000

which means: Ph = Wb + 0.4*B - 0.6*20,000 >=50,000 --------------------- Equation 1

Solving equation 1 and 3 we get :

Wb > 38888.8888

B <56777.77

So the maximum bonus is 56777

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