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 (put in high effort) has a 40 percent chance (probability of 0.4) of selling an instrument in a given year while a salesperson who chooses to slack off (put in low effort) has a 20 percent chance (probability of 0.2) of making a sale. 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 a salary of at least $50,000 not to seek alternate employment. (So, the worker's net payoff in alternative employment is $50,000.) Answer the following questions considering only the three mechanisms discussed in class: Fixed (Pure) wage; Pure Franchise; Wage-plus-bonus. a. Consider the optimal compensation scheme if Shimadzu is not concerned with whether the workers slack off and it pays the worker the same wage regardless of whether the worker makes a sale. The corresponding equilibrium level of fixed wage is b. Say the workers gets paid a bonus when they make a sale. So, the worker gets paid the low wage, WL, if they do not sell an instrument, and gets paid the high wage, WH, if they make a sale (interpret the low and high wage as was used in the examples we worked on, the high wage includes the base wage and bonus). The minimum level of high wage (WH) that the worker needs to get paid for working hard to be their best-response is
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 (put in high effort) has a 40 percent chance (probability of 0.4) of selling an instrument in a given year while a salesperson who chooses to slack off (put in low effort) has a 20 percent chance (probability of 0.2) of making a sale. 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 a salary of at least $50,000 not to seek alternate employment. (So, the worker's net payoff in alternative employment is $50,000.) Answer the following questions considering only the three mechanisms discussed in class: Fixed (Pure) wage; Pure Franchise; Wage-plus-bonus. a. Consider the optimal compensation scheme if Shimadzu is not concerned with whether the workers slack off and it pays the worker the same wage regardless of whether the worker makes a sale. The corresponding equilibrium level of fixed wage is b. Say the workers gets paid a bonus when they make a sale. So, the worker gets paid the low wage, WL, if they do not sell an instrument, and gets paid the high wage, WH, if they make a sale (interpret the low and high wage as was used in the examples we worked on, the high wage includes the base wage and bonus). The minimum level of high wage (WH) that the worker needs to get paid for working hard to be their best-response is
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text: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 (put in high effort) has a 40 percent chance (probability of 0.4) of
selling an instrument in a given year while a salesperson who chooses to slack off (put in low effort) has a 20
percent chance (probability of 0.2) of making a sale. 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 a salary of at least $50,000 not to seek alternate employment.
(So, the worker's net payoff in alternative employment is $50,000.)
Answer the following questions considering only the three mechanisms discussed in class: Fixed
(Pure) wage; Pure Franchise; Wage-plus-bonus.
a. Consider the optimal compensation scheme if Shimadzu is not concerned with whether the workers slack
off and it pays the worker the same wage regardless of whether the worker makes a sale. The corresponding
equilibrium level of fixed wage is
b. Say the workers gets paid a bonus when they make a sale. So, the worker gets paid the low wage, WL, if
they do not sell an instrument, and gets paid the high wage, WH, if they make a sale (interpret the low and
high wage as was used in the examples we worked on, the high wage includes the base wage and
bonus). The minimum level of high wage (WH) that the worker needs to get paid for working hard to be their
best-response is
c. Consider the case described in part (b) and assume that Shimadzu receives a profit of $300,000 from each
sale, and $0 profit if there are no sales. Also assume that Shimadzu has only one worker and, accordingly, its
payoff is the (profit-wage). The maximum level of high wage (WH) Shimadzu would be willing to pay to induce
high effort from the worker is
d. Given your answers to (b) and (c), under the wage-plus-bonus mechanism, the equilibrium level of low
wage is
and high wage is
+ '. Accordingly, the worker's best-response is to put in
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