A salesperson for Fuller Brush has three options: quit,put forth a low-effort level, or put forth a high-effort level.Suppose for simplicity that each salesperson will either sell$0, $5,000, or $50,000 worth of brushes. The probability ofeach sales amount depends on the effort level in the mannerdescribed in Table 8.If the salesperson is paid $w, then he or she earns abenefit w1/2. Low effort costs the salesperson 0 benefit units,while high effort costs 50 benefit units. If the salespersonwere to quit Fuller and work elsewhere, then he or she couldearn a benefit of 20. Fuller wants all salespeople to put fortha high-effort level. The question is how to minimize the costof doing it. The company cannot observe the level of effortput forth by a salesperson, but they can observe the size ofhis or her sale. Thus, the wage is completely determined bythe size of the sale. Fuller must then determine w0 wagepaid for $0 in sale, w5000 wage paid for $5,000 in sales,and w50,000 wage paid for $50,000 in sales. These wagesmust be set so that the salespeople value the expected benefitfrom high effort more than quitting and more than loweffort. Formulate (and solve on LINGO) an NLP that can beused to ensure that all salespeople put forth high effort. Thisproblem is an example of agency theory.† Effort LevelSize of Sale ($) Low High50,000 .6 .305,000 .3 .250,000 .1 .5
A salesperson for Fuller Brush has three options: quit,
put forth a low-effort level, or put forth a high-effort level.
Suppose for simplicity that each salesperson will either sell
$0, $5,000, or $50,000 worth of brushes. The probability of
each sales amount depends on the effort level in the manner
described in Table 8.
If the salesperson is paid $w, then he or she earns a
benefit w1/2. Low effort costs the salesperson 0 benefit units,
while high effort costs 50 benefit units. If the salesperson
were to quit Fuller and work elsewhere, then he or she could
earn a benefit of 20. Fuller wants all salespeople to put forth
a high-effort level. The question is how to minimize the cost
of doing it. The company cannot observe the level of effort
put forth by a salesperson, but they can observe the size of
his or her sale. Thus, the wage is completely determined by
the size of the sale. Fuller must then determine w0 wage
paid for $0 in sale, w5000 wage paid for $5,000 in sales,
and w50,000 wage paid for $50,000 in sales. These wages
must be set so that the salespeople value the expected benefit
from high effort more than quitting and more than low
effort. Formulate (and solve on LINGO) an NLP that can be
used to ensure that all salespeople put forth high effort. This
problem is an example of agency theory.†
Effort Level
Size of Sale ($) Low High
50,000 .6 .3
05,000 .3 .2
50,000 .1 .5
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