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An illustrative problem 347
Table 13.3 – Calculation of values for the tentative management–union deal
Value
Normalized
weight Value × weight
Management
Pay rise of 3% 100 0.625 62.5
3 extra days’ holiday 0 0.3125 0
Reinstatement of staff 0 0.0625 0
Value of deal 62.5
Union
Pay rise of 3% 0 0.348 0
3 extra days’ holiday 100 0.435 43.5
Reinstatement of staff 100 0.217 21.7
Value of deal 65.2
would receive an extra 3 days’ holiday per year and the sacked workers
would be reinstated. Table 13.3 shows how the value of this deal to the
management and the union was calculated.
During the negotiations one of the management team had used a
computer to calculate the management and union values for all possible
deals (assuming, for simplicity, that the percentage increase in pay
would be a whole number). The results of these calculations are shown
in Figure 13.8. On this graph the efficient frontier represents the set
of agreements which are such that no party can improve its position
without worsening the position of the other party. This means that if an
agreement does not lie on the efficient frontier then other agreements
are available which would either offer an improved position to both
parties or allow one party to improve its position without doing so at
the expense of the other.
It can be seen that the tentative deal (indicated by T on the graph) did
not lie on the efficient frontier. All the agreements on the frontier between
A and B were more efficient, and it was therefore in the interests of both
parties to try to improve on T by reaching one of these agreements. After
much more bargaining they eventually settled on deal X. This involved
a 7% pay rise but only one day’s extra holiday per year, though the staff
who had been fired would still be reinstated. Since the deal had a value
of 77.4 for the management and 74.9 for the union it represented a clear
improvement over the tentative deal for both parties.
It is obviously tempting to ask whether decision analysis can be used to
determine an ‘optimum’ agreement from those available on the efficient