9781118041581

Multiple-Issue Negotiations 647

profit increases as one moves north or west in the diagram, that is, as R

increases (for fixed Q) or Q falls (for fixed R).

The interpretation of the buyer’s contours (the colored curves) is analogous,

but the orientation is reversed: the buyer profits from lower R and/or higher Q,

that is, from south and east movements in Figure 15.2. In particular, note that the

zero-profit contour is uppermost in the figure and that the buyer’s profit increases

with moves to lower contours.^7 How can we use these profit contours to identify

efficient agreements? The answer is provided by the following important result:

An agreement is efficient if, and only if, it lies on buyer and seller profit contours

that are tangent to each other.

50

πS = 30

πB = 0

πB = 7.2

πS = 18

πS = 7

πS = 0

πB = 30

π πB = 23

B = 12

Payment (R)

40

30

20

10

0 5 1015202530

Quantity:

Q = 12

Optimal

quantity:

Q = 20

Quantity (Q)

B

A

C

D

E

FIGURE 15.2

A Quantity-Price

Contract

(^7) Both players’ contours are upward sloping but have opposite curvatures. The seller’s contours
are convex because cost increases more and more steeply with increases in Q. The buyer’s contours
are concave because the marginal benefit from extra Q declines.
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