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Fig. 14.2 Non-linear case
y
B(0,1) a
(1,1)
b
(0,0) A(1,0) x
symmetrical point with respect to C [conditions ( 14.1a ) and ( 14.1b )]. But A can be
better off if he moves towards the diagonal (a simple isoquant argument underpins
this), but B has then to retreat towards the diagonal, so a deal will be very
problematic, and the same will occur in the reverse situation. So a first solution
concept, taking into account externalities mentioned previously, is to try and end up
on the diagonal.
A then maximises:
1 ˁ
x A ˁ 1
ˆ A ¼
ð
x A
Þ
ð
14
:
6a
Þ
leading up to:
x A o
¼ ˁ
ð
14
:
6b
Þ
leaving 1
ρ
to B ; similarly, B with characteristic parameter
˃
, ends up with:
x B o
¼ ˃
ð
14
:
7
Þ
leaving A with 1
.; the so-called “Pareto-circlets” denote optimal values.
However, conditions ( 14.1a ) and ( 14.1b ) are clearly only satisfied if 1
˃
,so
individual maximising behaviour leads to non-compatible solutions. This compati-
bility can be restored—and this is a second solution concept—if a relative “price”
of y with respect to x is introduced; this leads to the system:
ρ ˃
x A ¼ ˁ
ð
14
:
8
Þ
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