Geoscience Reference
In-Depth Information
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