For Whom is MAI? A theoretical Perspective on Multilateral Agreements on Investments



residual MAI is instead impossible, because, when ° < °l, it occurs that ¢E <
0;
when β = °:

A.6 Appendix 6.

We prove here that there exist parameter constellations where countries gain
from participating to a partial MAI compared with what they could get in a
world without MAI. The condition for having a negative value for
μPMZ is

p>

z


βh(1 - βh)     ´ -

h - °)(1 - βh + °) ´ h:


(30)


We see that

@-h
@Ph


°[1 + ° - h(1 - 2βh + °)]0:
[(βh - °)(1 - βh + °)]2


(31)


Recall that by (25) of appendix A.3

P =_______________βt (1 - β*)_______________

z (β* - °)(1 - β* + °)(1 - z) + zβ* (1 - β*) ;

wlicrc 0 — 0:5 β—
where z = 05-βl .


Note that lim p =lim —h =
^*!0:5 βh!!05


---------1--------

4(0:5-°)(0:5+°) .


By evaluating the


total derivative of p with respect to β* = 0:5 we find


@ (P=z)            1 (1 - ι)(1 - ι - °)

(33)


_ _ ...                     --- --- “                                                         :

@β    '■' 0:5      2 (4 - 1 βι +2βι°2 - °2)

Since we are considering a partial MAI equilibrium, by Proposition 4 we need
°l <°<°u . The only ambiguous term in (33) is (1 - l - °), which is
decreasing in
°. Plugging the highest possible value for ° (i.e., °u) into this
term we find

1 - 2βι- -~ 2+6 q21+12β2 - 3oβι;              (34)

which is


always positive for βl < 0:5. It follows that @@p=*z)


j^*=0:5


< 0. So, one


can always choose a pair (°, βι) such that β* < 1=2 and some countries with βh


sufficiently close to 1/2 for which p=z > —h.


25




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