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) ´ -
(βh - °)(1 - βh + °) ´ h:
(30)
We see that
@-h
@Ph
°[1 + ° - 2βh(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!!0∙5
---------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 - 2βι)(1 - 2βι - °)
(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 - 2βl - °), 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
More intriguing information
1. The Folklore of Sorting Algorithms2. Implementation of the Ordinal Shapley Value for a three-agent economy
3. Dynamic Explanations of Industry Structure and Performance
4. The name is absent
5. The name is absent
6. Comparative study of hatching rates of African catfish (Clarias gariepinus Burchell 1822) eggs on different substrates
7. The name is absent
8. A Dynamic Model of Conflict and Cooperation
9. Equity Markets and Economic Development: What Do We Know
10. Explaining Growth in Dutch Agriculture: Prices, Public R&D, and Technological Change