5 Welfare
In this section, we establish the welfare properties of the possible equilibrium
configurations. We will limit the analysis to cases where ° < βl, so that all
countries are potential MAI members. We will ask in particular two questions.
How does world-wide welfare change across the different possible configurations?
Which countries are going to be better-off in a world with MAI compared to a
situation where MAI is not in place?
By the choice of Cobb-Douglas preferences, and since all prices are 1, coun-
tries’ welfare is just measured by their own expected income, and the utilitarian
world welfare indicator corresponds to aggregate countries’ income. The world
welfare associated with an equilibrium MAI (p; z) writes as follows
W (p; z)
L + p 0:5
0:5
7O:5-(O:5-^1)Z
(1 — (βh — °) )dβh
(9)
1 _p /.O:5-(O:5-^1)Z
+ (- )0:5 (1 — βh)dβh;
1 — z Jβl
where 0:5 (1 — (βh — °)2) and 0:5(1 — βhh) are the sum of country h rents and
hosted MNEs’ profits when country h is, respectively, in and outside MAI. It is
easy to see that, whenever at equilibrium z < 1, world welfare can be improved
upon by shifting some countries into MAI. This is checked by noting that
@W(p; z)
@z
(0:5 — βi) [1 + 4(0:5 — (0:5 — Z^ — +
(10)
p 12 +
I ∕l (0:5 — βi) [2(0:5 — (0:5 — +
+ (1 — P) ----------------ë----------------
The intuition is simple. Countries, when deciding upon entering MAI, just
compare expected rent extraction from FDIs in the two alternatives. However,
when participating into MAI, countries also boost the profits of hosted MNEs.
Since this latter effect is neglected by countries, the size of MAI emerging at
equilibrium is always suboptimal, except for the full MAI equilibrium.
The implementation of MAI improves world welfare as compared with a
situation where MAI is not in place. The comparison between world welfare
under full MAI and no MAI is readily obtained as
W(1; 1) — W(0; O) = 4°[1 + 2(βι — °)] > O; (11)
while the welfare comparisons with the case of partial MAI are more involved.24
Does this mean that all countries are always going to gain individually from
MAI membership? Let’s start by comparing the income of a generic country h
24Unreported simulations show that, in all cases, full MAI is preferable to partial MAI which
is in turn sup erior to no MAI. So, equilibria are welfare rankable.
17