Consider the same economy studied in LN2, which I repeat it here
for convenience: a pure exchange economy with two goods, apples and
bananas (a and b) and two consumers, Alice and Bob. Alice has utility
function
$U_A(a, b) = 0.4 \log(a) + 0.6 \log(b)$;
Bob has utility function
$U_B(a, b) = 0.5 \log(a) + 0.5 \log(b)$.
Alice is endowed with 10 apples and 10 bananas, while Bob is endowed
with 5 apples and 10 bananas.
Suppose a social planner wants to implement as a Walrasian equilib-
rium the feasible allocation that maximizes $U_A(a^A, b^A) + U_B(a^B, b^B)$.
Give all the possible reallocations of the social endowment that yield
the planner's desired allocation as a Walrasian equilibrium. (Hint:
first find the allocation desired by the social planner. Then find the
price which would support that allocation as WE in an economy where
the two agents are endowed with that allocation. Finally find the re-
quired reallocations)
