8. Consider a two-good, two-consumer exchange economy, with utility functions and endowments (15)

U1(x1, x2) = x₁ ^1/2 x₂^1/2 , e¹ = (2, 1).

U2(x1, x2) = min { x₁ , x₂ } , e² = (1, 2).

(a) Find the set of Pareto effcient allocations.

(b) Find the core of the economy.

(c) Find the aggregate excess demand functions

for goods 1 and 2.

(d) Find a Walrasian equilibrium for this economy and the associated WEA.

(e) Consider the allocation

(x¹₁ x¹₂) = (2/3, 4/3), (x²_{1 ,}x²₂) = (7/3,5/3).

i. Is this allocation feasible?

ii. Is the allocation Pareto optimal?

iii. Can this allocation be the Walrasian equilibrium allocation of a redistribution of

the endowment?

Provide explanation to your answers.