Suppose there are two individuals and two goods. The initial endowments are w₁ = (100, 0) and w₂ = (100,100). Preferences are given by

u₁(x, y) = x + y

and

u₂(x, y) = y

(a) Is there any equilibrium? If so, derive one. If not, prove that.

(b) Now suppose initial endowments are w₁ = (100, 1) and w₂ = (100, 99).

How does your answer change?

(c) What if initial endowments are w₁ = (100, 2) and w₂ = (100, 98)?