Offer curves in general equilibrium I'm having trouble understanding how to find the offer curves in general equilibrium. Is there a general way that we can use to find it?
I can understand the Pareto set and contract curve but when it comes to equilibrium I'm stuck.
For ex. if we have two consumers: Consumer 1 has as his initial bundle all of good $2:(0; 10)$ ;
while consumer 2 has all of good $1 : (10; 0)$.
Let their utilities be
$$u_1= min (x; y)$$
$$u_2= min (4x; 5y)$$
What would be the steps for finding the offer curves? Appreciate any help given.
In the picture below offer curve of individual 1 is given by lines connecting $E$ to $O_1$ and $O_1$ to $O_2$. And offer curve of individual 2 is given by lines connecting $E$ to $O_2$ and $O_2$ to $A$ and $A$ to $O_1$. Set of competitive equilibria are given by the intersection of two offer curves.
$p_X = 0$ and $p_Y = 1$ supports allocation at $O_2$ as competitive equilibrium. Allocations on the line segment $O_1A$ are supported by prices $p_X = 1$ and $p_Y = 0$.