# Core in a replicated economy

I'm trying to solve the following problem on general equilibrium:

Consider an economy with two individuals with utility functions $$u^A(x^A,y^A) = \min \{ x^A, y^A \}$$ and $$u^B(x^B,y^B) = \min \{ x^B, y^B \}$$, with initial endowments $$w^A = (1,0)$$ and $$w^B = (0,1)$$. First find the set of Pareto efficient (PE) allocations, then the set of core allocations in the unreplicated economy, $$C_1$$, and finally in the twofold replica, $$C_2$$.

My take:

Pareto Set = $$\{ (x^A,y^A,x^B,y^B) : x^A = y^A , x^A + x^B = 1, y^A + y^B = 1 \}$$.

Because $$I = 2$$ (the number of agents is 2), then Contract Curve = Core. Here the Contract Curve is the same as the Pareto Set. Then:

$$C_1 = \{ (x^A,y^A,x^B,y^B) : x^A = y^A , x^A + x^B = 1, y^A + y^B = 1 \}$$.

In the twofold replica now I've got two agents of each type and total endowments are $$w^A = (2,0)$$, $$w^B = (0,2)$$. Because of equal treatment in the core, $$x^A_1 = x^A_2$$ and $$y^A_1 = y^B_2$$, the same with the type-B individuals. So nothing change and the core is the same?

Shouldn't the core shrinks as the economy enlarges?