Imagine an economy where two individuals, A and B, trade two commodities, x1 and x2. Each individual has a distinct quasilinear utility function: For A, it's uA = ln x1,A + x2,A and for B, it's uB = 2 ln x1,B + x2,B (with x1,A denoting the quantity of good x1 that A possesses, and so on). The total available quantity of good 1 is 6 units, while that of good 2 is 5 units. This economy satisfies both the first and second welfare theorems.

In a competitive equilibrium scenario, how would good 1 be distributed between A and B? Can you briefly describe your rationale, referencing one or both of the mentioned welfare theorems?