Suppose the agents A and B have the following utility functions $x_A y_A+12x_A+3y_A $ and $x_By_B +8x_B+9y_B$ respectively with endowments (8,30) and (10,10).
The contract curve's equation turns out to be $y_A=2x_A-6$ for interior Pareto efficient allocations.
My question is whether some portion of the edges and the origins are also Pareto efficient, and if yes, how do we arrive at them without graphing the box. Once I draw the box, it seems to me that these portions should be included.