# Pareto Set with strictly convex preferences

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.

• Its clear that the origin cannot be included. Both agents start with positive endowments (and thus positive utility), so the origin, which gives 0 utility, cannot be a Pareto improving allocation. – Walrasian Auctioneer Feb 2 at 21:27
• Are you asking about Pareto set or the contract curve? – Art Feb 3 at 8:32
• You might want to edit your question accordingly. – Art Feb 3 at 10:51
• @WalrasianAuctioneer I meant to ask if the origin will also be Pareto efficient. Have edited my question. – PGupta Feb 3 at 10:51
• @Art Actually, to be precise I want to ask if the points will also be Pareto efficient. My edited post incorporates this change. – PGupta Feb 3 at 11:19