Assume we have 2 individuals and 2 goods and 1 individual has now all goods. So initially he is on a normal indifference curve without trade.
They all want to get on to the highest possible ind. curve. By trade they can get to higher indifference curve:
Originally at n1 (original endowement),
They trade to somewhere between. Point A on a smaller lens is more efficient, but don't maximise welfare.
Pareto optimality - it is impossibel to improve the welfare of one individual without damagin the welfare of the other.
Poiints of tangency between indifference curves is the contract curve.
Both indidualsuse their ibine )iniyial endowment.
When straight line utility, the only 1 is produced.
Fixed ratios of production(kinked ind.), then you don't care about the relative prices. In the long-run kink disappears.