General Equilibrium

The contract curve for flexible utility specifications

Drag the purple dot and watch out for overlaps (in orange) between the "better than" sets. An overlap means that we can improve at least one person's wellbeing without hurting the other - in other words, we are not at a Pareto-efficient point.
Whenever the dot is on the contract curve, there should be no overlap.

You can change the utility functions by typing directly in the formula. 

Competitive equilibrium with Cobb-Douglas preferences.

You can drag the initial endowment point and vary prices until the market clears (A and B choose to optimize at the same point in the Edgeworth box - meaning that their combined demand for each good exactly equals the total quantity available).

Once a competitive equilibrium has been reached, you can show the contract curve to verify that the 1st welfare theorem holds.