Resource Allocation and Pareto Efficiency

https://en.wikipedia.org/wiki/Edgeworth_box

^^^This is where the allocation of resources are decided between two people

https://en.wikipedia.org/wiki/Contract_curve

^^^This is how we find the optimal allocation of resources that will satisfy the two people

The allocation of goods between two people is the issue that will be dealt with here.

A similar method from previous will be used.

Two people need to agree on the allocation of resources. If only one is better off in the allocation of resources, it can be considered Pareto efficient. When the other does better off, the other has to be at least as well off.

We will try to find the tangent vectors of two equations in the Edgeworthbox.

If A takes resources x and y of resources K and T, B will take the resources total_K - x and total_T - y.

The will be put in their respect utility functions.

The partial derivative of uA in vector form = lambda*The partial derivative of uB in vector form

Equate the corresponding, eliminate lambda and get the equation of the contract curve.

If a point satisfies the contract curve, the point is pareto efficient.

Every one of the points in the contract curve is pareto efficient. No specific answer. Need constraints to find a specific answer.

Put the specified points in the corresponding utility function to get limits. The utility function may be equal to or larger than the limit. Now that the utility function has limits whereas before you did not, you can plot it.