General Equilibrium Pareto set allocations (2 producers/2 goods)

Hey there,

it is the first time I seek help on a math board as I have to study for this exam by books only due to a very inconvenient situation. I only have exercises (without solutions) and the referenced book to the class. The task is the following:Consider an economy with production formed by 2 agents (A and B) and two goods (1 and 2): f_{A}(x_{A1},x_{A2}) = x_{A1} * x_{A2} and f_{B}(x_{B1},x_{B2}) = x_{B1} * x_{B2}. The technology is X_{1} + X_{2} = 100.

Obtain the set of Pareto allocations and identify 3 allocations of the set.

At first I researched about the full Pareto solution for a task with Consumers and Utility functions, but could not make out the Utility part of the assignment. Now I suppose I am only supposed to get the possible **Pareto set** allocations from the production perspective.

My approach so far was to use the Marginal Technichal Rate of Substitution of the two goods which returned me:

x_{A2}/2x_{A1} = 2x_{B2}/x_{B1}

But I do not know where to go from here.

Am I on the right track at all, or how should I approach this kind of assignment properly? I strongly lack of numerical examples of a Pareto solution for only the production side (without consumer preferences).

What exactly does the "technology" define here and do f_{A }and f_{B} really describe production?

Any help is highly appreciated, I feel as if I misunderstand a key part. I have this exam on tuesday and this is the only major calculation topic I still struggle at.

Regards

Jens

Re: General Equilibrium Pareto set allocations (2 producers/2 goods)

Somehow I can't edit my previous post. I mixed up two assignments, so forget my inbetween result.

The correct functions are: fA(xA1,xA2) = xA1 * xA2 and fB(xB1,xB2) = (xB1)^{2} * xB2