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