Two firm two consumer economy efficiency (two goods)

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Two firm two consumer economy efficiency (two goods)

Hi,

For pareto efficiency (given everything is convex, returns to scale are <=1)

1. MRS of all consumers=Marginal rate of transformation (slope of production possibilites frontier)=p(x)/p(y)

2. MRTS (Rate of technical substitution) for all producers=wage rate/rental rate

Is it necessary that all conditions in 1 and 2 are equal among themselves too? As in, is MRS=MRTS=...==...?

Also, for 2nd welfare theorem to hold, do we require the PPF to be a convex set, or each individual production functions to be convex set?

 

 

 

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