Consider the 2 2 production model. Production functions are given by:
Consider the 2 × 2 production model. Production functions are given by:
f1(z11, z21) = (z11)^α1 · (z21)^1−α1
f2(z12, z22) = (z12)^α2 · (z22)^1−α2
where αj ∈ (0, 1) for all j = 1, 2 and zij ≥ 0 for all i = 1, 2 and j = 1, 2.
Show mathematically that if the set of technologically efficient factor allocations (the Pareto set) ever cuts the diagonal of the Edgeworth Box, then it must coincide with the diagonal.
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