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.