Aumann-Shapley prices as a Scarf social equilibrium (Q800808)

Considered are economies with a single output (a single consumption good) which is produced from \(\ell\) inputs by means of an increasing returns to scale production function f. We show that for quasi-concave and homogeneous functions f of degree \(r\geq 1\), the Aumann-Shapley prices constitute a simple Scarf Social Equilibrium. Put differently, Shapley value of the associated atomless game is in the core of that game. Such is not the situation, however, in the more general case when f exhibits increasing returns to scale (but is not homogeneous).