On Differentiated and Indivisible Commodities: An Expository Re-framing of Mas-Colell’s 1975 Model (with Takashi Suzuki)

With a pure exchange economy and its Walrasian equilibrium formalized as a distribution on the space of consumer characteristics, Mas-Colell (1975) showed the existence of equilibrium in a pure exchange economy with differentiated and indivisible commodities.  We present a variant of Mas-Colell’s theory; but more than for its own sake, we use it to expose and illustrate recent techniques due to Keisler-Sun (1009), as developed in Khan-Rath-Yu-Zhang (2015), to translate a result on a large distributionalized economy (LDE) to a large individualized economy (LIE), when the former can be represented by a saturated or super-atomless measure space of consumers, as formalized in Keisler-Sun (2009) and Podczeck (2008) respectively.  This also leads us to identify, hitherto unnoticed, open problems concerning symmetrisation of distributionalized equilibria of economies in their distributionalized formulations.  In relating our result to the antecedent literature, we bring into salience the notions of (i) “overriding desirability of the indivisible commodity”, as in Hicks (1956), Mas-Colell (1977) and Yamazaki (1978, 1981), and of (ii) “bounded marginal rates of substitution”, as in Jones (1983, 1984) and Ostroy-Zame (1994).  Our work also relies heavily on the technical notion of Gelfand integration.