Extending Edgeworth: Labour Exchange and Production

This study presents an account of the implicit’ treatment of production associated with Edgeworth’s illustration of Friday’s and Crusoe’s economic relationship and attempts to extend that illustration to incorporate production on an ‘explicit’ basis. It reflects on Edgeworth’s famous Figure 1 from mathematical Psychics and what the shape of Friday’s and Crusoe’s indifference curves would be, when mapped in an allocation plane, if the production of wheat implied by the Friday-Crusoe scenario is treated as merely ‘incidental’, in which case production is ignored, and if it is treated as ‘intentional’. Based on that reflection, Edgeworth’s figure is extended to explicitly illustrate how the exchange of Friday’s labour to Crusoe for remuneration influences, and is influenced by, Friday’s production of wheat for Crusoe. The extension to Edgeworth’s illustration has been undertaken for two cases: first, the simplified and unrealistic, although theoretically useful, case that sets aside Crusoe’s initial stock of wheat; and second, the more realistic but more complex case that incorporates Crusoe’s initial stock of wheat.