The production game
Players in the production game are agents with enough wealth to supply their own (negligible) consumption of corn and to command the labor of a team of workers. We may assume that relations between employees and workers in production are noncooperative and that employers face a cost of monitoring effort, and that this cost includes both an overhead component and a variable component that increases with the size of the workforce. We suppose that a workforce of just u workers is the team size that optimally balances the overhead cost against the variable cost. Thus, each production coalition will plan for a workforce of just that size.
In a corn economy, the formation of a coalition for production can be identified with the formation of capital through frugality, or obtaining capital by alienating land. Classical economics assumes that landlords never save nor employ labor in cultivation. Nevertheless they command purchasing power in the form of corn, from their rental income. In a classical model, they spend their income on the wages of servants. These servants are consequently not available as employees in the exchange game as just described, and constitute the “unproductive labor” in the classical schema.
Accordingly, we suppose that agents in the production game are of two types, with different intertemporal preferences: one type with a lower discount rate for future consumption and one with a higher discount rate. An agent of the first type, endowed with land, and an agent of the second kind, endowed with capital, might form a coalition to transfer the capital to the agent of the first type in exchange for land at a price in corn between the agents’ discounted present values of future rents. We also suppose that any attempt to consolidate production on two or more plots of land results in loss of efficiency due to “imperfect recall,” so that production coalitions with more than one capitalist will be unstable. Classical economics did not envision externalities, so they will play no part in this model. This is a counterfactual simplifying assumption. As noted, a property-owner with more than enough land or labor to put one work team to work in cultivation will enter the exchange game as a plurality of agents, one for each plot to be cultivated, and this is the stable partition for the production game.