The evolution of a labor market

Kenneth B. Vernon Scientific Computing and Imaging Institute, University of Utah

Kelsey Carlston School of Business Administration, Gonzaga University

Weston C. McCool Department of Social Sciences, CalPoly

Kurt M. Wilson Department of Anthropology, Lawrence University

Brian F. Codding Environmental Studies and Geography, UCSB

2026-04-01

kbvernon/saa_2026-labor_markets

Inspiration

Variations on the Patron-Client Model:

The marginal utility of inequality: A global examination across ethnographic societies

Human Nature 31 (2020)
Kurt M. Wilson and Brian F. Codding
10.1007/s12110-020-09383-4

The origins of inequality: Insiders, outsiders, elites, and commoners

Journal of Political Economy 121(3) (2013)
Gregoy K. Dow and Clyde G. Reed
10.1086/670741

Context

The circular economy…

Question

Challenge

We need to…

1. define the costs and benefits of each strategy and
2. explain why individuals would choose one strategy over another.

To that end, we will develop a formal equilibrium model,

i.e., we will apply neoclassical orthodoxy. [cue Wilhelm scream]

Economy

We assume an agrarian subsistence economy in which…

1. there is no trade or migration (the economy is isolated),
2. production occurs on farms privately held by households,
3. factors are limited to labor (a variable input) and land (a fixed input), and
4. competition is perfect (everyone is a price-taker).

Production

The energetic output of an individual farm is given by…

Utility

We assign to each farm a time budget, \(T\), and assume that they are utility maximizers:

Clients:	\(\max U_{c} = f(T-L) + wL \quad\;\; \text{s.t.}\;\; L \leq T\)
Patrons:	\(\max U_{p} = f(T+L) - wL\)

where \(w\) is the market wage and \(L\) is time invested in wage-labor.

note: When \(L = 0\), production reduces to pure subsistence, \(f(T)\), in which case, there are no patrons or clients.

Supply

Clients:

\(\max U_{c} = f(T-L) + wL \quad\;\; \text{s.t.}\;\; L \leq T\)

Total supply \(S(w)\) is sum of \(L^*\) for all client farms.

Demand

Patrons:

\(\max U_{p} = f(T+L) - wL\)

Total demand \(D(w)\) is sum of \(L^*\) for all patron farms.

Equilibrium

Obtained by setting supply equal to demand…

Environmental heterogeneity is necessary and sufficient for \(L^* > 0\) within this economy.

Strategy

But where did the patrons and clients come from?

note: Differentiation into market roles is most likely to start in the tails of the distribution.

Competition

Market frictions…

If A is sufficiently far, then competition between A and B for the household’s labor will be imperfect, as B will be able to set wages.

note: Failures of perfect competition in the Neolithic - notably the potential for monopsony power - is where we should look for the origins of inequality.

Conclusion

On this simple application of the neoclassical labor market model…

STRENGTHS

• Orthodox: Nothing in this should surprise an economist - it’s econ 101.
  
• Darwinian: There’s no collective action or group selection anywhere.
  
• Unifying: Many ideas about inequality can be consumed by this model.
• Simple: Promotes economy of thought, contra post-modernism.

WEAKNESSES, maybe

• Apolitical: As presented, the model is largely silent about institutions, but that doesn’t mean it has nothing to say about them!
  
• Static: The model does not account for population dynamics and changes in climate over time, but we can use it to do comparative statics!

Acknowledgments

• Scott Ortman COLORADO
• Scientific Computing and Imaging UTAH
• Environment, Society, and Sustainability UTAH
• Department of Anthropology UTAH