An animal must continually invest time and energy to obtain sufficient food and water, and to meet other immediate and long-term survival needs. Because time and energy are limited, considerable selection pressure would exist for animals to efficiently allocate their efforts, such that the effort directed toward each goal is sufficiently but not excessively energized. In the laboratory, rats will perform tasks to earn food or water rewards. It is well established that, given an alternative, rats choose options with larger rewards, and are willing to work harder for them. But little is known about the effect of average reward size on the total amount of work a rat is willing to do or the total amount of water the rat will consume per day at equilibrium. We tested this in rats and use the data to inform a low-parameter analytic utility model that can account for how much rats work and how much they consume. The model yields additional insight into the timing of when rats do work, and where in the brain the computation of utility might occur. Most importantly the model makes many testable quantitative predictions.

	Example data (symbols) and model (curves) for two rats that were tested with access to the task to earn water either 24h/day (red) or 2 hr/day (purple). Each symbol shows the expected reward (ml/trial) and the total work (L, trials/day, above) or total water consumed (H, ml/day, below). A single model was fit for both conditions with three free parameters corresponding to the rat's aversion to work and the rat's satiety point for free water with 24h/day access or with 2h/day access. In future experiments the latter two could be constrained by direct measurment which would make this a single free parameter model.
	Instantiation of the analytic model illustrating how the components of utility depend on reward size ("wage rate" w, colors) and the number of trials done per day ("labor" L) and how these predict trial number and total water consumption.
	For those used to seeing things in Economists' terms, here are example isoutility curves from a different instantiation of the model, and the resulting predicted observed back-bending labor supply curve.

Credits:

Thanks to Mark Machina for many valuable discussions of consumer demand theory and to Zack Knight and members of his lab for valuable discussions of rodent thirst regulatory circuits.