Abstract
Pursuit of one goal typically precludes simultaneous pursuit of another. Thus, each exclusive activity entails an “opportunity cost:” the forgone benefits from the next-best activity eschewed. The present experiment estimates, in laboratory rats, the function that maps objective opportunity costs into subjective ones. In an operant chamber, rewarding electrical brain stimulation was delivered when the cumulative time a lever had been depressed reached a criterion duration. The value of the activities forgone during this duration is the opportunity cost of the electrical reward. We determined which of four functions best describes how objective opportunity costs, expressed as the required duration of lever depression, are translated into their subjective equivalents. The simplest account is the identity function, which equates subjective and objective opportunity costs. A variant of this function called the “sigmoidal-slope function,” converges on the identity function at longer durations but deviates from it at shorter durations. The sigmoidal-slope function has the form of a hockey stick. The flat “blade” denotes a range over which opportunity costs are subjectively equivalent; these durations are too short to allow substitution of more beneficial activities. The blade extends into an upward-curving portion over which costs become discriminable and finally into the straight “handle,” over which objective and subjective costs match. The two remaining functions are based on hyperbolic and exponential temporal discounting, respectively. The results are best described by the sigmoidal-slope function. That this is so suggests that different principles of intertemporal choice are involved in the evaluation of time spent working for a reward or waiting for its delivery. The subjective opportunity-cost function plays a key role in the evaluation and selection of goals. An accurate description of its form and parameters is essential to successful modeling and prediction of instrumental performance and reward-related decision making.
Highlights
We investigated evaluation of opportunity costs by rats working for rewarding electrical stimulation of the medial forebrain bundle (MFB)
Substitution of brain-stimulation reward (BSR) for a natural reward and imposition of the fixed cumulative handling-time (FCHT) schedule collapses the components of the opportunity cost into one variable: the required cumulative work time
13) Analogous plots for the remaining rats are shown in Figs A, B, C, E and F in S1 File
Summary
Valuation of opportunity costs in study design, data collection and analysis, decision to publish, or preparation of the manuscript. The present paper concerns the psychophysical function that translates the objective time spent pursuing a reward into a subjective opportunity cost. Substitution of brain-stimulation reward (BSR) for a natural reward and imposition of the FCHT schedule collapses the components of the opportunity cost into one variable: the required cumulative work time (objective price). Ub a a þ Ue a ð2Þ where a = the payoff-sensitivity exponent T = the proportion of trial time spent holding down the lever (“time allocation”) Tmax = maximal time allocation Tmin = maximal time allocation Ub = payoff from a train of rewarding brain stimulation, and Ue = payoff from leisure activities Eqs 1 and 2 link the quantity we wish to infer, the subjective opportunity cost of the reward (Psub) to a quantity we observe: the proportion of trial time that the rat devotes to work (T). See S1 File for discussion and definition of units This composite function (fPsub ) translates objective work times (the price of the reward, Pobj) into subjective opportunity costs (Psub). The integral of a sigmoid has the required form: Z
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