Thank you very much for your interest, warm words and thoughtful comments. I will reply to each point in turn.

1) You are right that we did not emphasize how effects of cocaine on subjective effort costs could be distinguished from the effect of the drug on gain in the BSR substrate. Nonetheless, we did address this issue as follows on page 13 of the paper:

“Future experiments that entail unambiguous inference of subjective costs should help distinguish between the plausible explanations of the shifts along the price axis. Highly non-linear functions likely map objective effort and opportunity costs [77] into subjective ones. If so, then the approach adopted here to measure lateral shifts of the non-linear intensity-growth function for BSR could be adapted to measure lateral shifts of the functions that determine subjective costs. That said, observation of a change in the product of several numbers (‘‘payoff from BSR’’ in Figure 3a) does not reveal which of the inputs to the calculation has been altered, and thus, changes in the gain of the BSR substrate (or scalar changes in subjective costs) cannot be isolated within the framework of the mountain model. However, if the circuitry underlying the intensity-growth function for BSR can be identified, then observation of its output would provide direct measurement of gain changes.”

Let me try to unpack this. The schedule of reinforcement we employ requires the rat to “put time on a clock” by holding down a lever. When the accumulated time reaches a value set by the experimenter (the “price”), the rat is “paid” for its efforts. (A BSR train is delivered.) We are in the process of developing a device that controls the amount of physical work the rat must do in order for the credited work time to increment. The rat will have to turn a paddle-wheel against a calibrated drag. By varying the physical work requirement as well as a second independent variable, such as the pulse frequency or the opportunity cost, we propose to describe the psychophysical function that transforms the rate of physical work into a subjective effort cost. This function is almost surely non-linear. The difference between applying a force of 0.001 g and 0.002 g is no doubt inconsequential in terms of subjective effort. However, as the force requirement approaches the limits of the rat’s strength, the mapping function should “explode” (accelerate sharply upwards). Just as we took advantage of the non-linear form of the reward-growth function to distinguish changes in the sensitivity of the BSR substrate from other determinants of reward pursuit, we propose to use the non-linear form of the subjective effort-cost function to detect drug-induced changes in its lateral position (e.g., rightward displacement by cocaine).

As the paragraph quoted above indicates, the situation would be less clear if the drug were to alter the scale of the subjective effort-cost function rather than its position parameter. There are limits beyond which inferences drawn from behavioral data alone will not carry us, and I fear this is one of them. We should be able to measure lateral displacement in each individual psychophysical function (reward-growth, subjective-price, and subjective effort-cost). However, according to our model, scalar changes in all three functions will be pooled and thus, will not be distinguishable from each other, although they will be distinguishable from changes in the position parameter of each psychophysical function.

2) Our model and data make obvious predictions about the effects of cocaine on performance for non-drug rewards (i.e., changes in gain and/or subjective costs rather than increases in sensitivity). When applied to drug self-administration, our analysis may provide a new framework for posing questions and studying them empirically. For example, does sensitization alter a) the sensitivity of the neural substrate for the rewarding effect of cocaine, b) gain, or c) the proclivity of the subject to invest effort in pursuit of the drug? In principle, our approach can distinguish option a from options b&c. My reply to the first point you raised implies that we could distinguish options b and c, but only if the drug altered the position of the subjective effort-cost function along the axis representing physical work.

We would very interested indeed to learn your thoughts about how putative gain-boosting effects of cocaine could be integrated into your model.