The impact of outside reward on the subjective value of a pursuit.
A) Increasing the outside reward while holding the outside time constant increases the outside reward rate (slope of gold lines), resulting in increasing the global reward rate (slope of the purple lines), and decreasing the subjective value (green dots) of the pursuit. As the reward rate of the environment outside the considered pursuit type increases from lower than, to higher than that of the considered pursuit, the subjective value of the pursuit decreases, becomes zero when the in/outside rates are equivalent, and goes negative when ρout exceeds ρin. B) Plotting the subjective value of the pursuit as a function of increasing the outside reward (while holding tout constant) reveals that the subjective value of the pursuit decreases linearly. This linear decrease is due to the linear increase in the cost of time of the pursuit (purple dotted region). C) Time’s cost (the area, as in B, between the pursuit’s reward magnitude and its subjective value) is the sum of the opportunity cost of time (orange dotted region) and the apportionment cost of time (plum annuli region). When the outside reward rate is zero, time’s cost is composed entirely of an apportionment cost. As the outside reward increases, opportunity cost increases linearly as apportionment cost decreases linearly, until the reward rates in and outside the pursuit become equivalent, at which point the subjective value of the pursuit is zero. When subjective value is zero, the cost of time is entirely composed of opportunity cost. As the outside rate exceeds the inside rate, opportunity cost continues to increase, while the apportionment cost becomes negative (which is to say, the apportionment cost of time becomes an apportionment gain of time). Adding the positive opportunity cost and the negative apportionment cost (subtracting the purple & orange region of overlap from opportunity cost) yields the subjective value of the pursuit.