The purpose of this post is to provide rigorous microfoundations for %95 veganism. The post is structured as follows. This paragraph summarizes the post. The next paragraph models consumer utility as a function of animal welfare and a composite good, while the third paragraph derives a relationship between the two. The fourth paragraph shows that %95 is the optimal amount of veganism for a rational consumer. The last paragraph concludes.
Let a represent animal welfare and b a composite good consisting of all other goods. Assume a utility function of the form U(a, b) = ln a + ln b. It is easy to see that Ua > 0 for all a, indicating that the consumer benefits from the well-being of animals. This is consistent with the psychological evidence.
As noted in an earlier post consumption is inexorably linked to animal welfare, and therefore we can write b = f (a). It is reasonable to assume that f ‘ < 0. For tractability, assume that f takes the form f (a) = e-ka, where k is a constant. Testing the validity of these assumptions is left as an exercise for the reader.
Substituting into U gives U(a, f (a)) = ln a – ka. Note that beyond a certain point the second term is growing faster than the first, indicating that an optimum will be reached before a grows very large. This implies that consumers are boundedly compassionate in the sense that they are not willing to forgo consumption entirely for the sake of their furry friends. Maximizing with respect to a shows that U reaches an optimum at a = 1/k. Evaluating the ratio a/b at the optimum gives e/k which equals 0.95 for k = 2.86. This value of k is consistent with some empirical evidence.1
In conclusion, classical microeconomic theory behaviour predicts that consumers will be %95 vegan if they are boundedly compassionate and rational. Future research could discuss the implications of heterogeneous goods (i.e., food and non-food goods) for the model. I would like to thank my coauthor, therecreationalvegan, for his many useful suggestions in developing this post. All mistakes are my own.
1Consistent is being used in the probabilistic sense here, meaning that as r -> (where r is empirical research) the probability limit that empirical research will find evidence for k = 2.86 is 1.