The Calculus of Veganism

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 aka. 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 -> infinity (where r is empirical research) the probability limit that empirical research will find evidence for k = 2.86 is 1.


7 Responses to The Calculus of Veganism

  1. Darren says:

    And I thought *I* had too much time on my hands!!! 🙂

  2. vegetable95 says:

    One can, nay must, always make time for scientific inquiry!

  3. The Guerilla Economist says:

    To Whom It May Concern:

    Your analysis smacks the learned reader in the face with its ideological spin.

    As Subcommandante, I ask any would-be economist to respect the first rule of the true (and new) Academic Guerilla Economics Movement: mask not thy ideology with the seeming objectivity of mathematical anaysis. In response to your analytical blabber, I must follow Rule 6 of AGEM: should a Guerilla Economist encounter such ideology, the Guerilla Economist must smite it with his analytical sword.

    Your assumption of a utility represention of the form U(a,b)=log(a)+log(b) implicitly assumes that animal welfare and consumption of all other goods are perfect substitutes. Clearly, in general, they are not. An assumption to the otherwise would render your results completely incorrect. Anecdotally, one may argue quite forcefully that animal welfare and the consumption of all other goods are quite imperfect.

    Thou hast trampled upon the Truth. Do it again, and thou shalt face the ire of AGEM.

    Know thy limits, Rec Veg,

  4. vegetable95 says:

    Attn: G.E.

    In response to your comments, I must first point out that this blog will not be intimidated by terrorist tactics. Fortunately though, this does not prevent me from revealing the egregious errors in your statements.

    With “respect” to your “argument” against the substitutability of animal welfare and other goods, first notice that this type of substitution is observable in the real world. Environmentally friendly products improve animal welfare and typically are more expensive than their less friendly counterparts. Clearly, some degree of substitution does occur. What matters is not that substitution be perfect, but that sufficient flexibility exist in the range of interest for the model to produce accurate results. This is clearly the case here.

    For a similar but more complete exposition of this argument, I direct you to the following literature in which the authors defend the idea of substitutability between capital and natural resources. The same line of thinking applies here.

    Solow, Robert, 1997. Reply. Journal of Ecological Economics, 22, 267 – 268.
    Stiglitz, Robert, 1997. Reply. Journal of Ecological Economics, 22, 269 – 270.

    Thirdly, may I point out that your entire “movement” is a sham, as economics is by definition the masking of ideology with irrelevant mathematical rigour. Perhaps you are thinking of sociology?

    To end on a positive note, I should say that I do not disagree with your statement that your consumption of goods is “quite imperfect.” As you are not vegan I have no doubt that this is the case in your situation.

  5. Darren says:

    “… as economics is by definition the masking of ideology with irrelevant mathematical rigour.”

    No, no, no! That is what economics often IS, no doubt…. but that does not imply that this is what economics must be, either “by definition” or otherwise. Do not try to justify intellectual dishonesty with the weak plea: “hey, I’m just doing what everyone else does!”

    If you are convinced that economics is as you define it above, then you should stop doing economics, as no good can come of it.

  6. […] 95% veganism on its menu, one would expect King’s Café to be the perfect restaurant for economically rational %95 vegans. The restaurant was put to the test with a recent lunch-time […]

  7. Yes! Finally someone writes about juice fasting.

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