EDIT

Ethics and Elasticity

Imagine you're a vegetarian avoiding meat, an environmentalist reducing power consumption, or a fair-trade supporter who buys higher-priced coffee.

You might naively expect that not eating a chicken saves a chicken. This is not true. Likewise, for the other cases. Likewise, if you go out of your way to each chicken, this doesn't cause an entire chicken to die.

The reason? Market power. Just as your decision to avoid eating chicken slightly reduces the demand for chickens (in expectation), it also slightly reduces the price of chickens (in expectation). This fall in price, causes people to eat slightly more chickens. While these second-order effects don't negative the expected impact of avoiding chicken, they do reduce it.

It can help by considering edge cases. Imagine the demand for chicken is perfectly elastic. For instance, people might only buy chicken if it costs less than say $2 per pound. In this case, producers will keep farming chickens until they reach that marginal cost - regardless of whether you buy chicken. Hence, your decision to avoid chicken would have literally 0 impact on the number of chickens slaughtered.

On the other hand, if the demand for chicken is perfectly inelastic, then your decisions will not affect the price at all, meaning that every chicken you avoid is one saved (in expectation).

I've tried to more generally figure out how much markets reduce the impact of your ethical decisions, but the math became too hard for me. Howver, after looking at various special cases, I conjecture that for every chicken you avoid, you reduce the number of chickens slaughtered by $$\frac{\epsilon_S}{\epsilon_D + \epsilon_S}$$ where $\epsilon_S$ is the elasticity of supply and $\epsilon_D$ is the elasticity of demand.

Of course, this wouldn't just apply to avoiding meat. It would apply to all purchasing decisions. Similarly, if you make decisions with ethical costs, not accounting for market power will overstate how much harm you do.

I hope, in the future, to come back to this problem and either prove my conjecture or determine the correct formula.