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	economics Boycotts Imagine you're a vegetarian avoiding meat, an environmentalist reducing power consumption, or a fair-trade supporter who buys fair trade 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 eat 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 negate 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. It turns out there's an elegant formula for determining your true ethical impact. If you don't eat one chicken, the number of chickens saved (in expected value) is given by $$\frac{\epsilon_S}{\epsilon_D + \epsilon_S}$$ where $\epsilon_S$ is the elasticity of supply and $\epsilon_D$ is the elasticity of demand. Proof of Formula Let the supply curve be given by $ Q_S = S_0 \cdot P^{\epsilon_S} $ and let the demand curve be given by $ Q_D = D_0 \cdot P^{-\epsilon_D} $, where the $\epsilon$s are the elasticities, and $S_0$ and $D_0$ are to scale the curves. These definitions are nice in their elegance, but since we're talking only about marginal impact, it doesn't matter if you think these assumptions fail on the macro scale. Before we go on, let's compute the equilibrium price and quantity. We start with the identity $$ S_0 \cdot P^{\epsilon_S} = D_0 \cdot P^{-\epsilon_D} $$ Applying some algebra yields: $$ P^* = \left( \frac{D_0}{S_0} \right) ^ \frac{1}{\epsilon_S+\epsilon_D} $$ And solving for quantity is straightforward: $$ Q^* = D_0 \cdot \left( \frac{S_0}{D_0} \right) ^ \frac{\epsilon_D}{\epsilon_S+\epsilon_D} $$ Next, you change you decision to buy, which causes demand to shift: $ Q_D = D_0 \cdot P^{-\epsilon_D} + \delta $. We can write these curves in terms of quantity and set them equal to solve for the equilibrium price: $$ P^* = \left( \frac{Q}{S_0} \right)^{ 1/\epsilon_S} = \left( \frac{Q - \delta} {D_0} \right)^{-1/\epsilon_D} $$ Now, you're going to have to trust me. We're going to solve for $\delta$ [it's much easier than solving for $Q$]: $$ \delta = Q - D_0 \left( \frac{S_0}{Q} \right)^{ \epsilon_D/\epsilon_S} $$ Now, you're going to have to keep trusting me. Let's take the derivative of $\delta$ with respect to $Q$: $$ \frac{d\delta}{dQ} = 1 + D_0 \left( \frac{S_0}{Q} \right)^{\epsilon_D/\epsilon_S-1} \cdot \frac{\epsilon_D}{\epsilon_S} \cdot S_0 \cdot Q^{-2} $$ Some simplification yields: $$ \frac{d\delta}{dQ} = \frac{\epsilon_S + \epsilon_D \cdot D_0 \cdot S_0^{\epsilon_D/\epsilon_S} \cdot Q^{-1-\epsilon_D/\epsilon_S}} {\epsilon_S} $$ Since we're assuming these are all "microscopic" effects, we can use the slope at the old equilibrium as an estimate of the slope at the new equilbirium. This justifies a substitution: $$ \frac{d\delta}{dQ} = \frac{\epsilon_S + \epsilon_D \cdot D_0 \cdot S_0^{\epsilon_D/\epsilon_S} \cdot \left( D_0 \cdot \left( \frac{S_0}{D_0} \right) ^ \frac{\epsilon_D}{\epsilon_S+\epsilon_D} \right)^{-1-\epsilon_D/\epsilon_S}} {\epsilon_S} $$ Some simplification... $$ \frac{d\delta}{dQ} = \frac{\epsilon_S + \epsilon_D \cdot S_0^{\epsilon_D/\epsilon_S} \cdot D_0^{-\epsilon_D/\epsilon_S} \cdot \left( \frac{S_0}{D_0} \right) ^ {-\frac{\epsilon_D}{\epsilon_S} } } {\epsilon_S} $$ Somre more... $$ \frac{d\delta}{dQ} = \frac{\epsilon_S + \epsilon_D } {\epsilon_S} $$ Finally, we apply a math "trick" by taking the reciprocal of both sides: $$ \frac{dQ}{d\delta} = \frac{\epsilon_S}{\epsilon_S + \epsilon_D} $$ Of course, this doesn't just apply to avoiding meat. It applies to all purchasing decisions. Similarly, if you make decisions with ethical costs, not accounting for market power will overstate how much harm you do.

economics

Boycotts

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

It turns out there's an elegant formula for determining your true ethical impact. If you don't eat one chicken, the number of chickens saved (in expected value) is given by $$\frac{\epsilon_S}{\epsilon_D + \epsilon_S}$$ where $\epsilon_S$ is the elasticity of supply and $\epsilon_D$ is the elasticity of demand.

Proof of Formula

Let the supply curve be given by $ Q_S = S_0 \cdot P^{\epsilon_S} $ and let the demand curve be given by $ Q_D = D_0 \cdot P^{-\epsilon_D} $, where the $\epsilon$s are the elasticities, and $S_0$ and $D_0$ are to scale the curves. These definitions are nice in their elegance, but since we're talking only about marginal impact, it doesn't matter if you think these assumptions fail on the macro scale.

Before we go on, let's compute the equilibrium price and quantity. We start with the identity $$ S_0 \cdot P^{\epsilon_S} = D_0 \cdot P^{-\epsilon_D} $$

Applying some algebra yields: $$ P^* = \left( \frac{D_0}{S_0} \right) ^ \frac{1}{\epsilon_S+\epsilon_D} $$

And solving for quantity is straightforward: $$ Q^* = D_0 \cdot \left( \frac{S_0}{D_0} \right) ^ \frac{\epsilon_D}{\epsilon_S+\epsilon_D} $$

Next, you change you decision to buy, which causes demand to shift: $ Q_D = D_0 \cdot P^{-\epsilon_D} + \delta $.

We can write these curves in terms of quantity and set them equal to solve for the equilibrium price: $$ P^* = \left( \frac{Q}{S_0} \right)^{ 1/\epsilon_S} = \left( \frac{Q - \delta} {D_0} \right)^{-1/\epsilon_D} $$

Now, you're going to have to trust me. We're going to solve for $\delta$ [it's much easier than solving for $Q$]: $$ \delta = Q - D_0 \left( \frac{S_0}{Q} \right)^{ \epsilon_D/\epsilon_S} $$

Now, you're going to have to keep trusting me. Let's take the derivative of $\delta$ with respect to $Q$: $$ \frac{d\delta}{dQ} = 1 + D_0 \left( \frac{S_0}{Q} \right)^{\epsilon_D/\epsilon_S-1} \cdot \frac{\epsilon_D}{\epsilon_S} \cdot S_0 \cdot Q^{-2} $$

Some simplification yields: $$ \frac{d\delta}{dQ} = \frac{\epsilon_S + \epsilon_D \cdot D_0 \cdot S_0^{\epsilon_D/\epsilon_S} \cdot Q^{-1-\epsilon_D/\epsilon_S}} {\epsilon_S} $$

Since we're assuming these are all "microscopic" effects, we can use the slope at the old equilibrium as an estimate of the slope at the new equilbirium. This justifies a substitution: $$ \frac{d\delta}{dQ} = \frac{\epsilon_S + \epsilon_D \cdot D_0 \cdot S_0^{\epsilon_D/\epsilon_S} \cdot \left( D_0 \cdot \left( \frac{S_0}{D_0} \right) ^ \frac{\epsilon_D}{\epsilon_S+\epsilon_D} \right)^{-1-\epsilon_D/\epsilon_S}} {\epsilon_S} $$

Some simplification... $$ \frac{d\delta}{dQ} = \frac{\epsilon_S + \epsilon_D \cdot S_0^{\epsilon_D/\epsilon_S} \cdot D_0^{-\epsilon_D/\epsilon_S} \cdot \left( \frac{S_0}{D_0} \right) ^ {-\frac{\epsilon_D}{\epsilon_S} } } {\epsilon_S} $$

Somre more... $$ \frac{d\delta}{dQ} = \frac{\epsilon_S + \epsilon_D } {\epsilon_S} $$

Finally, we apply a math "trick" by taking the reciprocal of both sides: $$ \frac{dQ}{d\delta} = \frac{\epsilon_S}{\epsilon_S + \epsilon_D} $$

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