# Random

- A fascinating study found that (a) most of the male-female gap in economics graduates exists prior to college and (b) that while the grade they receive in their first class strongly predicts whether women will major in economics, it doesn't really predict whether men will at all Goldin.
- The Fermi Paradox is resolved if you account for uncertainty in the estimates Sandberg.
- A blog post explaining why Bryan Caplan thinks the minimum wage causes unemployment despite empirical evidence to the contrary Caplan. See also here Paradox of toil.
- A reflection on the use of rhetoric in economics McCloskey.

## Voting Theory

## Meta-analyses

Meditation has no effect on aggression, connectedness, prejudice, or compassion. It may have an effect on empathy. In general the evidence for the pro-social benefits of meditation is weak The limited prosocial effects of meditation: A systematic review and meta-analysis.

## IQ Diet

- A 1-week experiment on 23 young men found high-protein diets improve reaction time Effect of a high protein meat diet on muscle and cognitive functions.
- A trial is underway to examine the effects of lean red meat and exercise on cognition in older The effects of a protein enriched diet with lean red meat.

## Math

Consider any computable set of positive integers X (e.g. "prime numbers", "multiples of 7", "factorial numbers", etc.). There exists a (multivariate) polynomial f(x1, x2, ...) with integer coefficients such that X = image(f). In fact, the sets constructible in either the Turing-sense or the polynomial-sense are exactly the same.

## Econ Equilibriums

Suppose a good has equilibrium price $1$ and equilibrium quantity $Q$. A small tax $t$ on the good causes the equilibrium quantity to shrink by

$$ t \frac{\epsilon_S \epsilon_D}{\epsilon_S + \epsilon_D} Q $$where $\epsilon_S$ and $\epsilon_D$ are the elasticity of supply and demand, respectively.

In this sense, $\frac{\epsilon_S \epsilon_D}{\epsilon_S + \epsilon_D} $ is the elasticity of the market as a whole (call it $\epsilon$).

The deadweight loss is a triangle with area

$$ \frac{t^2}{2} \epsilon Q $$The marginal deadweight loss is $ t Q \epsilon $ while the marginal revenue is simply $ Q $.

Note, that with optimal commodity taxation, the ratio between the marginal deadweight loss and the marginal revenue must be some fixed constant. This means the above directly implies the Ramsey Rule: the optimal consumption tax on each good is the inverse of that good's elasticity.

If a good has a small positive (negative) externality of $a$, then the dearth (excess) in exchange reduces overall surplus (relative to optimum) the same amount as if there was a tax of $a$. That is, by

$$ \frac{a^2}{2} \epsilon Q $$And internalizing that externality with a Pigovian tax increases total surplus by the same amount.

Note: this implies that if the externality is smaller than the equilibrium price, the externality's net-effects ($\frac{a^2}{2} \epsilon Q$) on surplus are much smaller than its direct effects $(a Q)$.