# Random

- 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.

## Alcohol Facts

- 7.1 cal / g
- 1 standard drink = 14 g (1 tbsp = 15 g)
- Average person has ~5500g of blood, so 1 standard drink theoretically raises blood alcohol content (BAC) by 14/5500 = 0.25%. But in practice, it only raises BAC by 0.02%.
- BAC decreases by about 0.016% per hour (about 2x higher for kids or alcoholics)

## Voting Theory

## 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 $(a Q)$.

*Clinical nutrition, 30*(3), 303-311.s

*Trials, 16*(1), 339.