#untagged

# 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)

## 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 $(a Q)$.

Jakobsen, L. H., Kondrup, J., Zellner, M., Tetens, I., & Roth, E. (2011). Effect of a high protein meat diet on muscle and cognitive functions: a randomised controlled dietary intervention trial in healthy men. Clinical nutrition, 30(3), 303-311.s Daly, R. M., Gianoudis, J., Prosser, M., Kidgell, D., Ellis, K. A., O’Connell, S., & Nowson, C. A. (2015). The effects of a protein enriched diet with lean red meat combined with a multi-modal exercise program on muscle and cognitive health and function in older adults: study protocol for a randomised controlled trial. Trials, 16(1), 339. Caplan, B. (2013). The Myopic Empiricism of the Minimum Wage. https://www.econlib.org/archives/2013/03/the_vice_of_sel.html Wikipedia contributors. (2020, October 19). Paradox of toil. In Wikipedia, The Free Encyclopedia. Retrieved 04:12, October 20, 2020, from https://en.wikipedia.org/w/index.php?title=Paradox_of_toil&oldid=984404456 McCloskey, D. (1986). The Rhetoric of Economics. http://www.deirdremccloskey.com/docs/pdf/Article_116.pdf