• Economics

    Ricardo’s Law of Rent

    British economist David Ricardo’s Law of Rent comes from his 1809 work On the Principles of Political Economy and Taxation. The term rent here, or economic rent, doesn’t refer to the usual meaning of the payment a tenant makes to a landlord for use of land, but refers to something that is closer to producer surplus (i.e. producer’s profit, simply the producer’s revenue minus cost). Ricardo’s motivation to explore the nature of economic rent was due to rising grain and land prices during his time. He wanted to explore the question of whether rising land prices caused grain prices to rise or whether rising grain prices caused land prices to…

  • Economics,  Math

    Terms of Trade

    The Terms of Trade, very generally, is a ratio of the prices of a country’s exports to the country’s imports. Investopedia’s definition of terms of trade: What are ‘Terms of Trade – TOT’? Terms of trade represent the ratio between a country’s export prices and its import prices. The ratio is calculated by dividing the price of the exports by the price of the imports and multiplying the result by 100. But how exactly do you calculate the “price of exports and imports” of a country like, say Brazil, that has USD 190B of exports a year comprising surely thousands, if not more, of different products, and what to do…

  • Math

    A Thing About the Hot Hand Fallacy and the “Law of Small Numbers”

    There was an interesting post and discussion on the NBA subreddit of Reddit on the Hot Hand phenomenon and whether or not it is a fallacy. Comment from discussion RyanLeafgOaT8’s comment from discussion "[OC] Going Nuclear: Klay Thompson’s Three-Point Percentage after Consecutive Makes". A Numberphile video on the topic: An article on the topic: https://www.scientificamerican.com/article/do-the-golden-state-warriors-have-hot-hands/ In some parts of the Numberphile video, Professor Lisa Goldberg emphasizes that issues of the “Law of Small Numbers,” which is described in the Scientific American article as: Early in their careers, Amos Tversky and Daniel Kahneman considered the human tendency to draw conclusions based on a few observations, which they called the ‘‘law of…

  • Economics

    The First Economic “Laws”

      Ferdinand Lassalle’s Iron Law of Wages, following from Malthus, and David Ricardo’s Law of Rent are some of the very first relatively quantitative attempts at statements or observations of economics and can IMHO be considered a sort of ancestor of modern economics.  In the Iron Law of Wages (coined by Lassalle in 1863 according to Wikipedia), as population increases, the labor supply increases and thus the wage price decreases – which does mean that we assume labor demand is unaffected by the size of the population and thus labor demand is effectively exogenous.  Wages continue to decrease until they hit subsistence levels for laborers.  A further decrease in wages…

  • Economics,  Math

    The Terms of Trade of Brazil

    Source: https://www.nytimes.com/2018/11/09/opinion/what-the-hell-happened-to-brazil-wonkish.html An article in the New York Times by Paul Krugman talked about a current economic downturn in Brazil. What happened: First, the global environment deteriorated sharply, with plunging prices for the commodity exports still crucial to the Brazilian economy. Second, domestic private spendingf also plunged, maybe because of an excessive buildup of debt. Third, policy, instead of fighting the slump, exacerbated it, with fiscal austerity and monetary tightening even as the economy was headed down. What didn’t happen: Maybe the first thing to say about Brazil’s crisis is what it wasn’t. Over the past few decades those who follow international macroeconomics have grown more or less accustomed to…

  • Uncategorized

    test WordPress default latex, no mathjax

    Centered regular text.   Non-centered latex text: In-line latex text – does not work with certain WordPress themes: Centering equation by centering the latex text: Above does not work with tables.  Multiple lines with \\ look awkward.  First line is centered but later lines start from the same position as the first line.   Aligning equations using \begin{array}.  To center, begin latex with <p align=”center”></p>.  Will need to check by going between Visual and Text modes.  Note that there probably will be strange behavior by the location of </p> in the Text mode when going between the two modes and will probably have to correct it multiple times.  Note that…

  • Math

    Test Coin2

    https://math.stackexchange.com/questions/2033370/how-to-determine-the-number-of-coin-tosses-to-identify-one-biased-coin-from-anot/2033739#2033739   Suppose there are two coins and the percentage that each coin flips a Head is \(p\) and \(q\), respectively. \(p, q \in [0,1] \), \(p \neq q \), and the values are given and known. If you are free to flip one of the coins any number of times, how many times \(n\) do you have to flip the coin to decide with some significance level \( \left( \textrm{say } \alpha = 0.05 \right) \) that it’s the \(p\) coin or the \(q\) coin that you’ve been flipping? The distribution of heads after \(n\) flips for a coin will be a binomial distribution with means at \(pn\) and…

  • Math

    Test Coin

    https://math.stackexchange.com/questions/2033370/how-to-determine-the-number-of-coin-tosses-to-identify-one-biased-coin-from-anot/2033739#2033739 Suppose there are two coins and the percentage that each coin flips a Head is \(p\) and \(q\), respectively. \(p, q \in [0,1] \) and the values are given and known. If you are free to flip one of the coins, how many times \(n\) do you have to flip the coin to decide with some significance level \( \left( \textrm{say } \alpha = 0.05 \right) \) that it’s the \(p\) coin or the \(q\) coin that you’ve been flipping? The distribution of heads after \(n\) flips for a coin will be a binomial distribution with means at \(pn\) and \(qn\). The Usual Hypothesis Test In the usual hypothesis…

  • Random,  Science

    Test

    Test The Usual Colors of the Sky Why is the sky blue? Why are sunsets red? The answers and explanations to these questions can be found fairly easily on the internet. But there are many subtle “Wait a minute…”-type questions in between the cracks that seem to necessitate subtle answers and more “difficult” searching around the internet to find those answers. So, why is the sky blue? No, but first, what color is sunlight? Visible light generally is from 390 nm (violet) to 720 nm (red). Visible sunlight is a mix of these colors at the intensities we see in the figure above. , with maximum eye sensitivity at 555…

  • Math

    Barcodes and Modular Arithmetic

    Barcodes Here is an example of a UPC-A barcode, taken from wikipedia: A UPC-A barcode has 12 digits.  The first digit is something that tells how the numbers are generally used – for example, a particular industry might use a certain number for certain kinds of items.  The last twelfth digit is a check digit that can try to tell whether or not the numbers have an error.  This check digit is constructed in a certain way at first.  Later on, the check digit may be able to tell us if the numbers have an error or not.   The check digit is constructed as follows: We have 11 digits:…