Economics 113 Slides J. Bradford Delong http://bradford-delong.com brad.delong@gmail.com @delong 2017-01-23 KNT: https://www.icloud.com/keynote/ 0LrGo9XoEQ-6Plw4xIs8hEe6Q#2017-01-23_Econ_113_Slides
Outline • Office Hours • Tools: Analyzing Growth • iClickers: Analyzing Growth • Background: Economic Growth: The Bird’s- Eye View • Assignment: Letter to GSIs • Background: This Is Berkeley
Office Hours • Scheduled: Evans Hall 691A: M 3:30-4:30 pm; W 11-12 noon • By appointment: email delong@econ.berkeley.edu • By internet (depending on your course): • 113: < https://bcourses.berkeley.edu/ courses/1456905/discussion_topics/ 5127644/ > • 115: < https://bcourses.berkeley.edu/ courses/1456906/discussion_topics/ 5109740 > • 210a: < https://bcourses.berkeley.edu/ courses/1456907/discussion_topics/ 5130849 > • 210b: < https://bcourses.berkeley.edu/ courses/1456908/discussion_topics/ 5127924 >
Tools: Analyzing Growth • Economics gives us numbers: prices and quantities over time • Proportional growth—compound interest • The time over which some growth process takes place • The rate at which growth (or shrinkage) takes place • The amount that the variable grows to • T, g, y… with little t standing in for any potential moment • Don’t get snowed! Accurately assess how important or consequential things are!
Listen to Richard Feynman “An analogy…. The Maya Indians were interested in… Venus…. To make calculations, the Maya had invented a system of bars and dots to represent numbers… and had rules by which to calculate and predict not only the risings and settings of Venus, but other celestial phenomena…. Only a few Maya priests could do such elaborate calculations…. Suppose we were to ask one of them how to do just one step in the process of predicting when Venus will next rise as a morning star—subtracting two numbers….. How would the priest explain? ….
Listen to Richard Feynman II “He could either teach us the… bars and dots and the rule… or he could tell us what he was really doing: ‘Suppose we want to subtract 236 from 584. First, count out 584 beans and put them in a pot. Then take out 236 beans and put them to one side. Finally, count the beans left in the pot. That number is the result….’ You might say, ‘My Quetzalcoatl! What tedium… what a job!’ To which the priest would reply, ‘That’s why we have the rules…. The rules are tricky, but they are a much more efficient way of getting the answer…. We can predict the appearance of Venus by counting beans (which is slow, but easy to understand) or by using the tricky rules (which is much faster, but you must spend years in school to learn them).’ ”
The Uses of Math: Al-Khwarizmi Muḥammad ibn Mūsā al- Khwārizmī (c. 780-850) • Al-Kitāb al-Mukhtaṣar fī Hisāb al-Jabr wa’l-Muḳābala • The Compendious Book on Calculation by Restoration and Balancing • Worked in Baghdad at the House of Wisdom established by the Kalif Al-Mamun
The Uses of Math: Newton Isaac Newton (1642-1727) • Philosophiæ Naturalis Principia Mathematica • Mathematical Principles of Natural Philosophy • Worked in Cambridge t the university there • Arithmetic and accounting • Algebra and calculus • What-if machines—ways of doing a huge number of potential calculations all at once…
Exponential Growth • (dy/dt) = g(y - a) • start at t = -500 with y = a + 0.006 • g = 0.01; a = 10 • does nothing for a long time—stays very near 10—then explodes • y = 10 + exp(.01(t-10))
Exponential Growth • And keeps on exploding… • Rules of thumb for an annual growth rate g: • (y-a) doubles every 0.693/g years • (y-a) grows a thousandfold every 6.91/g years
“EXP” “E” • It’s a function: we feed it a number x, and get out exp(x) (or E^x) • We can calculate it: • exp(x) = 1+x+(x^2)/2+(x^3)/6+(x^4)/24+… • exp(0)=1 • exp(1)=2.71828182846 … • But we don’t have to… • Over 1618-1731, Napier, Oughtred, Bernoulli, Leibnitz, and Euler did it for us…
Exponential Convergence • (dy/dt) = g(k - y) • start at t = 0 with y = 0 • g = 0.01; k = 100 • heads rapidly for k • and then stays there • (k-y) halves in… • …guess what? 0.693/g • (k-y) shrinks to a thousandth of its initial value in… • …guess what? 6.91/g
Combine the Two: Logistic Growth • (dy/dt) = g(y-a)(k-y)/k, for k>>y • y = a + (k-a)[exp(gx)]/(k-a+exp(gx)-1) • a is the initial population • k is the carrying capacity • g is the unimpeded growth rate (you’ll see this called “r”) • Pierre-Francois Verhulst in 1838, building a mathematical model of Thomas Malthus’ Essay on the Principal of Population • Rediscovered by McKendrick, by Pearl and Reed, and by Lotka
Logistic Growth II
Things to Remember • Asymptote: a (in the negative direction, for growth and logistic) • Asymptote: k (in the positive direction, for convergence and logistic) • Rule of 72 : 72 divided by the growth rate gives you the doubling (for growth) or halving (for convergence) time • Rule of 720 : Multiply the doubling time by 10 to get the thousand-fold time • Why 72? Why not 0.693? 72 is easier to do in your head • 72 = 36x2=24x3=18x4=12x6=9x8 • If things aren’t continuous but come in steps…
Catch Our Breath… • Comments? • Questions?
Analyzing Growth: To Your iClickers… Something is growing at 6%/ year. How long (roughly) does it take to double? A. 36 years B. 120 years C. 12 years D. 17 years E. None of the above
Something is Growing at 4%/Year How long (roughly) does it take to multiply a thousandfold? A. 54 years B. 180 years C. 18 years D. 250 years E. None of the above
Something is Growing at 0.03%/ Year How long (roughly) does it take to multiply eightfold? A. 2400 years B. 7200 years C. 72 years D. 24000 years E. None of the above .72/.0003
Human Populations Grew from 5 to 50 Million between 10 and 3 Thousand Years Ago Between the invention of agriculture and 1000 BC. Had that pace continued, about what would the human population be now? A. 500 million B. 7.5 billion C. 140 million D. 1.4 billion E. None of the above 3+ doublings in 7000 years 1 doubling 2000+ years 1.5- doublings since 1000 BC
Catch Our Breath… • Comments? • Questions?
Economic Growth: The Bird’s-Eye View: Anatomically Modern Humans • Anatomically modern humans —Home Sapiens Sapiens— evolved about 200,000 years ago : • In the Horn of Africa. • Omo Kibish remains in Ethiopia. • Behaviorally modern humans: • 80KYrs ago? 50KYrs ago? • Gradual or sudden? • Toba (Indonesia) volcanic supereruption of 75K: • Did it knock our breeding population down to 1K—did we almost go extinct? • Or did about 1K of us gain key advantageous traits of behavioral modernity, and then out compete the rest?
Behaviorally Modern Humans • By 50KYrs ago… • Archaeological evidence of behavioral modernity: • Art: cave paintings, petroglyphs, figurines • Pigment and jewelry for adornment • Bone tools • Long-distance transport • Blades • Hearths • Regional distinctions but standardization within regions • burial
Behaviorally Modern Humans II • We use language: • Thus we become an anthology intelligence. • What one person learns, soon everybody knows. • We make and use tools: • Complex, composite tools. • We are sociable: • Much more sociable than our chimp, gorilla, orangutang cousins • Perhaps less than our bonobo cousins?
Civilized Sociable Language- and Tool-Using East African Plains Ape • What would an alien intelligence—vast, cool, and sympathetic or unsympathetic —say about us? • Form: • Mammals with opposable thumbs, upright posture, and big brains • Numbers: A lot of us: 7.4 billion now • Behavior • Sociable, linguistic, tool-using • Gossip (about food, threats, mating, etc.) • Alter our environment • Large-scale social division of labor— greater than seen in the social insects —mediated by markets and exchange • Gift-exchang e
Adam Smith • Natural propensity to “truck, barter, and exchange”. • We form gift-exchange relationships with those we trust and to create trust—patterns of mutual obligation. • We have developed money to create trust between strangers. • On top of this natural propensity to develop gift-exchange relationships and the social institution of money- as-trust we have built our largely peaceful 7.4B-strong prosperous societal division of labor.
The Wealth of Nations and the System of Natural Liberty • Adam Smith's 1776 Wealth of Nations contains a genuinely game-changing insight : • The “system of natural liberty” — markets and exchange— • Has some remarkable advantages. • Just let people exchange things freely: • in an environment in which property is secure, and • in which there is an alternative deal almost as good just down the street, and • things will work out remarkably well…
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