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Efficiency of Competitive Equilibrium - Adam Smith's Big Idea

Explore the efficiency of competitive equilibrium and Adam Smith's concept of markets promoting the public interest. Understand the relationship between efficiency and the size of the pie in resource allocation. Witness a dramatic proof of the efficiency of competitive equilibrium through a trading experiment.

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Efficiency of Competitive Equilibrium - Adam Smith's Big Idea

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  1. Adam Smith: (1723-1790)Wealth of Nations: 1776

  2. Smith’s Home Town:Edinburgh, Scotland

  3. Today’s topics • The efficiency of competitive equilibrium • Finding a competitive equilibrium

  4. How did you get to UCSB today? • Walked • Rode a bicycle • Skateboarded • Drove • Used Public Transportation

  5. How long is your commute to UCSB?(in miles, round to nearest mile)

  6. A demander with Buyer Value $50 buys an object from a supplier with Seller Cost $20. The sum of the buyer’s and the seller’s profit : • depends on the price. Higher price means larger sum. • is the same at all prices between $20 and $50. • depends on the price. Lower price means smaller sum. • None of the above.

  7. Why is that? • Buyer’s profit=BV-Price • Seller’s Profit =Price –SC • Buyers Profit +Seller’s profit= (BV-Price)+(Price-SC)=BV-SC So sum of buyer’s and seller profit is BV-SC regardless of price.

  8. Clicker test • Press the button A on your clicker.

  9. One more test • Enter the number 12501 with your clicker

  10. Adam Smith’s Big Idea: Efficiency of Competitive Markets “Every individual neither intends to promote the public interest, nor knows how much he is promoting it. He intends only his own gain and he is in this led by an invisible hand to promote an end which was no part of his intention.” Adam Smith, Wealth of Nations, 1776

  11. What did Smith mean? • He said “markets promote the public interest.” • What is that? • A modern interpretation: “Competitive equilibrium is efficient.” • In the case of our experimental markets, this means the competitive equilibrium outcome maximizes total profits over all possible allocations. • This does not mean it maximizes every individual’s profits---just the sum.

  12. Efficient is not the same as fair • An outcome can be efficient, but grossly inequitable. • A system that gives almost all of the benefits go to only a few people would not be satisfactory to most people, even if it is efficient. • So why do we care about efficient?

  13. Efficiency and the size of the pie • A system is efficient if it maximizes the amount of resources to be divided. • If a pie is made larger, it becomes possible to give everyone a larger piece. • But of course it is also possible to increase the size of a pie while reducing the size of pieces given to some. • Efficiency is about the potential for mutual gain.

  14. A Dramatic Proof • We are going to act out a proof of the efficiency of competitive equilibrium. • We need: • 15 volunteers in dark shirts • 15 volunteers in light shirts • 2 accountants

  15. Trade as matchmaking • Dark shirts are “buyers”. Height of a buyer (in inches) is his or her Buyer Value. • Light shirts are “sellers”. Height of a seller (in inches) is his or her Seller Cost. • A trade is a match between a dark-shirted “buyer” and a light-shirted “seller”. • Total profits (or loss) from a match are the difference between the height of the dark shirt partner and that of the light shirt partner.

  16. Random matching • First we pair light and dark shirts at random and have them “trade” only if the dark shirt is taller than the light shirt. • Accountants will measure the total profits from these trades. • How many trades were there? • How much was total profit?

  17. Maximizing total profits • How could we arrange partnerships to maximize total profits? • One idea: Pair tallest dark shirt with shortest light shirt, second tallest dark with second shortest light, and so on until the next dark shirt is shorter than the next light shirt. • Other ways?

  18. Living Supply and Demand Curves • Line up Dark Shirt demanders in order of height, facing the class, with tallest at left of class. • Line up Light Shirt suppliers in front of the demanders in order of height, facing the class, with shortest at left of class. • These form a “demand curve” and a supply curve. • Where do the curves cross? • Suppliers turn and face demanders. You make a trade if Dark Shirt is taller than White Shirt partner and otherwise not.

  19. What is the total amount of profits? • Our Accountants will measure distances between buyer heights and seller heights and add them to compute total profits. • Could profits be increased by rearranging partners among those who trade? • Could total profits be increased by adding more trades? • Could profits be increased by exchanging somebody who traded with somebody who didn’t?

  20. What is the price? • How tall is shortest dark shirt who got a partner? • How tall is tallest light shirt who got a partner? • Let p be any number between these two heights. • How is p like an equilibrium price? • Suppose that we announced price p and said that anybody could buy or sell at price p. • Who would buy and who would sell? • Who would neither buy nor sell?

  21. Market Limbo • Line up dark shirts at left of stage, light shirts at right. • Accountants hold a broomstick 3” lower than “equilibrium height.” • Everyone from either side who can walk under the broomstick without stooping must do so. • Trades take place at left side of the room. • Is there excess demand or supply?

  22. Now too high • Return to original positions, Dark shirts on left, light shirts on right. • Set the broomstick 3” higher than equilibrium. • Everyone who can walk under without stooping goes to other side. • Is there excess demand or excess supply on the left side of the room?

  23. Getting it ju…ssst right • Return to original position. • Set broomstick at equilibrium height. • Everyone who can walk under does so. • Now supply equals demand. • Every dark shirt on left is taller than every light shirt on left. • All could profit by trading at equilibrium price.

  24. Could profits be higher than competitive equilibrium profits? • Could we increase total profits without changing who the traders are but rearranging who trades with who? • Could we increase profits without changing number of trades by exchanging some non-traders for traders? • Could we increase profits by having more trades? • Could we increase profits by having less trades?

  25. Maximizing number of transactions • Choose a broker, who gets a $1 commission on every trade. • Broker can pair people up, but they will trade only if the dark shirt is taller than the light shirt. • How should he do it? Can he make more trades than the competitive number? • Will total profits be higher or lower than in competitive equilibrium?

  26. What have we done • Shown how to prove that competitive equilibrium maximizes sum of gains in a simple demand and supply economy. • A generalization is true in economies with many simultaneous markets. That is proved in more advanced courses. • Shown how adjusting prices equilibrates supply and demand. • Price as a limbo bar • Shown that competitive equilibrium does not necessarily maximize number of profitable trades.

  27. Assignment: • Before class on Wednesday: • Read Bergstrom and Miller Appendix A.1-A.4 and McAfee Chaps 2.2-2.4 • Do Excel exercises on demand for iPods and iPhones (Link on class web page) • Before your section meets: • Read instructions for Experiment 2

  28. And we’re out of here

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