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Economics 2: Spring 2014

Economics 2: Spring 2014. J. Bradford DeLong <jbdelong@berkeley.edu>; Maria Constanza Ballesteros <mc.ballesteros@berkeley.edu>; Connie Min <conniemin@berkeley.edu> http://delong.typepad.com/sdj/econ-2-spring-2014/. Economics 2: Spring 2014: Supply and Demand Algebra.

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Economics 2: Spring 2014

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  1. Economics 2: Spring 2014 J. Bradford DeLong <jbdelong@berkeley.edu>; Maria Constanza Ballesteros <mc.ballesteros@berkeley.edu>; Connie Min <conniemin@berkeley.edu> http://delong.typepad.com/sdj/econ-2-spring-2014/

  2. Economics 2: Spring 2014: Supply and Demand Algebra http://delong.typepad.com/sdj/econ-1-spring-2012/ January 29, 2014, 4-5:30 101 Barker, U.C. Berkeley

  3. We Are Never More Going to Have Ugly Kinked Supply Curves…

  4. Everything Is Going to Be Smooth, and Mathy! • Supply: • P = Ps0 + a x Qs • P = Ps1 x Qs(a)

  5. Everything Is Going to Be Smooth, and Mathy! • Supply: • P = Ps0 + a x Qs • P = Ps1 x Qs(a) • Which means: • To call forth 1 more unit of quantity supplied requires a price increase of 1/a • To call forth a 1% increase in quantity supplied requires a price increase of 1/a%

  6. Everything Is Going to Be Smooth, and Mathy! • Supply: • P = Ps0 + a x Qs • P = Ps1 x Qs(a) • Demand: • P = Pd0 - b x Qd • P = Pd1 x Qd(-b) • Which means: • To call forth 1 more unit of demand requires a price decrease of 1/b • To call forth a 1% increase in quantity demanded requires a price decrease of 1/b%

  7. Everything Is Going to Be Smooth, and Mathy! • Linear Case: • P = Ps0 + a x Qs • P = Pd0 - b x Qd • Solve: • Pd0 - b x Qd = Ps0 + a x Qs • Pd0 - Ps0 = (a+b) x Qs • Equilibrium • Q = (Pd0 - Ps0 )/(a+b) • P = (b/(a+b))Ps0 + (a/(a+b))Pd0

  8. Everything Is Going to Be Smooth, and Mathy! • Equilibrium: Q = (Pd0 - Ps0 )/(a+b) :: P = (b/(a+b))Ps0 + (a/(a+b))Pd0

  9. Everything Is Going to Be Smooth, and Mathy! • Equilibrium: Q = (Pd0 - Ps0 )/(a+b) :: P = (b/(a+b))Ps0 + (a/(a+b))Pd0

  10. And the Exponential-Function Case?: P=Ps1xQsa P=Pd1xQd-b • Take logarithms • ln(P) = ln(Ps1) + a x ln(Qs) • ln(P) = ln(Pd1) – b ln(Qd) • And find: • ln(Q) = (ln(Pd1) - ln(Ps1))/(a+b) • ln(P) = (b/(a+b)) x ln(Ps1) + (a/(a+b)) x ln(Pd1) • Log-linearity: • Take the (log of the) quotient of the unit-quantity prices, and divide by the sum of the log slopes—that’s your equilibrium (log) quantity • The equilibrium (log) price is the slope-weighted average of the unit-quantity (log) prices

  11. We Will Do a Lot of These on Problem Set 2! • Suppose: P = Ps0 + a x Qs :: P = Pd0 - b x Qd • Supply curve for dragon-training missions is: • Ps0 = 10 • a = 7 • Demand curve for dragon-training missions is: • Pd0 = 100 • b = 2

  12. Ladies and Gentlemen, to Your i>Clickers! • Suppose: P = Ps0 + a x Qs :: P = Pd0 - b x Qd • Ps0 = 10 :: a = 7 :: Pd0 = 100 ::b = 2 • What is the market equilibrium price going to be? • A. 55 • B. 30 • C. 74.29 • D. 35.71 • E. None of the Above

  13. Ladies and Gentlemen, to Your i>Clickers! • Suppose: P = Ps0 + a x Qs :: P = Pd0 - b x Qd • Ps0 = 10 :: a = 7 :: Pd0 = 100 ::b = 2 • What is the market equilibrium price going to be? • A. 55 • B. 30 • C. 74.29 • D. 35.71 • E. None of the Above • You take the slope-weighted average of the two zero quantity prices, 10 and 100. • That means you are 2/9 of the way from one ZQ value to the other • Which one is it? The demanders don’t care much about higher prices, so that means they have less bargaining power—and to the equilibrium price of 80 is much closer to the demanders’ ZQ price than to the suppliers…

  14. Ladies and Gentlemen, to Your i>Clickers! • Suppose: P = Ps0 + a x Qs :: P = Pd0 - b x Qd • Ps0 = 10 :: a = 7 :: Pd0 = 100 ::b = 2 • What is the market equilibrium quantity going to be? • A. 10 • B. 12 2/9 • C. 9 • D. 4.5 • E. 55

  15. Ladies and Gentlemen, to Your i>Clickers! • Suppose: P = Ps0 + a x Qs :: P = Pd0 - b x Qd • Ps0 = 10 :: a = 7 :: Pd0 = 100 ::b = 2 • What is the market equilibrium quantity going to be? • A. 10 • B. 12 2/9 • C. 9 • D. 4.5 • E. 55 • The market equilibrum quantity is the difference between the ZQ prices divided by the sum of the slopes. • That’s 90 divided by 9 = 10

  16. On the Graph

  17. The Curse of Paul Samuelson • A guy who wanted to use a lot more math in economics… • A guy who was fired from Harvard around World War II for being too Jewish, and went to MIT… • A guy who was teaching MIT students going to college on the GI Bill… • A guy who wrote a Principles textbook that worked well with them… • Words, graphs, equations… • But you are close to the target audience…

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