Transcript Everything Is Going to Be Smooth, and Mathy!

Economics 2: Spring 2014
J. Bradford DeLong <[email protected]>; Maria
Constanza Ballesteros <[email protected]>;
Connie Min <[email protected]>
http://delong.typepad.com/sdj/econ-2-spring-2014/
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
We Are Never More Going to Have
Ugly Kinked Supply Curves…
Everything Is Going to Be Smooth,
and Mathy!
• Supply:
– P = Ps0 + a x Qs
– P = Ps1 x Qs(a)
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%
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%
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
Everything Is Going to Be Smooth,
and Mathy!
• Equilibrium: Q = (Pd0 - Ps0 )/(a+b) :: P = (b/(a+b))Ps0 + (a/(a+b))Pd0
Everything Is Going to Be Smooth,
and Mathy!
• Equilibrium: Q = (Pd0 - Ps0 )/(a+b) :: P = (b/(a+b))Ps0 + (a/(a+b))Pd0
• 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
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
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
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…
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
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
On the Graph
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…