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:
Demand and Equilibrium
http://delong.typepad.com/sdj/econ-1-spring-2012/
February 3, 2014, 4-5:30
101 Barker, U.C. Berkeley
We Also Need Demand
• Supply:
– P = Ps0 + a x Qs
– P = Ps1 x Qs(a)
• Demand:
– P = Pd0 - b x Qd
– P = Pd1 x Qd(-b)
Demand Coefficients: The Price at
Which Demand Is Zero, and the Slope
• 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 b
– To call forth a 1%
increase in quantity
demanded requires a
price decrease of b%
We Will Do a Lot of These on
Problem Set 2!
• Suppose: P = Pd0 - b x Qd
– Demand curve for dragon-training missions is:
• Pd0 = 100
• b=2
Ladies and Gentlemen, to Your
i>Clickers!
• Suppose: P = Pd0 - b x Qd
• Pd0 = 100 :: b = 2
• At what price is the quantity demanded going
to be 0?
–
–
–
–
–
A. 55
B. 30
C. 100
D. 35
E. None of the Above
Ladies and Gentlemen, to Your
i>Clickers!
• Suppose: P = Pd0 - b x Qd
• Pd0 = 100 :: b = 2
• At what price is the quantity demanded going to
be 0?
–
–
–
–
–
A. 55
B. 30
C. 100
D. 35
E. None of the Above
• That’s what the Pd0 is: the price at which the
quantity demanded is zero…
With This Demand and Supply Curve, Where Is
Quantity Demanded = Quantity Supplied?
• Linear Case:
– P = Ps0 + a x Qs
– P = Pd0 - b x Qd
Ladies and Gentlemen, to Your
i>Clickers...
• Suppose: P = Ps0 + a x Qs :: P = Pd0 - b x Qd
– Supply: Ps0 = 10; a = 7
– Demand: Pd0 = 100; b = 2
• Is quantity demanded equal to quantity
supplied when the price is 38?
– A. Yes
– B. No
– C. There is not enough information to calculate…
Ladies and Gentlemen, to Your
i>Clickers...
• Suppose: P = Ps0 + a x Qs :: P = Pd0 - b x Qd
– Supply: Ps0 = 10; a = 7
– Demand: Pd0 = 100; b = 2
• Is quantity demanded equal to quantity supplied
when the price is 38?
– A. Yes
– B. No
– C. There is not enough information to calculate…
• At a price of 38, quantity supplied is… 4
• At a price of 38, quantity demanded is… 31
• These are not equal…
Ladies and Gentlemen, to Your
i>Clickers...
• Suppose: P = 10 + 7 x Qs :: P = 100 - 2 x Qd
• Is price = 38 an equilibrium, and if not what is the
price going to do?
– A. Yes, it is.
– B. No, there is excess demand, and the price is going to
rise
– C. No, there is excess demand, and the price is going to
fall
– D. No, there is excess supply, and the price is going to
rise
– E. No, there is excess supply, and the price is going to fall
Ladies and Gentlemen, to Your
i>Clickers...
•
Suppose: P = 10 + 7 x Qs :: P = 100 - 2 x Qd
• Is price = 38 an equilibrium, and if not what is the price going to do?
–
–
–
–
–
A. Yes, it is.
B. No, there is excess demand, and the price is going to rise
C. No, there is excess demand, and the price is going to fall
D. No, there is excess supply, and the price is going to rise
E. No, there is excess supply, and the price is going to fall
• At a price of 38, quantity supplied is 4, quantity demanded is 31, and so
there is excess demand
• When there is excess demand, suppliers will think that they can charge
more and raise their prices…
• When there is excess demand, demanders will find themselves unable to
buy, and offer to bid more in order not to be left disappointed…
• Thus excess demand will cause prices to rise…
With This Demand and Supply Curve, Where Is
Quantity Demanded = Quantity Supplied?
• 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)
Calculating the Equilibrium
Quantity
• Equilibrium: Q = (Pd0 - Ps0 )/(a+b)
Ladies and Gentlemen, to Your
i>Clickers!
• Suppose: P =10 + 7 x Qs :: P = 100 - 2 x Qd
• What is the market equilibrium quantity going
to be?
–
–
–
–
–
A. 10
B. 30
C. 74.29
D. 35.71
E. None of the Above
Ladies and Gentlemen, to Your
i>Clickers!
• Suppose: P =10 + 7 x Qs :: P = 100 - 2 x Qd
• What is the market equilibrium quantity going to be?
–
–
–
–
–
•
–
A. 10
B. 30
C. 74.29
D. 35.71
E. None of the Above
Remember our equation: Q = (Pd0 - Ps0 )/(a+b)
The gap between the zero-quantity reservation prices—(Pd0 Ps0 )—is 90.
– The sum of the slopes is 9
– The equilibrium quantity is (the gap between the zeroquantity reservation prices)/(the sum of the slopes) = 90/9 =
10
And, Yes, the Equilibrium Quantity
Is Where the Curves Cross!
• 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)
Calculating the Equilibrium Price
• Linear Case:
– P = Ps0 + a x Qs
– P = Pd0 - b x Qd
– Q = (Pd0 - Ps0 )/(a+b)
• Solve
– P = Ps0 + a x ((Pd0 - Ps0 )/(a+b))
– P = (b/(a+b))Ps0 + (a/(a+b))Pd0
Calculating the Equilibrium Price
• P = (b/(a+b))Ps0 + (a/(a+b))Pd0
Ladies and Gentlemen, to Your
i>Clickers!
• Suppose: P =10 + 7 x Qs :: P = 100 - 2 x Qd
• 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 = 10 + 7 x Qs :: P = 100 - 2 x Qd
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…
A Slope-Weighted Average of the
Zero-Quantity Price Intercepts…
• Equilibrium: P = (b/(a+b))Ps0 + (a/(a+b))Pd0Q = (Pd0 - Ps0 )/(a+b)
In the Words of Moses: Write
These Down!
•Equilibrium Quantity:
–Q = (Pd0 - Ps0 )/(a+b)
• Equilibrium Price:
– P = (b/(a+b))Ps0 + (a/(a+b))Pd0
And Memorize This!
• Equilibrium: Q = (Pd0 - Ps0 )/(a+b) :: P = (b/(a+b))Ps0 + (a/(a+b))Pd0
Ladies and Gentlemen, to Your
i>Clickers!
• Suppose: P =40 + 7 x Qs :: P = 150 - 4 x Qd
• What is the market equilibrium price going to
be?
–
–
–
–
–
A. 55
B. 30
C. 110
D. 50
E. None of the Above
Ladies and Gentlemen, to Your
i>Clickers!
• Suppose: P =40 + 7 x Qs :: P = 150 - 4 x Qd
• What is the market equilibrium price going to be?
–
–
–
–
–
A. 55
B. 30
C. 110
D. 50
E. None of the Above
• The equilibrium price will be a slope-weighted average of
the ZQ prices
– The ZQ prices are 40 and 150
– Since demand is moreelastic, the price will be closer to the ZQ
demand value…
– Since the slopes are 4 and 7, the equilibrium price will be 4/11 of
the way from one ZQ value and 7/11 of the way from the other…
– THAT MEANS 110