Transcript Recap - Typepad

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:
Recap
http://delong.typepad.com/sdj/econ-1-spring-2014/
February 5, 2014, 4-5:30
101 Barker, U.C. Berkeley
The Y-Intercept: Price at Which Supply Is
0.
• Supply:
– P = Ps0 + a x Qs
Ladies and Gentlemen, to Your
i>Clickers!
• Suppose: P = Ps0 + a x Qs
– Ps0 = 10 :: a = 7
• At what price will the quantity supplied be 0?
–
–
–
–
–
A. 59
B. 30
C. 10
D. 35.71
E. None of the Above
Ladies and Gentlemen, to Your
i>Clickers!
• Suppose: P = Ps0 + a x Qs
– Ps0 = 10 :: a = 7
• At what price will the quantity supplied be 0?
– A. 59
– B. 30
– C. 10
– D. 35.71
– E. None of the Above
• That is what the Ps0 parameter is: the price
at which the quantity supplied is zero.
The Slope: What Change in Price Calls
Forth One More Unit of Supply?
• Supply:
– P = Ps0 + a x Qs
• Which means:
– To call forth 1
more unit of
quantity supplied
requires a price
increase of the
quantity a
Ladies and Gentlemen, to Your
i>Clickers!
• Suppose: P = Ps0 + a x Qs
– Ps0 = 10 :: a = 7
• If the price is 38, what is the quantity
supplied?
–
–
–
–
–
A. 276
B. 17
C. 5 3/7
D. 4
E. None of the Above
Ladies and Gentlemen, to Your
i>Clickers!
• Suppose: P = Ps0 + a x Qs
– Ps0 = 10 :: a = 7
• If the price is 38, what is the quantity
supplied?
–
–
–
–
–
A. 276
B. 17
C. 5 3/7
D. 4
E. None of the Above
• 38 = 10 + 7 x ??  Q = 4
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%
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
• 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
Calculating the Equilibrium Price
• P = (b/(a+b))Ps0 + (a/(a+b))Pd0
Ladies and Gentlemen, to Your
i>Clickers!
• Suppose: P =10 + 2 x Qs :: P = 100 - 7 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: Supply: P = 10 + 2 x Qs :: Demand: P = 100 - 7 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 care a lot about higher prices, so that
means they have morebargaining power—and to the equilibrium price
of 30 is much closer to the suppliers’ ZQ price than to that of the
demanders…
Equilibrium Quantity Is the Gap Between the ZQ
Parameters Divided by the Sum of the Slopes…
• Supply: P = Ps0 + a x Qs Demand: P = Pd0 – b x Qd
• Equilibrium: Q = (Pd0 - Ps0 )/(a+b) :: P = (b/(a+b))Ps0 + (a/(a+b))Pd0
Ladies and Gentlemen, to Your
i>Clickers!
• Suppose: P =10 + 7 x Qs :: P = 175 - 4 x Qd
• What is the market equilibrium quantity going
to be?
–
–
–
–
–
A. 14.5454
B. 115
C. 70
D. 15
E. None of the Above
Ladies and Gentlemen, to Your
i>Clickers!
• Suppose: P =10 + 7 x Qs :: P = 175 - 4 x Qd
• What is the market equilibrium quantity going to be?
–
–
–
–
–
A. 14.5454
B. 115
C. 70
D. 15
E. None of the Above
• The equilibrium quantity will be the net intensity of
relative demand—the gap between the ZQ reservation
prices—divided by the sum of the slopes
– The ZQ prices are 10 and 175, so the gap is 165
– The sum of the slopes is 15
– 165/11 = 15
Equilibrium Price Is a Slope-Weighted Average
of the Zero-Quantity Price Intercepts…
• Supply: P = Ps0 + a x Qs Demand: P = Pd0 – b x Qd
• Equilibrium: Q = (Pd0 - Ps0 )/(a+b) :: P = (b/(a+b))Ps0 + (a/(a+b))Pd0
Memorize This!
• Supply: P = Ps0 + a x Qs Demand: P = Pd0 – b x Qd
• Equilibrium: Q = (Pd0 - Ps0 )/(a+b) :: P = (b/(a+b))Ps0 + (a/(a+b))Pd0
Ladies and Gentlemen, to Your
i>Clickers!
• Suppose: P =10 + 7 x Qs :: P = 175 - 4 x Qd
• What is the market equilibrium price going to
be?
–
–
–
–
–
A. 55
B. 30
C. 110
D. 115
E. None of the Above
Ladies and Gentlemen, to Your
i>Clickers!
•
Suppose: P =10 + 7 x Qs :: P = 175 - 4 x Qd
• What is the market equilibrium price going to be?
– A. 55
– B. 30
– C. 110
– D. 115
– E. None of the Above
• The equilibrium price will be a slope-weighted average of the ZQ prices
– The ZQ prices are 10 and 175
– 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 115