Economics 2: Spring 2014 J. Bradford DeLong ; Maria Constanza Ballesteros ; Connie Min

Economics 2: Spring 2014: Supply and Demand Algebra: Demand and Equilibrium February 3, 2014, 4-5: Barker, U.C. Berkeley

We Also Need Demand Supply: – P = P s0 + a x Q s – P = P s1 x Q s (a) Demand: – P = P d0 - b x Q d – P = P d1 x Q d (-b)

Demand Coefficients: The Price at Which Demand Is Zero, and the Slope Supply: – P = P s0 + a x Q s – P = P s1 x Q s (a) Demand: – P = P d0 - b x Q d – P = P d1 x Q d (-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 = P d0 - b x Q d – Demand curve for dragon-training missions is: P d0 = 100 b = 2

Ladies and Gentlemen, to Your i>Clickers! Suppose: P = P d0 - b x Q d P d0 = 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 = P d0 - b x Q d P d0 = 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 P d0 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 = P s0 + a x Q s – P = P d0 - b x Q d

Ladies and Gentlemen, to Your i>Clickers... Suppose: P = P s0 + a x Q s :: P = P d0 - b x Q d – Supply: P s0 = 10; a = 7 – Demand: P d0 = 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 = P s0 + a x Q s :: P = P d0 - b x Q d – Supply: P s0 = 10; a = 7 – Demand: P d0 = 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 = x Q s :: P = x Q d 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 = x Q s :: P = x Q d 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 = P s0 + a x Q s – P = P d0 - b x Q d Solve: – P d0 - b x Q d = P s0 + a x Q s – P d0 - P s0 = (a+b) x Q s Equilibrium – Q = (P d0 - P s0 )/(a+b)

Calculating the Equilibrium Quantity Equilibrium: Q = (P d0 - P s0 )/(a+b)

Ladies and Gentlemen, to Your i>Clickers! Suppose: P = x Q s :: P = x Q d What is the market equilibrium quantity going to be? – A. 10 – B. 30 – C – D – E. None of the Above

Ladies and Gentlemen, to Your i>Clickers! Suppose: P = x Q s :: P = x Q d What is the market equilibrium quantity going to be? – A. 10 – B. 30 – C – D – E. None of the Above Remember our equation: Q = (P d0 - P s0 )/(a+b) – The gap between the zero-quantity reservation prices—(P d0 - P s0 )—is 90. – The sum of the slopes is 9 – The equilibrium quantity is (the gap between the zero- quantity reservation prices)/(the sum of the slopes) = 90/9 = 10

And, Yes, the Equilibrium Quantity Is Where the Curves Cross! Linear Case: – P = P s0 + a x Q s – P = P d0 - b x Q d Solve: – P d0 - b x Q d = P s0 + a x Q s – P d0 - P s0 = (a+b) x Q s Equilibrium – Q = (P d0 - P s0 )/(a+b)

Calculating the Equilibrium Price Linear Case: – P = P s0 + a x Q s – P = P d0 - b x Q d – Q = (P d0 - P s0 )/(a+b) Solve – P = P s0 + a x ((P d0 - P s0 )/(a+b)) – P = (b/(a+b))P s0 + (a/(a+b))P d0

Calculating the Equilibrium Price P = (b/(a+b))P s0 + (a/(a+b))P d0

Ladies and Gentlemen, to Your i>Clickers! Suppose: P = x Q s :: P = x Q d What is the market equilibrium price going to be? – A. 55 – B. 30 – C – D – E. None of the Above

Ladies and Gentlemen, to Your i>Clickers! Suppose: P = x Q s :: P = x Q d What is the market equilibrium price going to be? – A. 55 – B. 30 – C – D – 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))P s0 + (a/(a+b))P d0 Q = (P d0 - P s0 )/(a+b)

In the Words of Moses: Write These Down! Equilibrium Quantity: – Q = (P d0 - P s0 )/(a+b) Equilibrium Price: – P = (b/(a+b))P s0 + (a/(a+b))P d0

And Memorize This! Equilibrium: Q = (P d0 - P s0 )/(a+b) :: P = (b/(a+b))P s0 + (a/(a+b))P d0

Ladies and Gentlemen, to Your i>Clickers! Suppose: P = x Q s :: P = x Q d 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 = x Q s :: P = x Q d 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