Lecture 03 Demand Supply cont Lecturer Martin Paredes

Lecture # 03 Demand Supply (cont. ) Lecturer: Martin Paredes

Definition: The Market Supply function tells us how the quantity of a good supplied by the sum of all producers in the market depends on various factors Qs = f (p, po, w, …) 2

Definition: The Supply Curve plots the aggregate quantity of a good that will be offered for sale at different prices Qs = Q (p) 3

Example: Supply Curve for Wheat in Canada Price (dollars per bushel) Supply curve for wheat in Canada 0 0. 15 Quantity (billions of bushels per year) 4

Definition: The Law of Demand Curve states that the quantity of a good offered increases when the price of this good increases. ¡ Empirical regularity 5

l The supply curve shifts when factors other than own price change… If the change increases the willingness of producers to offer the good at the same price, the supply curve shifts right ¡ If the change decreases the willingness of producers to offer the good at the same price, the supply curve shifts left ¡ 6

l. A move along the supply curve for a good can only be triggered by a change in the price of that good. l A shift in the supply curve for a good can be triggered by a change in any other factor ¡A change that affects the producers’ willingness to offer the good. 7

Example: Canadian Wheat • QS = p +. 05 r • QS = quantity of wheat (billions of bushels) • p = price of wheat (dollars per bushel) • r = average rainfall in western Canada (inches) • • • Suppose price is $2 Quantity supplied no rainfall = $2 Quantity supplied with rainfall of 3” = $2. 15 • As rainfall increases, supply curve shifts right • (e. g. , r = 4 => Q = p + 0. 2) 8

Price ($) 0 Quantity, Billion bushels 9

Price ($) r=0 Supply with no rain 0 Quantity, Billion bushels 10

Price ($) r=0 r=3 Supply with no rain Supply with 3” rain 0. 15 Quantity, Billion bushels 11

Definition: A market equilibrium is a price such that, at this price, the quantities demanded and supplied are the same. l Demand supply curves intersect at equilibrium. 12

Example: Market for Cranberries • Suppose • QD = 500 – 4 P • QS = – 100 + 2 P • Where • P = price of cranberries (euros per barrel) • Q = demand or supply (in millions of barrels/year) 13

Example: Market for Cranberries • The equilibrium price is calculated by equating demand to supply: QD = Q S or 500 – 4 P = – 100 + 2 P • Solving for P: • To get equilibrium quantity, plug equilibrium price into either demand or supply • Into demand: Q* = 500 – 4(100) = 100 • Into supply: Q* = – 100 + 2(100) = 100 P* = 100 14

Example: The Market For Cranberries Price Market Supply: QS = -100 + 2 P 50 Quantity 15

Example: The Market For Cranberries Price 125 Market Supply: QS = -100 + 2 P 50 Market Demand: Qd = 50 – 4 P Quantity 16

Example: The Market For Cranberries Price 125 P*=100 Market Supply: QS = -100 + 2 P • 50 Market Demand: Qd = 50 – 4 P Q* = 100 Quantity 17

Definition: If at a given price, sellers cannot sell as much as they would like, there is excess supply. Definition: If at a given price, buyers cannot purchase as much as they would like, there is excess demand. 18

Example: Excess Supply in the Market For Cranberries Price 125 Market Supply 50 Market Demand Quantity 19

Example: Excess Supply in the Market For Cranberries Price 125 Market Supply 50 Market Demand Qd Q* QS Quantity 20

Example: Excess Supply in the Market For Cranberries Price 125 • Excess Supply • Market Supply 50 Market Demand Qd Q* QS Quantity 21

l If there is no excess supply or excess demand, there is no pressure for prices to change and we are in equilibrium. l When a change in an exogenous variable causes the demand curve or the supply curve to shift, the equilibrium shifts as well 22

Definition: The own price elasticity of demand is the percentage change in quantity demanded brought about by a one-percent change in the price of the good Q, P= ( % Q) = ( Q/Q) = ( % P) ( P/P) d. Q. P d. P Q 23

l Elasticity is not the slope l Slope is the ratio of absolute changes in quantity and price. (= d. Q/d. P). l Elasticity is the ratio of relative (or percentage) changes in quantity and price. 24

Q, P = 0 Perfectly inelastic demand l Quantity demanded is completely insensitive to changes in price 2. Q, P (-1, 0) Inelastic demand l Quantity demanded is relatively insensitive to changes in price 3. Q, P = -1 Unitary elastic demand l Percentage increase in quantity demanded equals percentage decrease in price 1. 25

4. Q, P (- , -1) Elastic demand l Quantity demanded is relatively sensitive to changes in price 5. Q, P = - Perfectly elastic demand l Any increase in price results in quantity demanded decreasing to zero l Any increase in price results in quantity demanded increasing to infinity. 26

Example: Linear Demand Curve • Suppose QD = a – b. P • a, b : positive constants • P: price • Notes: • -b is the slope • a/b is the choke price 27

Example: Linear Demand Curve • The elasticity is Q, P= d. Q. P = – b. P d. P Q Q • So for linear demand curves • Slope is constant. • Elasticity falls from 0 to - along the demand curve. • • E. g. , suppose Q = 400 – 10 P At P = 30, Q = 100, so Q, P= d. Q. P = – b. P = – 10. 30 = – 3 (elastic) d. P Q Q 100 28

Example: Elasticity with a Linear Demand Curve P 0 Q 29

Example: Elasticity with a Linear Demand Curve P a/b a/2 b 0 • a/2 a Q 30

Example: Elasticity with a Linear Demand Curve P a/b Q, P = - Elastic region a/2 b • Q, P = -1 Inelastic region Q, P = 0 0 a/2 a Q 31

Example: Constant Elasticity Demand Curve • Suppose QD = Apε • A: constant • P: price • ε : elasticity of demand • The elasticity is Q, P= d. Q. P = εApε-1. P = ε d. P Q Q • So for Constant Elasticity demand curves • Elasticity is constant. • Slope falls from 0 to - along the demand curve. 32

Example: A Constant Elasticity versus a Linear Demand Curve Price • P 0 Q Observed price and quantity Quantity 33

Example: A Constant Elasticity versus a Linear Demand Curve Price • P Observed price and quantity Linear demand curve 0 Q Quantity 34

Example: A Constant Elasticity versus a Linear Demand Curve Price • P Observed price and quantity Constant elasticity demand curve 0 Q Quantity 35

Example: A Constant Elasticity versus a Linear Demand Curve Price • P Observed price and quantity Constant elasticity demand curve Linear demand curve 0 Q Quantity 36

Example: A Constant Elasticity versus a Linear Demand Curve Price • 0 Quantity 37

l Factors that determine price elasticity of demand l Demand tends to be more price-elastic when there are good substitutes for the good l Demand tends to be more price-elastic when consumer expenditure in that good is large l Demand tends to be less price-elastic when consumers consider the good as a necessity. 38

Price Elasticity of Demand for Selected Grocery Products, Chicago, 1990 s 39

Source: Berry, Levinsohn and Pakes, "Automobile Price in Market Equilibrium, " Econometrica 63 (July 1995), 841 -890. Example: Price Elasticities of Demand for Automobile Makes, 1990. 40

l In general, for the elasticity of “Y” with respect to “X”: Y, X= ( % Y) = ( Y/Y) = ( % X) ( X/X) d. Y. X d. X Y 41

l Price elasticity of supply: measures curvature of supply curve ( % QS) = ( QS/QS) = d. QS. P ( % P) ( P/P) d. P QS 42

l Income elasticity of demand measures degree of shift of demand curve as income changes… ( % QD) = ( QD/QD) = d. QD. I ( % I) ( I/I) d. I QD 43

l Cross price elasticity of demand measures degree of shift of demand curve when the price of another good changes ( % QD) = ( QD/QD) = d. QD. P 0 ( % P 0) ( P 0/P 0) d. P 0 QD 44

Source: Berry, Levinsohn and Pakes, "Automobile Price in Market Equilibrium, " Econometrica 63 (July 1995), 841 -890. Example: The Cross-Price Elasticity of Demand for Cars 45

Source: Gasmi, Laffont and Vuong, "Econometric Analysis of Collusive Behavior in a Soft Drink Market, " Journal of Economics and Management Strategy 1 (Summer, 1992) 278 -311. Example: Elasticities of Demand for Coke and Pepsi 46

Use Own Price Elasticities and Equilibrium Price and Quantity 2. Use Information on Past Shifts of Demand Supply 1. 47

Choose a general shape for functions l Linear l Constant elasticity 2. Estimate parameters of demand supply using elasticity and equilibrium information l We need information on ε, P* and Q* 1. 48

Example: Linear Demand Curve • • Suppose demand is linear: QD = a – b. P Then, elasticity is Q, P = -b. P/Q • Suppose • Notice that, if = -b. P/Q b = - Q/P • • Then …and • Hence QD = 108. 5 – 55 P P = 0. 7 Q = 70 Q, P = -0. 55 b = -(-0. 55)(70)/(0. 7) = 55 a = QD + b. P = (70)+(55)(0. 7) = 108. 5 49

Example: Constant Elasticity Demand Curve • Suppose demand is: QD = APε • Suppose again • Notice that, if QD = APε A = QP-ε • Then • Hence QD = 57. 53 P-0. 55 P = 0. 7 Q = 70 Q, P = -0. 55 A = (70)(0. 7)0. 55 = 57. 53 50

Example: Broilers in the U. S. , 1990 Price • . 7 0 70 Observed price and quantity Quantity 51

Example: Broilers in the U. S. , 1990 Price • . 7 Observed price and quantity Linear demand curve 0 70 Quantity 52

Example: Broilers in the U. S. , 1990 Price • . 7 Observed price and quantity Constant elasticity demand curve 0 70 Quantity 53

Example: Broilers in the U. S. , 1990 Price • . 7 Observed price and quantity Constant elasticity demand curve Linear demand curve 0 70 Quantity 54

1. A shift in the supply curve reveals the slope of the demand curve 2. A shift in the demand curve reveals the slope of the supply curve. 55

Example: Shift in Supply Curve • • Old equilibrium point: New equilibrium point: • Both equilibrium points would lie on the same (linear) demand curve. • Therefore, if QD = a - b. P • • (P 1, Q 1) (P 2, Q 2) b = d. Q/dp = (Q 2 – Q 1)/(P 2 – P 1) a = Q 1 - b. P 1 56

Example: Identifying demand by a shift in supply Price Supply Market Demand 0 Quantity 57

Example: Identifying demand by a shift in supply Price New Supply Old Supply Market Demand 0 Quantity 58

Example: Identifying demand by a shift in supply Price New Supply Old Supply • P 2 P 1 • Market Demand 0 Q 2 Q 1 Quantity 59

This technique only works if the curve we want to estimate stays constant. Example: Shift in Supply Curve • We require that the demand curve does not shift 60

Price Supply Demand 0 Quantity 61

Price New Supply Old Demand New Demand 0 Quantity 62

Price New Supply • • P 2 P 1 Old Supply Old Demand New Demand 0 Q 2 = Q 1 Quantity 63

1. First example of a simple microeconomic model of supply and demand (two equations and an equilibrium condition) 2. Elasticity as a way of characterizing demand supply 3. Elasticity changes as market definition changes (commodity, geography, time) 64

4. Elasticity a very general concept 5. Back of the envelope calculations: ·Estimating demand supply from own price elasticity and equilibrium price and quantity ·Estimating demand supply from information on past shifts, assuming that only a single curve shifts at a time. 65