Econ Dept, UMR Presents The Demand Side of the The Demand Side of the Market Market
Starring Starring � Utility Theory � Consumer Surplus � Elasticity
Featuring Featuring The MU/P Rule � The MU/P Rule � � The Meaning of Value The Meaning of Value � Four Elasticities: � Four Elasticities: � Price Elasticity of Demand � Price Elasticity of Demand � Income Elasticity � Income Elasticity � Cross Price Elasticity � Cross Price Elasticity � Price Elasticity of Supply � Price Elasticity of Supply � � The Elasticity The Elasticity- -TR Relationship TR Relationship �
In Three Parts In Three Parts Consumer Choice Theory Consumer Choice Theory Consumer Surplus Consumer Surplus Elasticity Elasticity A. Price Elasticity of Demand A. Price Elasticity of Demand B. Other Important Elasticities B. Other Important Elasticities
Part 3 Elasticity Elasticity Measures of Response Measures of Response
Consumers and producers move along their demand and supply curves when the price of the good changes QUESTION: HOW CAN WE PREDICT THE MAGNITUDE OF THESE REACTIONS? Demand and supply curves shift when factors other than price change in the marketplace QUESTION: HOW CAN WE PREDICT THE MAGNITUDE OF THESE REACTIONS? ANSWER: ELASTICITIES!!
A Generic Definition of A Generic Definition of Elasticity Elasticity � Y = f(x) Y = f(x) � , , , = % ∆ y/ ∆ x, where ∆ is read = % ∆ % ∆ x, where ∆ � Elasticity, Elasticity, , y/% is read � “change in change in” ” “ ∆ Y = ( ∆ y/y)*100; ∆ X = ( ∆ x/x)*100 % ∆ Y = ( ∆ % ∆ X = ( ∆ � % y/y)*100; % x/x)*100 � ∆ Y/y)/( ∆ x/x), or ( ∆ Y/y)/( ∆ � ( x/x), or � [( ∆ ∆ Y/ Y/ ∆ ∆ x)/(x/y)] � [( x)/(x/y)] � � In words, elasticity gives us the estimated In words, elasticity gives us the estimated � percentage change in one variable, y, in percentage change in one variable, y, in response to a percentage change in another response to a percentage change in another variable, x, c.P c.P variable, x,
G eneric Interpretation of Elasticity G eneric Interpretation of Elasticity = % ∆ ∆ Y/ % ∆ ∆ x = 2 Y/% x = 2 = % � , � , � This means if x were to change by 1 percent This means if x were to change by 1 percent � we would expect y to change by 2 percent we would expect y to change by 2 percent in the same same direction, direction, c.p. c.p. in the ∆ Y/ ∆ x = = % ∆ % ∆ Y/% x = - - 2 2 = % � , � , � This means if x were to change by 1 percent This means if x were to change by 1 percent � we would expect y to change by 2 percent we would expect y to change by 2 percent in the opposite in the opposite direction, direction, c.p. c.p.
Rewriting the Formula for Elasticity Rewriting the Formula for Elasticity ∆ Y/ ∆ x = % ∆ % ∆ Y/% x = % � , � , ∆ y = ( ∆ y/y)*100 % ∆ y = ( ∆ Percentage change, % y/y)*100 � Percentage change, � � E.G., Percentage change from 50 to 100 is change E.G., Percentage change from 50 to 100 is change � (= +50), divided by the base (=100) times 100 = (= +50), divided by the base (=100) times 100 = (50/100)* 100 = 50% (50/100)* 100 = 50% � Since the numerator and denominator have 100, Since the numerator and denominator have 100, � they cancel, and they cancel, and ∆ Y/ ∆ x = ( ∆ y/y)*( ∆ x/x) or = % ∆ % ∆ x = ( ∆ y/y)*( ∆ Y/% x/x) or = % � , � , ∆ Y/ ∆ x)*(x/y) ( ∆ Y/ ∆ = ( = x)*(x/y) � , � , � It It’ ’s this last formula that is most convenient s this last formula that is most convenient � to use as we see later to use as we see later
Some Important Elasticities Some Important Elasticities � Price elasticity of demand Price elasticity of demand � % ∆ in Q D ∆ Q D P = - , D = - % ∆ in P ∆ P Q � Cross price elasticity of demand Cross price elasticity of demand � % ∆ in D 1 ∆ D 1 P 2 = , D1,P2 = % ∆ in P 2 ∆ P 2 D 1 � Income elasticity Income elasticity � % ∆ in D ∆ D I % ∆ in I = , I = ∆ I D � Price elasticity of supply Price elasticity of supply � % ∆ in Q S ∆ Q S P = , S = % ∆ in P ∆ P Q
This Slide Show Discusses This Slide Show Discusses Price Elasticity of Demand Price Elasticity of Demand Other Elasticities are discussed in slide � Other Elasticities are discussed in slide � show III.B. show III.B.
Price Elasticity of Demand Price Elasticity of Demand Measures How Responsive Measures How Responsive Consumers Are to Changes Consumers Are to Changes in the Price of a Product in the Price of a Product
Demand Demand � We know, from the law of demand, that We know, from the law of demand, that � price and quantity demanded are price and quantity demanded are inversely related inversely related � Now, we are going to get more specific Now, we are going to get more specific � in defining that relationship in defining that relationship � We want to know just We want to know just how much how much will will � quantity demanded change when price quantity demanded change when price changes? That is what elasticity of elasticity of changes? That is what demand measures measures demand
Price Elasticity of Demand Price Elasticity of Demand Price elasticity of demand ( ( , ) � Price elasticity of demand D ) , D � measures the responsiveness of Q D measures the responsiveness of Q D of a of a in its P good to a change in its P good to a change ∆ In Q % ∆ % In Q D � � D , D = - ∆ in P % ∆ % in P � Note that Note that ∆ ∆ means “change” means “change” � Also note that the law of demand � Also note that the law of demand � ∆ Q ∆ P is negative. Our implies ∆ D ∆ implies Q D P is negative. Our definition of , includes a negative definition of D includes a negative , D sign, so , will always be a positive sign, so D will always be a positive , D number (I know its confusing but …) number (I know its confusing but …)
Ambiguity of the Sign of , Ambiguity of the Sign of , D D � Some economists define Some economists define , D with with a a , D � negative sign, that’ ’s what we do s what we do negative sign, that Some economists leave the negative sign � Some economists leave the negative sign � out of the formula and then talk about out of the formula and then talk about about the absolute value of about the absolute value of , , D D � Some economists are just sloppy and talk Some economists are just sloppy and talk � of negative , sometimes and positive of negative D sometimes and positive , D sometimes sometimes Regardless the interpretation is the same: � Regardless the interpretation is the same: � � If If = 2 or - -2 the meaning is clear, a 10% 2 the meaning is clear, a 10% = 2 or , D � change in price is expected to change change in price is expected to change quantity demanded in the opposite direction quantity demanded in the opposite direction by 20% by 20%
Calculating Elasticity of Calculating Elasticity of Demand Demand Consider the following Demand Curve: P Q D = 16 - 2P 6 5 2 D 1 0 Q/t 4 6 12 14 16
Calculating Elasticity Calculating Elasticity P A …and let’s say we want to find 6 the Elasticity of Demand at point A 5 Notice the slope of the demand curve, ) P/ ) Q, = -1/2 2 D 1 0 Q/t 4 6
Calculating Elasticity Calculating Elasticity � We know We know � % ∆ in Q D ∆ Q P = - , D = - % ∆ in P ∆ P Q % ∆ ∆ Can be calculated as the change divided � % Can be calculated as the change divided � by starting point by starting point ) P P is In this case, ∆ ∆ Q � In this case, Q D / ) is - -2 (the inverse of the 2 (the inverse of the D / � slope of the demand curve) slope of the demand curve) � P/Q is 6/4 (we use the initial P and Q as our P/Q is 6/4 (we use the initial P and Q as our � base base D = = - - ( (- - 2 2 )( )( 6/4 6/4 ) ) = 3 = 3 � , � , D
Calculating Elasticity Calculating Elasticity P A Now, let’s find the Elasticity of 6 Demand at point C 5 C 2 D 1 0 Q/t 12 4
Calculating Elasticity Calculating Elasticity � Again, Again, � % ∆ in Q D ∆ Q P = - , D = - % ∆ in P ∆ P Q � ∆ ∆ Q / ∆ ∆ P P is still Q D D / is still - -2 (the inverse of the slope of 2 (the inverse of the slope of � the demand curve) the demand curve) � P/Q is 2/12 (again use the initial P and Q as P/Q is 2/12 (again use the initial P and Q as � the base the base ) = 1/3 2)(2/12 ) D = = - - ( (- - 2)(2/12 = 1/3 � , � , D
Calculating Elasticity Calculating Elasticity � Note that is different at different places Note that is different at different places � , D along the curve along the curve � Specifically, it gets smaller as you move Specifically, it gets smaller as you move � down the curve down the curve � Note that elasticity and slope are NOT the Note that elasticity and slope are NOT the � same thing same thing
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