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Demand and Supply: Elasticity

Demand and Supply: Elasticity. Principles Microeconomics Professor Dalton ECON 202 – Spring 2013 Boise State University. Elasticity. Elasticity - measure of responsiveness Measures how much a dependent variable changes due to a change in an independent variable

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Demand and Supply: Elasticity

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  1. Demand and Supply:Elasticity Principles Microeconomics Professor Dalton ECON 202 – Spring 2013 Boise State University

  2. Elasticity • Elasticity - measure of responsiveness • Measures how much a dependent variable changes due to a change in an independent variable • Elasticity = %Δ X / %Δ Y • Elasticity can be computed for any two related variables

  3. Elasticity Measures • Elasticities economists are interested in: • a change in price on the quantity demanded • a change in income on the demand function for a good • a change in the price of a related good on the demand function for a good • a change in the price on the quantity supplied

  4. Price Elasticity of Demand • The “law of demand” tells us that as the price of a good increases the quantity that will be bought decreases but does not tell us by how much. • The price elasticity of demand,ε, is a measure of that information • “If you change price by 5%, by what percent will the quantity purchased change?

  5. % D Q εº % D P Q2 - Q1 = D Q Q2 - Q1 D Q Q1 Q1 ε = = P2 - P1 = D P P2 - P1 D P P1 P1 Price Elasticity of Demand At a point on a demand function this can be calculated by:

  6. +2 [2/3 = .66667] 3 % DQ = 67% =-2.3 [rounded] = -2 % DP = -28.5% 7 [-2/7=-.28571] Px A $7 B $5 D Qx/t 5 3 D Q Q1 ε= D P P1 The “own” price elasticity of demand at a price of $7 is -2.3 Price decreases from $7 to $5 This is “point” price elasticity. It is calculated at a point on a demand function. It is not influenced by the direction or magnitude of the price change. P2- P1= 5 - 7 = D P = -2 P1 = D P = -2 Q2 - Q1= 5 - 3 = D Q = +2 P2 = There is a problem! If the price changes from $5 to $7 the coefficient of elasticity is different! D Q = +2 Q1= Q2 = .

  7. -2 D Q % DQ = -40% 5 = -1 [this is called “unitary elasticity] = % DP = 40% +2 5 Px A P2= $7 B P1= $5 D Qx/t Q2= Q1= 5 3 ε= Q1 D P P1 the ε= -1[“unitary”] When the price increases from $5 to $7, In the previous slide, when the price decreased from $7 to $5, ε= -2.3 The point price elasticity is different at every point! ep= -2.3 ep= -1 D P = +2 There is an easier way! D Q = -2

  8. this is a point on the demand function P1 D Q D Q P1 = * * D P Q1 D P Q1 this is the slope of the demand function P1 = $7, Q1 = 3 7 -1 P2 = $5, Q2= 5 3 P2- P1= 5 - 7 = D P = -2 Q2 - Q1= 5 - 3 = D Q = +2 Then, +2 D Q = D P -2 By rearranging terms An easier way! D Q ε= Q1 = Q1 D P P1 Given that when: D Q P1 ε = -2.33 = * Q1 D P P1 = $7, Q1 =3 On linear demand functions the slope remains constant so you just put in P and Q = -1 This is the slope of the demand Q = f(P)

  9. Use of Price Elasticity • Ruffin and Gregory[Principles of Economics, Addison-Wesley, 1997, p 101] report that: • short run |ε| of gasoline is = .15 (inelastic) • long run |ε| of gasoline is = .78 (inelastic) • short run |ε| of electricity is = . 13 (inelastic) • long run |ε| of electricity is = 1.89 (elastic) • Why is the long run elasticity greater than short run? • What are the determinants of elasticity?

  10. Determinants of Price Elasticity • Availability of substitutes • greater availability of substitutes makes a good more elastic • Proportion of budget expended on good • higher proportion – more elastic • Time to adjust to the price changes • longer time period means more adjustments possible and increases elasticity • Price elasticity for “brands” tends to be more elastic than for the category

  11. D2 P D1 De ¥ 0 % D Q εº = 0 ¥ % D P P Q/t 0 D1is a “perfectly elastic” demand function. perfectly inelastic ε = 0 For an infinitesimally small change in price, Q changes by infinity. Buyers are very responsive to price changes. An infinitely small change in price changes Q by infinity. perfectly elastic |ε| = undefined As the demand function becomes more horizontal, [buyers are more responsive to price changes],|ε|approaches infinity. = undefined D2 is a “perfectly inelastic” demand function, no matter how much the price changes the same amount is bought. Buyers are not responsive to price changes! |ε| = 0, perfectly inelastic. . .

  12. Income Elasticity • Income elasticity [ey] is a measure of the effect of an income change on demand. • When ey > 0, the good is a normal or superior good an increase in income increases demand, a decrease in income decreases demand. • 0 < ey < 1 is a normal good • 1 < ey is a superior good • When ey < 0, the good is an inferior good

  13. Examples of Income Elasticity • normal goods, [0 < ey < 1 ], (between 0 and 1) • coffee, beef, Coca-Cola, food, Physicians’ services, hamburgers, . . . • Superior goods, [ey > 1], (greater than 1) • movie tickets, foreign travel, wine, new cars, . . • Inferior goods, [ey < 0], (negative) • “top ramen,” flour, lard, beans, . . .

  14. Cross-Price Elasticity • Cross-price elasticity [exy] is a measure of how responsive the demand for a good is to changes in the prices of related goods. • Given a change in the price of good Y, what is the effect on the demand for good X? • exy is defined as:

  15. Cross-Price Elasticity • In the case of beef and pork • theebp is not the same asepb • ebp is the % change in the demand for beef with respect to a % change in the price of pork • epb is the % change in the demand for pork with respect to a % change in the price of beef

  16. +DQb %D Q of beef +ebp positive ebp = %DP of pork + DPp - DQb %D Q of beef +ebp positive ebp = %DP of pork -DPp Cross-Price Elasticity The cross elasticity of the demand for beef with respect to the price of pork, ebeef-pork or ebp can be calculated: An increase in the price of pork, “causes” an increase in the demand for beef. cross elasticity is positive A decrease in the price of pork, “causes” a decrease in the demand for beef. If goods are substitutes, exy will be positive. The greater the coefficient, the more likely they are good substitutes.

  17. Cross-Price Elasticity • exy > 0suggests substitutes, the higher the coefficient the better the substitute • exy < 0suggests the goods are complements, the greater the absolute value the more complimentary the goods are • exy = 0suggests the goods are not related • exycan be used to define markets in legal proceedings

  18. Elasticity of Supply • Elasticity of supply is a measure of how responsive sellers are to changes in the price of the good. • Elasticity of supply [es] is defined:

  19. %DQsupplied es = %DP P supply Q /t Elasticity of supply Given a supply function, at a price [P1], Q1 is produced and offered for sale. a larger quantity, Q2, will be produced and offered for sale. At a higher price [P2], P2 The increase in price [ DP ], induces a larger quantity goods [ DQ]for sale. +DP P1 The more responsive sellers are to DP, the greater the absolute value of es. +DQ [The supply function is “flatter”ormore elastic] Q1 Q2

  20. P Si as supply approaches horizontal es approaches infinity Se Q /ut The supply function is a model of sellers behavior. a perfectly inelastic supply, es = 0 Sellers behavior is influenced by: 1. technology 2. prices of inputs a perfectly elastic supply [es is undefined.] 3. time for adjustment market period short run long run very long run 4. expectations 5. anything that influences costs of production taxes regulations, . . .

  21. Elasticity • Price elasticity of demand • elastic, inelastic or unitary elasticity • Income elasticity • superior, normal, and inferior • Cross-Price elasticity • complements/substitutes • Price elasticity of supply • Elastic, inelastic

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