Price Elasticity of DemandIncome Elasticity of DemandCross Price Elasticity of DemandComparison Between Elasticity Over Short Run and Long RunCite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 1 1 Price Elasticity of Demand 14.01 Principles of Microeconomics, Fall 2007 Chia-Hui Chen September 10, 2007 Lecture 3 Elasticities of Demand Elasticity. Elasticity measures how one variable responds to a change in an-other variable, namely the percentage change in one variable resulting a one percentage change in another variable. (The percentage change is independent of units.) Outline 1. Chap 2: Price Elasticity of Demand 2. Chap 2: Income Elasticity of Demand 3. Chap 2: Cross Price Elasticity of Demand 4. Chap 2: Comparison of Elasticity Over Short Run and Long Run 1 Price Elasticity of Demand Price elasticity of demand. Price elasticity o f demand measures the p e r-centage change in quantity demanded resulting from one percentage change in price. QQ P P QQ PP △△Example Calculation Figure 1 shows a demand curve: Q(P ) = 8 − 2P. When the price changes from 2 to 1, the pr ice elasticity of demand is: ΔΔ%△QPDEE = = . %△P 2 DP4E |p=2→1 = −1.= = −1 2Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 2 1 Price Elasticity of Demand Figure 1: Price Elasticity of Demand. If the direction o f change is o pposite, from 1 to 2, then the price elasticity of demand is: ΔQ −2 1 EPD|P =1→2 = ΔQP = 16 = − 3 . P The two quantities are different. To solve this conflict, co ns ider small changes in P and Q, and define: 1 dQ Q P dQ EPD = dP = . Q dP P Thus, at the point P = 2, the price elasticity of demand is: EPD|P =2 = P dQ =2 × (−2) = −1. Q dP 4 Properties of Price Elasticity of Demand 1. Price elasticity of demand is usually a negative number. 2. |EP | > 1 indicates that the good is price elastic, perhaps because the good has many substitutes; |EP | < 1 indicates that the good is price inelastic, perhaps because the g ood has few substitutes. 3. Given a linear demand curve, EP is not a constant along the curve. For example, for curve in Figure 1, EP = −∞ at top portion, but zero at bottom portion. 4. Discuss two extreme situations: |EP | = 0, quantity independent of price Figure 2 and |EP | = ∞, quantity very sensitive to price. See Figure 3.Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 3 2 Income Elasticity of Demand Figure 2: Extreme demand elas- Figure 3: Extreme demand elas-ticity. |EP | = 0, quantity inde- ticity. |EP | = −∞, q uantity very pendent of pr ice. sensitive to price. 5. The constant elasticity demand function is Q = aP b , since dQ P P aP b EP = = abP b−1= b = b. dP Q Q Q Refer to Figure 4. 6. How do total consumer expenditure change when the price o f a good changes? dExp d(P QD (P )) dQ = = Q + P = Q(1 + EP ) = Q(1 − |EP |). dP dP dP • If |EP | > 1, total expenditure decreases when pr ic e increases; • If |EP | < 1, total expenditure increases when price increases. Example (Cell phone). People need to do business in the morning, so EP is low, so cell phone companies increase the rate while customers will expend more; but EP is high in the evening since people do not have to talk, so cell phone co mpanies lower the ra te to encourage customer e xpenditure. 2 Income Elasticity of Demand Income elasticity of demand. Income elasticity of demand meas ures the per-centage change in quantity demanded resulting from one percentage change in income. Similarly, dQ Q I dQ = = .EI dI Q dI I The income elasticity of demand is usually positive.Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 4 3 Cross Price Elasticity of Demand Figure 4: Constant Demand Elasticity. 3 Cross Price Elasticity of Demand Cross price elasticity of demand. Cross price e lasticity o f demand measures the percentage change in quantity demanded of a good (x) resulting from one percentage change in price of another good (y). dQx Qx Py dQxEQxP y = = .dPy Qx dPyPy • If y is a substitute of x, the cross price elasticity of demand is positive. • If y is a complement of x, the cross pric e elasticity of demand is negative. 4 Comparison Between Elasticity Over Short Run and Long Run Is demand more elastic in the long run or s hort run? Consumption goods. For co nsumption goods, the demand is more elastic in the long run. Because people need goods for daily life a nd buy them constantly, the short run demand is inelastic. Faced with high prices in the long run, they may change habits or find more substitutes.Cite as: Chia-Hui Chen, course materials for 14.01 Principles of Microeconomics, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 4 Comparison Between Elasticity Over Short Run and Long Run 5 Durable goods. For durable goods, the demand is more elastic in the short run. Consider cars. If price of of cars increase, in the short run people might use their current cars longer. In the long run, though, people have to replace their