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ELASTICITY LEC 4 ELASTICITY A general concept used to quantify the response in one variable when another variable changes elasticity of A with respect to B = % A/ %B Calculating Elasticities Price per P Pound P Price per Pound P1 = 3 P1 = 3 P2 = 2 P2 = 2 D 0 Q1 = 5 Q2= 10 Pounds of X per week Pounds of X per month Slope: Y = P2 – P1 X = Q2 – Q1 = 2 – 3 = -1 10 – 5 = 5 Q D 0 Q1 = 80 Q2= 160 Ounces of X per week Ounces of X per month Slope: Y = P2 – P1 X = Q2 – Q1 = 2 – 3 = -1 160 –80 = 80 Q Point Price Elasticity of Demand Ratio of the percentage of change in quantity demanded to the percentage change in price. % Q Ep = Point Definition % P Q / Q Q P EP P / P P Q Point Price Elasticity of Demand For P approaching 0 Q/P = dQ/dP Linear equation = dQ/dP = constant dQ/dP = ap Qd = B + apP = B + dQ/dP P Point Price Elasticity of demand 7 -5 A 6 B 5 -2 C -1 Px 4 F 3 -0.5 G 2 Dx -0.2 H 1 J 0 0 100 200 300 400 Qx 500 600 700 Arc Price Elasticity of Demand Ep = Q2 - Q1 (Q2 + Q1)/2 EP Q 2 Q1 P2 P1 P2 - P1 (P2 + P1)/2 P2 P1 Q 2 Q1 Example Calculate the arc price elasticity from point C to point F. = (300 – 200)/ (3-4) * ((3+4)/ (300+200)) = -1.4 Problem Present Loss : $ 7.5 million Present fee per student : $3,000 Suggested increase : 25% Total number of students : 10000 Elasticity for enrollment at state universities is -1.3 with respect to tuition changes 1% increase in tuition = 1.3% decrease in enrollment Increase of 25% decline in enrollment by 32.5% 3000 * 10000 = $30,000,000 3750 * 6750 = $25,312,500 Perfectly Inelastic Demand Price P Perfectly Elastic Demand Price P D D 0 Qty Demanded Q 0 Qty Demanded Q Perfectly inelastic demand Qd does not change at all when price changes Inelastic demand -1 < E 0 Unitary elastic demand E = -1 Elastic demand E < -1 Perfectly elastic demand Qd drops to zero at the slightest increase in price Exercise For each of the following equations, determine whether the demand is elastic, inelastic or unitary elastic at the given price. a) Q =100 – 4P and P = $20 b) Q =1500 – 20 P and P = $5 c) P = 50 – 0.1Q and P = $20 a) -4, elastic b) -0.07, Inelastic c) -0.67, Inelastic TOTAL AND MARGINAL REVENUE & ELASTICITY P=Price, Q=Quantity TR (Total Revenue)=P X Q MR (Marginal Revenue)= d(TR)/dQ= d(PQ)/dQ Price Quantity 10 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10 Total Marginal Revenue Revenue 10 18 8 24 6 28 4 30 2 30 0 28 -2 24 -4 18 -6 10 -8 Total and Marginal Revenue Price Quantity 10 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10 Total Marginal Revenue Revenue 10 18 8 24 6 28 4 30 2 30 0 28 -2 24 -4 18 -6 10 -8 Total Revenue 35 30 Total Revenue 25 20 15 10 5 0 0 2 4 6 8 10 12 Quantity per period MR/Price 15 10 5 Average Revenue 0 0 2 4 6 8 12 Quantity Demanded -5 Marginal Revenue -10 10 Marginal Revenue Equation Demand Equation Q = B + ap P P = -B/ap + Q/ap TR = PQ = -B/ap*Q + Q2/ap MR = d(PQ)/dQ = -B/ap+ 2Q/ap MR = 0 For Q < B/2 , MR = +ve , Q = B/2 Q > B/2 , MR = -ve Relation of Demand & Marginal Revenue Curve The curves intercept y-axis at same point Intercept of MR & Demand (DD) curve = -B/ap Slope of (DD) curve = 1/ ap Slope of MR curve = 2/ ap = 2 DD curve Calculate Elasticity Price Quantity 10 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10 Total Marginal Revenue Revenue 10 18 8 24 6 28 4 30 2 30 0 28 -2 24 -4 18 -6 10 -8 Total Marginal Elasticity Price Quantity 10 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10 Total Marginal Price Revenue Revenue Elasticity 10 -10.00 18 8 -4.50 24 6 -2.67 28 4 -1.75 30 2 -1.20 30 0 -0.83 28 -2 -0.57 24 -4 -0.38 18 -6 -0.22 10 -8 -0.10 Total Revenue 35 30 Total Revenue 25 20 15 10 5 0 0 2 4 6 8 10 12 Quantity per period 15 MR/Price Elastic Ep < - 1 10 Unitary elastic Ep = - 1 Inelastic 5 -1 < Ep < 0 0 0 2 4 6 8 12 Quantity Demanded -5 Marginal Revenue -10 10 Marginal Revenue and Price Elasticity of Demand MR = d(PQ) = dQ*P + dP*Q dQ dQ dQ = P + QdP = P 1 + dP.Q dQ dQ P 1 M R P 1 EP P * Qd = TR Elastic Demand P * Qd = TR Elastic Demand P * Qd = TR Inelastic Demand P * Qd = TR Inelastic Demand Exercise1 A consultant estimates the price-quantity relationship for New World Pizza to be at P = 50 – 5Q. At what output rate is demand unitary elastic? Over what range of output is demand elastic? At the current price, eight units are demanded each period. If the objective is to increase total revenue, should the price be increased or decreased? Explain. P =50 -5Q MR = 50-10Q For unitary elastic MR = 0 so Q =5 MR will be +ve when Q<5, so demand will be elastic when 0<=Q<5. P for Q=8 is P=50-5*8 = 50-40 = 10 Ep= -1/5*10/8 = -0.25. As demand is inelastic, when we increase price, TR increases. Q / P 1 / 5 Exercise2 The coefficient of price elasticity of a commodity is given by –1.5. Find the percentage change in Total Revenue when its price falls by 10% If Price decreases by 10% corresponding increase in quantity demanded will be 15% and therefore change in TR = (1.15*.9 PQ – PQ)/PQ *100 = 3.5% Determinants of Price Elasticity of Demand Demand for a commodity will be less elastic if: It has few substitutes Requires small proportion of total expenditure Less time is available to adjust to a price change Determinants of Price Elasticity of Demand Demand for a commodity will be more elastic if: It has many close substitutes Requires substantial proportion of total expenditure More time is available to adjust to a price change Income Elasticity of Demand The responsiveness of demand to changes in income. Other factors held constant, income elasticity of a good is the percentage change in demand associated with a 1% change in income Point Definition EI Q / Q I / I Q I I Q Income Elasticity of Demand Arc Definition EI Q 2 Q1 I 2 I1 I 2 I1 Q 2 Q1 Normal Goods ΔQ/ΔI = +ve, EI = +ve Necessities 0 < EI 1 Luxuries EI > 1 Inferior Goods ΔQ/ΔI = -ve, EI = -ve Exercise1 Demand of automobiles as a function of income is Q = 50,000 + 5(I) Present Income = $10,000 Changed Income = $11,000 I1 = $10,000, I2 = $11,000, Q = 100,000 Q = 105,000 EI = 0.512 Exercise2 The coefficient of income for the quantity demanded for a commodity on price, income and other variables is 10. Calculate the income elasticity of demand for this commodity at income of $ 10,000 and sales of 80000 units. What would be the income elasticity of demand if sales increased from 80000 to 90000 units and income rose from $10000 to $11000? What type of good is this commodity? aN = 10 EI = 10*10000/80000= 1.25 EI = {(90000-80000)/(11000-10000)}* {(11000+10000)/(90000+80000)} = 1.235 Luxury Cross-Price Elasticity of Demand Responsiveness in the demand for commodity X to a change in the price of commodity Y. Other factors held constant, cross price elasticity of a good is the % change in demand for commodity X divided by the % change in the price of commodity Y Point Definition E XY Q X / Q X PY / PY Q X PY PY QX Cross-Price Elasticity of Demand Arc Definition Substitutes E XY 0 E XY QX 2 QX1 PY 2 PY 1 PY 2 PY 1 QX 2 QX1 Complements E XY 0 Exercise Acme Tobacco is currently selling 5000 pounds of pipe tobacco per year. Due to competitive pressures, the average price of a pipe declines from $15 to $12. As a result, the demand for Acme pipe tobacco increase to 6,000 pounds per year. What is the cross elasticity of demand for pipes and pipe tobacco? Assuming that the cross elasticity does not change, at what price of pipes would the demand for the pipe tobacco be 3,000 pounds per year? Use $15 as the initial price of a pipe. EXY = {(6000-5000)/(12-15)}*{(12+15)/(6000+5000) = -0.818 P1 = $15, Q2 = 3000 and Q1 = 5000 Therefore, P2 = 28.23 Importance of Elasticity in Decision making To determine the optimal operational policies To determine the most effective way to respond to policies of competing firms To plan growth strategy Importance of Income Elasticity Forecasting demand under different economic conditions To identify market for the product To identify most suitable promotional campaign Importance of Cross price Elasticity Measures the effect of changing the price of a product on demand of other related products that the firm sells High positive cross price elasticity of demand is used to define an industry Problem Qx = 1.5 – 3.0Px + 0.8I + 2.0Py – 0.6Ps + 1.2A Px=$2 I=$2.5 Ps=$0.50 Py=$1.8 A=$1 Qx =1.5 – 3*2 + 0.8*2.5 + 2*1.8 – 0.6*0.50 + 1.2*1 =2 Ep = -3(2/2) = -3 Exy = 2(1.8/2) = 1.8 EI = 0.8(2.5/2) = 1 Exs = -0.6(0.50/2) = -0.15 EA = 1.2(1/2) = 0.6 Next Year: P=5% A=12% I=4% Py=7% Ps=8% Q’x = Qx + Qx(Px /Px) Ep + Qx (I/ I) EI + Qx (Py/Py)Exy +Qx (Ps/Ps)Exs + Qx (A/A)EA =2+2(0.05)(-3)+2(0.04)(1)+2(0.07)(1.8)+2(-0.08)(-0.15)+2(0.12)(0.6) =2(1.1) =2.2