VIEWS: 34 PAGES: 37 POSTED ON: 1/23/2012
Price Quantity Total Marginal Revenue Revenue 10 1 10 9 2 18 8 8 3 24 6 7 4 28 4 6 5 30 2 5 6 30 0 4 7 28 -2 3 8 24 -4 2 9 18 -6 1 10 10 -8 Total and Marginal Revenue Price Quantity Total Marginal Revenue Revenue 10 1 10 9 2 18 8 8 3 24 6 7 4 28 4 6 5 30 2 5 6 30 0 4 7 28 -2 3 8 24 -4 2 9 18 -6 1 10 10 -8 35 Total Revenue 30 25 Total Revenue 20 15 10 5 0 0 2 4 6 8 10 12 Quantity per period 15 MR/Price 10 5 Average Revenue 0 0 2 4 6 8 10 12 -5 Quantity Demanded Marginal Revenue -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 , Q = B/2 For Q < B/2 , MR = +ve 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 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 Price per P Pound P1 = 3 P1 = 3 P2 = 2 P2 = 2 D D 0 Q1 = 5 0 Q2= 10 Q Q1 = 80 Q2= 160 Q Pounds of X per week Ounces of X per week Pounds of X per month Ounces of X per month Slope: Y = P2 – P1 Slope: Y = P2 – P1 X = Q2 – Q1 X = Q2 – Q1 = 2 – 3 = -1 = 2 – 3 = -1 10 – 5 = 5 160 –80 = 80 Point Price Elasticity of Demand Ratio of the percentage of change in quantity demanded to the percentage change in price. % Q Ep = % P Q / Q Q P Point Definition 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 6 A 5 B 4 C Px 3 F G Dx 2 1 H 0 J 0 100 200 300 400 500 600 700 Qx • B = -5 • C = -2 • F = -1 • G = -0.5 • H = -0.2 Arc Price Elasticity of Demand Ep = Q2 - Q1 P2 - P1 (Q2 + Q1)/2 (P2 + P1)/2 Q2 Q1 P2 P EP 1 P2 P Q2 Q1 1 Example • Calculate the arc price elasticity from point C to point F. = (300 – 200)/ (3-4) * ((3+4)/ (300+200)) = -1.4 Calculate Elasticity Price Quantity Total Marginal Revenue Revenue 10 1 10 9 2 18 8 8 3 24 6 7 4 28 4 6 5 30 2 5 6 30 0 4 7 28 -2 3 8 24 -4 2 9 18 -6 1 10 10 -8 Total Marginal Elasticity Price Quantity Total Marginal Price Revenue Revenue Elasticity 10 1 10 -10.00 9 2 18 8 -4.50 8 3 24 6 -2.67 7 4 28 4 -1.75 6 5 30 2 -1.20 5 6 30 0 -0.83 4 7 28 -2 -0.57 3 8 24 -4 -0.38 2 9 18 -6 -0.22 1 10 10 -8 -0.10 35 Total Revenue 30 25 Total Revenue 20 15 10 5 0 0 2 4 6 8 10 12 Quantity per period 15 Elastic Ep < - 1 MR/Price 10 Unitary elastic Ep = - 1 Inelastic 5 -1 < Ep < 0 0 0 2 4 6 8 10 12 -5 Quantity Demanded Marginal Revenue -10 Perfectly Inelastic Demand Perfectly Elastic Demand Price P D Price P D 0 Q 0 Q Qty Demanded Qty Demanded 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 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 MR P 1 EP • P * Qd = TR Elastic Demand • P * Qd = TR Elastic Demand • P * Qd = TR Inelastic Demand • P * Qd = TR Inelastic Demand 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 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 Q / Q Q I Point Definition EI I / I I Q Income Elasticity of Demand Q2 Q1 I 2 I1 Arc Definition EI I 2 I1 Q2 Q1 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, Q = 100,000 I2 = $11,000, Q = 105,000 EI = 0.512 • Normal Goods ΔQ/ΔI = +ve, EI = +ve – Necessities 0 < EI 1 – Luxuries EI > 1 • Inferior Goods ΔQ/ΔI = -ve, EI = -ve 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 QX / QX QX P Point Definition E XY Y P / PY Y PY QX Cross-Price Elasticity of Demand QX 2 QX 1 PY 2 PY 1 Arc Definition E XY P 2 P 1 QX 2 QX 1 Y Y Substitutes Complements EXY 0 EXY 0 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 Exercise • 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 Q / P 1 / 5 • Ep= -1/5*10/8 = -0.25. As demand is inelastic, when we increase price, TR increases. Question: Demand for a firm’s product has been estimated to be Qd = 1000-200P If the price of the product is Rs 3 per unit, find out the price elasticity of demand at this price. Solutuion: Price elasticity of demand is ep= dQ/dP*P/Q in the given demand function 200 is the coefficient of price which measures dQ/dP. In order to find out price elasticity of demand at price Rs3, we have first to find out the quantitydemanded at this price by using the given demand equation. Thus, Q=1000-200*3=400 Thus, P=Rs3 and quantity demanded at the price is 400 units. Substituting the values of dQ/dP, P and Q in the price elasticity formula, we have ep= dq/dp*P/Q=200*3/400=3/2=1.5 Q. The price elasticity of demand for colour TVs is estimated to be -2.5. if the price of colour TVs is reduced by 20 percent, how much percentage increase in the quantity of colour TVs sold do you expect? Solu. Price elasticity of demand being equal to -2.5 means that one pwercent change in price causes 2.5 percent change in quantity demanded or sold. 20 percent reduction in price of colour will cause increase in quantity sold by 2.5*20=50 percent.