Download - Elasticity
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Price Quantity Total MarginalRevenue Revenue
10 1 109 2 18 88 3 24 67 4 28 46 5 30 25 6 30 04 7 28 -23 8 24 -42 9 18 -61 10 10 -8
Total and Marginal Revenue
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Quantity Demanded
MR
/Pric
e
-10
-5
0
5
10
Total Revenue
0
5
10
15
20
25
30
35
0 2 4 6 8 10 12Quantity per period
Tota
l Rev
enue
15
0 2 4 6 8 10 12
Marginal Revenue
Average Revenue
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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
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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
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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
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Calculating Elasticities
P1 = 3
P2 = 2
Q1 = 5 Q2= 10
D
Price perPound
Pounds of X per week
Pounds of X per month
Slope: Y = P2 – P1
X = Q2 – Q1
= 2 – 3 = -1
10 – 5 = 5
Ounces of X per month
Slope: Y = P2 – P1
X = Q2 – Q1
= 2 – 3 = -1
160 –80 = 80
PP
P1 = 3
P2 = 2
Q1 = 80 Q2= 160
D
Price perPound
Ounces of X per weekQ Q00
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Point Price Elasticity of Demand
//P
Q Q Q PEP P P Q
Point Definition
Ratio of the percentage of change in quantity demanded to the percentage change in price.
% QEp =
% P
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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
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Point Price Elasticity of demand
0
1
2
3
4
5
6
7
0 100 200 300 400 500 600 700Qx
Px
A
F
G
H
J
B
C
Dx
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• B = -5• C = -2• F = -1• G = -0.5• H = -0.2
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Arc Price Elasticity of Demand
2 1 2 1
2 1 2 1PQ Q P PEP P Q Q
Ep = Q2 - Q1 P2 - P1
(Q2 + Q1)/2 (P2 + P1)/2
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Example
• Calculate the arc price elasticity from point C to point F.
= (300 – 200)/ (3-4) * ((3+4)/ (300+200)) = -1.4
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Price Quantity Total MarginalRevenue Revenue
10 1 109 2 18 88 3 24 67 4 28 46 5 30 25 6 30 04 7 28 -23 8 24 -42 9 18 -61 10 10 -8
Calculate Elasticity
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Price Quantity Total Marginal Price Revenue Revenue Elasticity
10 1 10 -10.009 2 18 8 -4.508 3 24 6 -2.677 4 28 4 -1.756 5 30 2 -1.205 6 30 0 -0.834 7 28 -2 -0.573 8 24 -4 -0.382 9 18 -6 -0.221 10 10 -8 -0.10
Total Marginal Elasticity
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Quantity Demanded
MR
/Pric
e
-10
-5
0
5
10
Total Revenue
0
5
10
15
20
25
30
35
0 2 4 6 8 10 12Quantity per period
Tota
l Rev
enue
15
0 2 4 6 8 10 12
Marginal Revenue
ElasticEp < - 1
Unitary elasticEp = - 1
Inelastic-1 < Ep < 0
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Price
Qty Demanded0 Q
P Price
Qty Demanded0 Q
PD
D
Perfectly Inelastic Demand Perfectly Elastic Demand
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Perfectly inelastic demandQd 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
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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 = $20b) Q =1500 – 20 P and P = $5c) P = 50 – 0.1Q and P = $20
a) -4, elastic
b) -0.07, Inelastic
c) -0.67, Inelastic
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Marginal Revenue and Price Elasticity of Demand
11P
MR PE
MR = d(PQ) = dQ*P + dP*Q
dQ dQ dQ
= P + QdP = P 1 + dP.Q dQ dQ P
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• P * Qd = TR Elastic Demand
• P * Qd = TR Elastic Demand
• P * Qd = TR Inelastic Demand
• P * Qd = TR Inelastic Demand
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Present Loss : $ 7.5 millionPresent fee per student : $3,000Suggested increase : 25%Total number of students : 10000Elasticity for enrollment at state universities is -1.3 with respect to tuition changes
1% increase in tuition = 1.3% decrease in enrollmentIncrease of 25% decline in enrollment by 32.5%
3000 * 10000 = $30,000,0003750 * 6750 = $25,312,500
Problem
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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
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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
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Income Elasticity of Demand
Point Definition//I
Q Q Q IEI I I Q
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
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Income Elasticity of Demand
Arc Definition 2 1 2 1
2 1 2 1IQ Q I IEI I Q Q
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Demand of automobiles as a function of income isQ = 50,000 + 5(I)
Present Income = $10,000 Changed Income = $11,000
I1 = $10,000, Q = 100,000I2 = $11,000, Q = 105,000
EI = 0.512
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• Normal Goods ΔQ/ΔI = +ve, EI = +ve – Necessities 0 < EI 1
– Luxuries EI > 1
• Inferior Goods ΔQ/ΔI = -ve, EI = -ve
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Cross-Price Elasticity of Demand
Point Definition //
X X X YXY
Y Y Y X
Q Q Q PEP P P Q
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
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Cross-Price Elasticity of Demand
Arc Definition 2 1 2 1
2 1 2 1
X X Y YXY
Y Y X X
Q Q P PEP P Q Q
Substitutes
0XYE
Complements
0XYE
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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
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Importance of Income Elasticity
– Forecasting demand under different economic conditions
– To identify market for the product
– To identify most suitable promotional campaign
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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
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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.
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P =50 -5QMR = 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.
5/1/ PQ
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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
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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.