Total and Marginal Revenue
Total and Marginal Revenue
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
Quantity Demanded
MR
/Pri
ce
-10
-5
0
5
10
Total Revenue
0
5
10
15
20
25
30
35
0 2 4 6 8 10 12
Quantity per period
To
tal R
even
ue
15
0 2 4 6 8 10 12
Marginal Revenue
Average Revenue
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
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 week
Q Q00
Point Price Elasticity of Demand
/
/P
Q Q Q PE
P P P Q
Point Definition
Ratio of the percentage of change in quantity demanded to the percentage change in price.
% QEp =
% P
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
Point Price Elasticity of demand
0
1
2
3
4
5
6
7
0 100 200 300 400 500 600 700
Qx
Px
A
F
G
H
J
B
C
Dx
• B = -5
• C = -2
• F = -1
• G = -0.5
• H = -0.2
Arc Price Elasticity of Demand
2 1 2 1
2 1 2 1P
Q Q P PE
P P Q Q
Ep = Q2 - Q1 P2 - P1
(Q2 + Q1)/2 (P2 + P1)/2
Example
• Calculate the arc price elasticity from point C to point F.
= (300 – 200)/ (3-4) * ((3+4)/ (300+200))
= -1.4
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
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
Marginal Revenue and Price Elasticity of Demand
11
P
MR PE
MR = d(PQ) = dQ*P + dP*Q
dQ dQ dQ
= P + QdP = P 1 + dP.Q dQ dQ P
Quantity Demanded
MR
/Pri
ce
-10
-5
0
5
10
Total Revenue
0
5
10
15
20
25
30
35
0 2 4 6 8 10 12
Quantity per period
To
tal R
even
ue
15
0 2 4 6 8 10 12
Marginal Revenue
ElasticEp < - 1
Unitary elasticEp = - 1
Inelastic-1 < Ep < 0
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
Price
Qty Demanded0 Q
P Price
Qty Demanded0 Q
PD
D
Perfectly Inelastic Demand Perfectly Elastic Demand
• P * Qd = TR Elastic Demand
• P * Qd = TR Elastic Demand
• P * Qd = TR Inelastic Demand
• P * Qd = TR Inelastic Demand
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
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
Point Definition/
/I
Q Q Q IE
I 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
Income Elasticity of Demand
Arc Definition 2 1 2 1
2 1 2 1I
Q Q I IE
I I Q Q
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 = 100,000
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
Point Definition/
/X X X Y
XYY Y Y X
Q Q Q PE
P 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
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 PE
P P Q Q
Substitutes
0XYE
Complements
0XYE
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
ProblemQx = 1.5 – 3.0Px + 0.8I + 2.0Py – 0.6Ps + 1.2A
Px=$2 I=$2.5 Py=$1.8
Ps=$0.50 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 EI = 0.8(2.5/2) = 1
Exy = 2(1.8/2) = 1.8 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 =2.2
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 -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
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