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