# ELASTICITY by yurtgc548

VIEWS: 34 PAGES: 37

• pg 1
```									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.

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