1. ELASTICITY
LEC 4

2. 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

3. Calculating Elasticities
P1 = 3
P2 = 2
Q1 = 5
Q2= 10 D
Price per
Pound
Pounds of X per week P P
P1 = 3
P2 = 2
Q1 = 80
Q2= 160 D
Price per
Pound
Ounces of X per week Q
Ounces of X per month
Slope: Y = P2 – P1
X = Q2 – Q1
= 2 – 3 = -1
160 –80 = 80
Pounds of X per month
Slope: Y = P2 – P1
X = Q2 – Q1
= 2 – 3 = -1
10 – 5 = 5

4. Point Price Elasticity of Demand
Ratio of the percentage of change in quantity demanded to the percentage change in price.
% Q
Ep =
% P
Point Definition

5. 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

6. Point Price Elasticity of demand7 -5 A 6 B -2 5 C -1 4 Px F
-0.5 3 Dx G
-0.2 2 H 1 J
100
200
300
400
500
600
700 Qx

7. Arc Price Elasticity of Demand
Ep = Q2 - Q P2 - P1
(Q2 + Q1)/ (P2 + P1)/2

8. Example Calculate the arc price elasticity from point C to point F.
= (300 – 200)/ (3-4) * ((3+4)/ ( ))
= -1.4

9. 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 * = $30,000,000
3750 (new fee)* (no. of students) = $25,312,500

10. Perfectly Inelastic Demand Perfectly Elastic Demand
Price
Price D D Q Q
Qty Demanded
Qty Demanded

11. Exercise -4, elastic -0.07, Inelastic -0.67, Inelastic
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
-4, elastic
-0.07, Inelastic
-0.67, Inelastic

12. TOTAL AND MARGINAL REVENUE & ELASTICITY

13. P=Price, Q=Quantity
TR (Total Revenue)=P X Q
MR (Marginal Revenue)= d(TR)/dQ= d(PQ)/dQ

15. Total and Marginal Revenue

16. Total Revenue Quantity per period MR/Price Average Revenue5 10 15 20 25 30 35 2 4 6 8 12
Quantity per period 10
MR/Price 5
Average Revenue 2 4 6 8 10 12 -5
Quantity Demanded
Marginal Revenue
-10

17. 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

18. 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

19. Calculate Elasticity

20. Total Marginal Elasticity

21. Elastic Unitary elastic Ep = 1 Inelastic
Total Revenue 5 10 15 20 25 30 35 2 4 6 8 12
Quantity per period
Elastic
Ep > 1
Unitary elastic
Ep = 1 10
MR/Price
Inelastic
Ep< 1 5 2 4 6 8 10 12 -5
Quantity Demanded
Marginal Revenue
-10

22. 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

23. P * Qd = TR Elastic Demand
P * Qd = TR Inelastic Demand

24. Exercise1 At what output rate is demand unitary elastic?
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.

25. 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 = = 10
Ep= -1/5*10/8 = As demand is inelastic, when we increase price, TR increases.

26. 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

27. 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

28. 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
Point Definition

29. Income Elasticity of Demand
Arc Definition

30. Normal Goods ΔQ/ΔI = +ve, EI = +ve
Necessities 0 < EI  1
Luxuries EI > 1
Inferior Goods ΔQ/ΔI = -ve, EI = -ve

31. Demand of automobiles as a function of income is
Exercise1
Demand of automobiles as a function of income is
Q = 50, (I)
Present Income = $10,000
Changed Income = $11,000
I1 = $10,000, Q = 100,000
I2 = $11,000, Q = 105,000
EI = 0.512

32. Exercise2
The coefficient of income for the quantity demanded for a commodity on price, income and other variables is 10.
Calculate the income elasticity of demand for this commodity at income of $ 10,000 and sales of units.
What would be the income elasticity of demand if sales increased from to units and income rose from $10000 to $11000? What type of good is this commodity?

33. aN = 10
EI = 10*10000/80000= 1.25
EI = {( )/( )}*
{( )/( )}
= 1.235
Luxury

34. 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
Point Definition

35. Cross-Price Elasticity of Demand
Arc Definition
Substitutes
Complements

36. Exercise
Acme Tobacco is currently selling 5000 pounds of pipe tobacco per year. Due to competitive pressures, the average price of a pipe declines from $15 to $12. As a result, the demand for Acme pipe tobacco increase to 6,000 pounds per year.
What is the cross elasticity of demand for pipes and pipe tobacco?
Assuming that the cross elasticity does not change, at what price of pipes would the demand for the pipe tobacco be 3,000 pounds per year? Use $15 as the initial price of a pipe.

37. EXY = {(6000-5000)/(12-15)}*{(12+15)/(6000+5000)=
P1 = $15, Q2 = 3000 and Q1 = 5000
Therefore, P2 = 28.23

38. 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

39. Importance of Income Elasticity
Forecasting demand under different economic conditions
To identify market for the product
To identify most suitable promotional campaign

40. 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

41. Problem Qx = 1.5 – 3.0Px + 0.8I + 2.0Py – 0.6Ps + 1.2A=2
Ep = -3(2/2) = -3 EI = 0.8(2.5/2) = 1
Exy = 2(1.8/2) = Exs = -0.6(0.50/2) = -0.15
EA = 1.2(1/2) = 0.6

42. Qx + Qx(Px /Px) Ep + Qx (I/ I) EI + Qx (Py/Py)Exy
Next Year:
P=5% A=12% I=4% Py=7% Ps=8%
Q’x =
Qx + Qx(Px /Px) Ep + Qx (I/ I) EI + Qx (Py/Py)Exy
+Qx (Ps/Ps)Exs + Qx (A/A)EA
=2+2(0.05)(-3)+2(0.04)(1)+2(0.07)(1.8)+2(-0.08)(-0.15)+2(0.12)(0.6)
=2(1.1)
=2.2