Okay, here are the steps: 1) Demand function: P = 15 - Q/10 2) Total Revenue function: TR = P * Q 3) Substitute P into TR: TR = (15 - Q/10) * Q 4) Take the derivative of TR with respect to Q to find MR: MR = 15 - 2Q/10 5) Set MR = 0 to find the quantity where TR is maximized: 15 - 2Q/10 = 0 2Q/10 = 15 Q = 75 So total revenue is maximized at a quantity of 75 units, where the price is €7.50 (using the demand function) and elasticity is

1. EC2204- Business Economics
2: Demand, Supply and Elasticity

2. Learning Outcomes
Upon completing this section, you should be able to:
 Differentiate between demand and supply.
 Calculate equilibrium price and output.
 Define price and income elasticity.
 Apply formulas for price and income elasticity.
 Interpret price and income elasticity values.
 Describe factors influencing price elasticity.
 Show that total revenue is maximized at unit elasticity

3. Figure 3.1: Individual and Market Demand
•The market demand curve is obtained through the horizontal
summation of the quantities demanded at each price.

4. Demand Function
Algebraically, the demand function can be represented as:
Qd = f (P, Ps, Pc, Y, A, A’, N, CP, PE, TA, T/S )
 where Qd = quantity demanded of the good or service
 P = price of the good or service
 Ps = price of substitute goods or services
 Pc = price of complementary goods or services.
 Y = income of consumers.
 A = advertising expenditures (and other marketing expenditures)
 A’ = competitors' advertising expenditures on the good or service.
 N = population (and other demographic factors).
 CP = consumer tastes and preferences for the good or service.
 PE= expected (future) changes in price.
 TA= adjustment time period.
 T/S = taxes or subsidies.

5. Supply Function
The main determinants of the supply of a commodity can be represented as:
Qs = f (P, Ps, Pc, C, Tn, Tx, Ms, O)
 where P = the market price of the good or service
 Ps = price of substitute goods or services
 Pc = price of complementary goods or services.
 C = Costs of producing the good/service
 Tn = state of technology.
 Tx = indirect taxation (VAT).
 Ms = market size
 O = objectives of the business.

6. Market Equilibrium
 When Qd = Qs at a given price, the market for the product is said to be in
equilibrium.
 Aldi wants to know at what price will clear all its stock of Chateauneuf Du
Pape. The Firms manager has established both its demand and supply
functions.
 Aldi’s Demand function is for Chateauneuf Du Pape: Qd = 90 – 2p.
 Aldi’s Supply function is for Chateauneuf Du Pape: Qs = 10 + 3p
At what Price and Quantity is Qd = Qs?
Let Qd = Qs
90 – 2p = 10 +3p
80 = 5p, so p = 16
 Equilibrium price (Supply = Demand) Chateauneuf Du Pape = €16/bottle.
 Substitute p into either demand [90 – 2(16) = 58] or supply [10 + 3(16) = 58]
 Equilibrium level of output = 58 units. Aldi can clear their stock of
Chateauneuf Du Pape if they charge €16 per bottle. Drama Queen

7. Market Equilibrium
€90
Supply=10 + 3p
€16
€10
Demand = 90-2p
0
58 bottles Q

8. Price Elasticity of Demand
 Effective demand management requires that the firm should be able to
measure the impact of changes in price on the quantity demanded.
 To predict consumer behaviour, economists use well-defined techniques
evaluating the sensitivity of consumers to changes in price.
 The most commonly used measure of consumers' sensitivity to price is
known as "price elasticity of demand."
 We define the price elasticity of demand (Ed) as the ratio of the percentage
change in quantity demanded to percentage change in price:
%∆ D
Q
ED = , where ΔQD is change in quantity demanded and ΔP is the change in price
%∆P
∆QD P
This formula can also be expressed as ED =
∆P QD (2.1)

9. Price Elasticity of Demand
Giffen, snob value goods,
Unit Elastic if Ed = -1 exclusive goods have +ive
E d’s, do not obey the law of
demand
Furniture Ed = -3
Caviar, Designer clothes
-∞
-4 -3 -2 -1 0 1 2 3 4 5
Shoes Ed = -0.73
Luxuries
Necessities 0 to -1
Goods with E d between 0 and -1 tend to be necessities, food – no close
substitutes available - inelastic
Goods with E d from -1 to - ∞ tend to be luxury goods with many substitutes
available – elastic

10. Price Elasticity of Demand
P P P P D
Perfectly Inelastic
Inelastic Elastic Perfectly
Elastic
D
D Fixed in price
D
Q Q Q Q
chicken Plasma Units of Insulin
screens electricity
telephones
Furniture Chemotherapy
Shoes`, food
Ipod’s

11. Price Elasticity Estimates
Good O’Riordan 1976 Conniffe 1980 Madden 1993
Food -0.43 -0.42 -0.57
Alcohol -0.48 -0.56 -0.65
Tobacco -0.35
Clothes &Footwear -1.01 -0.70 -0.69
Petrol -0.19
Fuel & Power 0.11 -0.06 -0.17
Durables -0.48 -0.84 -1.05
Transport -1.59 -1.02 -1.06
Services -.1.01
Other Goods -0.76 -0.35 -0.69

12. Total Revenue and Price Elasticity of
Demand
•The aim of the business manager is to maximize profit.
•Profit is total revenue less total cost (TR-TC).
•Your aim should be to maximise your revenue while minimizing your costs.
•As TR = price per unit of output (P*Q), you can increase your revenue by
either increasing price and/or increasing your output or market share.
•Increasing market share is undertaken by strategies such as advertising
campaigns, which we deal with later.
•Here we concentrate on pricing strategies.
•Understanding the relationship between price elasticity and changes in total
revenue is an important component of pricing strategy for the business
manager.
•It is vital that the manager knows whether the good s/he sells or produces is
price elastic or inelastic.

13. Total Revenue and Price Elasticity of
Demand
If you raise price, does TR automatically rise? Suppose you are selling I-products, Ipods,
Iphones etc and you raise price what happens to your TR?
if P ↑ , then Q ↓ a lot – customers will shop around, you’ll lose market share
Hence your TR FALLS !!!
Suppose food outlets (TESCO, DUNNES) raise price. What happens to their TR and
profit?
Inelastic: P ↑ → Q↓ → TR ↑ (Necessities, Food
etc.)
Inelastic: P ↓ → Q↑ → TR ↓
Elastic: P ↑ → Q↓ → TR ↓ (Luxury Goods)
Elastic: P ↓ → Q↑ → TR ↑
Unit Elastic: P ↑ → Q↓ → TR unchanged → π ↑
(E d = -1)

14. 1979 Deregulation of Airfares
 Prices declined
 Passengers increased
 Total Revenue Increased
• P ↓ → Q↑ → TR ↑
 What does this imply about the price elasticity of air
travel ?
 Is air travel elastic or inelastic
 Is air travel a necessity or a luxury

15. Determinants of Price Elasticity of Demand:
 Substitutes: The more substitutes, the higher the elasticity, as people can
easily switch from one good to another if a minor price change is made.
 Percentage of income: The higher the percentage that the product's price
is of the consumers’ income, the higher the elasticity, as people will be
careful with purchasing the good because of its cost.
 Necessity: The more necessary a good is, the lower the elasticity, as
people will buy it no matter the price, such as insulin
 Time: The longer a price change holds, the higher the elasticity, as more
and more people will stop demanding the good (i.e. if you go to the
supermarket and find that blueberries have doubled in price, you'll buy it
because you need it this time, but next time you won't, unless the price
drops back down again)
 Breadth of definition: The broader the definition, the lower the elasticity.
For example, McDonalds burger will have a relatively high elasticity, where
as food in general will have an extremely low elasticity Blonde

16. Cross Price Elasticity
 Two goods are substitutes if an increase (decrease) in the price of
Good 1 results in an increase (decrease) in the quantity demanded of
Good 2, holding other factors constant, such as the price of Good 2,
other prices, income, and so on, or vice versa-(pepsi/coke)
 Similarly, two goods are complements if an increase in the price of
Good I results in a decrease in the quantity demanded of Good 2. An
increase in the price of DVD players would have the effect of decreasing the
demand for DVDs, ceteris paribus. (petrol/cars, shoes/socks)
∆Q D A PB
ED = Where ΔQDA = change in quantity demanded of Good A
∆PB Q DA ΔPB = change in price of Good B
Substitutes have a positive cross price elasticity: Butter & Margarine (+0.81)
Complements have a negative cross price elasticity: VCR machines and the rental
price of tapes, computer hardware and software (-0.5)
When the cross price elasticity is zero or insignificant, the products are not related.

17. Income Elasticity of Demand
Income elasticity of demand measures the responsiveness of a change
in quantity demanded of some good or service to a change in income.
It can be expressed as:
∆QD I
ID = where ΔQD= change in quantity
∆I QD demanded, ΔI= change in Income
A normal good or service is a good/service you demand more of as your income
increases.
An inferior good or service is a good/service you demand less of as your income
increases.

18. Sample Questions
Suppose the demand function is Q = 10 - 2P + 3I. Find the income
and price elasticities at a price, P = 2, and income, I = 10.
Characterise the good.
Step 1: Calculate quantity demanded?
Q = 10 -2(2) + 3(10) = 36
Step 2: Determine Price Elasticity of Demand
∆QD P 2
ED = E D = −2 = -0.111 - inelastic
∆P QD 36
Step 3: Determine income Elasticity of Demand
∆Q D I 10 = 0.833 – normal good
ID = ID =3
∆I QD 36

19. Sample Questions
Question 1: In September 2008, when Meteor charged €10 for mobile phone credit, they
found the average number of units used per week was 1,000. When Meteor cut their charges
to €6 the average number of units increased to 1,200 units. Calculate the point price
elasticity of demand for mobile phone credit, and interpret your result.
= - 0.5
Interpretation: A 1% increase in price of mobile phone credit reduces quantity demanded by
0.5 percent.
Car Accident

20. Sample Questions
Question 3: In January 2009, when the average price of a litre of petrol was €1.00,
Ford sold 1000 units of their car range. By September the price of petrol had increased
to €1.40, the demand had Ford cars had dropped to 800 units. Calculate the cross-
price elasticity of demand for Ford cars, and interpret your result.
∆QD PB − 200 A 100
ED = A
ED = =-0.5
∆PB Q D A
40 1000 A
Interpretation: A 10% increase in the price of petrol reduces quantity demanded
of cars by 5%. Note: Cars and Petrol are compliments. Why?
Question 4: In January 2009, when the average price of a bottle of both Pepsi Coca
and Cola was €1.00, Coca Cola sold 1000 per day in Tesco. By September when the
price of Pepsi Cola increased to €1.40, the demand had Coca Cola increased to 1500
units. Calculate the cross-price elasticity of demand , and interpret your result.
∆Q DA PB 500 A 100
ED = ED = =0.25
∆PB QDA 40 1000 A
Interpretation: A 10% increase in the price of Pepsi Cola increases the quantity
demanded of Coca Cola by 2.5%. Note: Pepsi and Coca Cola are substitutes. Why?

21. Sample Questions
Question 5 (See QB1- S 2009):
Find the point price elasticity, the point income elasticity, and the point cross-price
elasticity at P=10, I=20, and Ps=9, if the demand function were estimated to be:
Qd = 90 - 8P + 2I + 2Ps/c
Is the demand for this product elastic or inelastic? Is it a luxury or a necessity?
Does this product have a close substitute or complement?
Recall the Differentiation Rule:
Multiply the coefficient by the Power and reduce the power by 1.
Example: if y = 6x3 – 4x2 + 5x + 3 , Δy/Δx = 18x2 - 8x + 5
Qd = 90 - 8P + 2I +2Ps/c
ΔQ/ΔP = -8
ΔQ/ΔI = 2
ΔQ/ΔPs/c = 2
Step 1: Calculate quantity demanded?
Qd = 90 – 8(10) + 2(20) + 2(9) = 68

22. Sample Questions
Step 2: Determine Price elasticity of demand
∆QD P 10
ED = E D = −8 =-1.176
∆P Q D 68
Step 3: Determine Income elasticity of demand
∆Q D I I D =2
20
ID =
68 = 0.588
∆I QD
Step 4: Determine cross elasticity of demand
∆Q DA PB 9
ED = CrossE D = 2 = 0.263
∆PB QDA 68
Conclusion: The good/service is price elastic, not essential, it’s a normal good, it has a
substitute but not a close substitute.

23. Sample Questions
Question 7: Find the level of output that maximizes Total Revenue for the
demand function P = 18 – Q ?
Demand Function for Soft Drinks Q = 18 – P
TR = P * Q so P = 18 – Q
TR = (18 - Q) * (Q )
so TR = 18Q – Q²
MR = ∆TR/∆Q = 18 – 2Q
TR is maximised at MR = 0
Set MR = 18 – 2Q = 0
18 = 2Q
Q = 9 ( TR is Max where at Q = 9 where MR = 0)
TR is maximised where Q =9

24. Sample Questions
Question 8 (See Q B3-Summer 2009):
Show that Total Revenue is maximized where MR = 0 at unit elasticity
for the demand function for Printed t-shirts is Q = 150 – 10P where P
= price in € per unit and Q = quantity demanded in units?
Write the demand function in terms of Price: P = 15 – Q/10
[TR = P * Q] [TR = (15-10/ Q) * Q] = 15 Q – Q2 / 10
MR = change in revenue associated with a unit change in quantity or the
first derivative of TR with respect to Q.
∆TR
MR = = 15 – 1/10(2Q) = 15 - Q/5
∆QD

25. Sample Questions
Recall TR is Max when MR = 0 therefore set 15 – Q/5 = 0
Q/5 = 15 so, Q = 75 units
(Solve for Price)
Substitute Q = 75 units into original demand function 15 – Q /10
P = 15 – (75/10) = €7.50 per unit
TR is maximised at Q = 75 and P = €7.50
∆Q D P
ED = of Q = 150 –10P
∆P Q D
7 .5
E D = −10 = −1 So when MR = 0, ED = -1
75

26. Recall Our Learning Outcomes
You should now be able to:
 Differentiate between demand and supply.
 Calculate equilibrium price and output.
 Define price and income elasticity.
 Apply formulas for price and income elasticity.
 Interpret price and income elasticity values.
 Describe factors influencing price elasticity.
 Show that total revenue is maximized at unit elasticity