2 demand-supply and elasticity

EC2204- Business Economics2: Demand, Supply and Elasticity

EC2204- Business Economics2: Demand, Supply and Elasticity

Learning OutcomesLearning 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

Figure 3.1: Individual and Market Demand

•The market demand curve is obtained through the horizontal summation of the quantities demanded at each price.

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.

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.

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 + 3pAt what Price and Quantity is Qd = Qs?

Let Qd = Qs90 – 2p = 10 +3p80 = 5p, so p = 16p = 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

Market Equilibrium

Demand = 90-2p

Supply=10 + 3p€90

€16

€10

058 bottles Q

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: P

QE DD

%

%, where ΔQD is change in quantity demanded and ΔP is the change in price

This formula can also be expressed as D

DD Q

P

P

QE

(2.1)

-4 -3 -2 -1 0 1 2 3 4 5

Giffen, snob value goods, exclusive goods have +ive Ed’s, do not obey the law of demand

Goods with Ed between 0 and -1 tend to be necessities, food – no close substitutes available - inelasticinelastic

Goods with Ed from -1 to - ∞ tend to be luxury goods with many substitutes available – elasticelastic

Unit ElasticUnit Elastic if Ed = -1

Furniture Ed = -3

Shoes Ed = -0.73

Caviar, Designer clothes


Necessities 0 to -1Luxuries

- ∞


P P P P

Q Q Q QD

D

D

D

Inelastic Elastic Perfectly

Elastic

Per

fect

ly I

nela

stic

chicken

telephones

Shoes`, food

Plasma screens

Furniture

Ipod’s

Insulin

Chemotherapy

Fixed in price

Units of electricity

Price Elasticity EstimatesPrice 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

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.

Total Revenue and Price Elasticity of Demand

Inelastic: P Inelastic: P ↑ → Q↓ → TR ↑ → Q↓ → TR ↑ (Necessities, Food ↑ (Necessities, Food etc.)etc.)

Inelastic: P ↓ → Q↑ → TR ↓Inelastic: P ↓ → Q↑ → TR ↓

Elastic: P ↑ → Q↓ → TR ↓ (Luxury Goods)Elastic: P ↑ → Q↓ → TR ↓ (Luxury Goods)

Elastic: P ↓ → Q↑ → TR ↑Elastic: P ↓ → Q↑ → TR ↑

Unit Elastic: P ↑ → Q↓ → TR unchanged Unit Elastic: P ↑ → Q↓ → TR unchanged →→ ππ ↑↑(E(Ed d = -1)= -1)Unit Elastic: P ↓ → Q↑ → TR unchangedUnit Elastic: P ↓ → Q↑ → TR unchanged

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 shareHence your TR FALLS !!!Suppose food outlets (TESCO, DUNNES) raise price. What happens to their TR and profit?

1979 Deregulation of Airfares

Prices declined Passengers increased Total Revenue Increased

• P ↓ → Q↑ → TR ↑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

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

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)

A

A

D

B

B

DD Q

P

P

QE

Where ΔQDA = change in quantity demanded of

Good AΔPB = 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.

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:

D

DD Q

I

I

QI

where ΔQD= change in quantity 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.

Sample QuestionsSample 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

D

DD Q

P

P

QE

Step 3: Determine income Elasticity of Demand

D

DD Q

I

I

QI

36

22DE = -0.111 - inelastic

36

103DI

= 0.833 – normal good

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.

D

DD Q

P

P

QE

1000

10

106

10001200

DE

1000

10

4

200

DE = - 0.5

Interpretation: A 1% increase in price of mobile phone credit reduces quantity demanded by 0.5 percent.

Car Accident

Sample Questions

A

A

D

B

B

DD Q

P

P

QE

A

A

DE 1000

100

40

200

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.

Interpretation: A 10% increase in the price of petrol reduces quantity demanded of cars by 5%. Note: Cars and Petrol are compliments. Why?

=-0.5

A

A

D

B

B

DD Q

P

P

QE

A

A

DE 1000

100

40

500

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.

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?

=0.25

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/cIs 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/cΔQ/ΔP = -8ΔQ/ΔI = 2ΔQ/ΔPs/c = 2

Step 1: Calculate quantity demanded?Qd = 90 – 8(10) + 2(20) + 2(9) = 68

Sample Questions

Conclusion: The good/service is price elastic, not essential, it’s a normal good, it has a substitute but not a close substitute.

D

DD Q

P

P

QE

68

108DE

Step 2: Determine Price elasticity of demand

=-1.176

Step 3: Determine Income elasticity of demand

D

DD Q

I

I

QI

68

202DI = 0.588

Step 4: Determine cross elasticity of demand

A

A

D

B

B

DD Q

P

P

QE

68

92DCrossE = 0.263

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 – PTR = P * Q so P = 18 – QTR = (18 - Q) * (Q ) so TR = 18Q – Q²

MR = TR/Q = 18 – 2Q

TR is maximised at MR = 0Set MR = 18 – 2Q = 0 18 = 2QQ = 9 ( TR is Max where at Q = 9 where MR = 0)

TR is maximised where Q =9

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.

DQ

TRMR

= 15 – 1/10(2Q) = 15 - Q/5

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

D

DD Q

P

P

QE

of Q = 150 –10P

175

5.710 DE So when MR = 0, ED = -1

Recall Our Learning OutcomesRecall 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

2 demand-supply and elasticity

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