Demand Function [PDF]

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Unit III: Demand and Supply • Demand: Concept Function • Use of demand analysis in business decision • Elasticity of demand • Types and measurement

Introduction • In a market economy, individual consumers make plans of consumption and individual firms make plans of production based on the changes in market prices. • Economists use the term invisible hand to describe the frequent exchanges in the market • The price system works in a market economy only if there is free choice within the market • The following sections explain how the market price is determined by the interaction of consumers (demand) and producers (supply).

The Market forces –

Supply and Demand are the two words that economists use most often.

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Supply and Demand are the forces that make market economies work!

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Modern microeconomics is about supply, demand, and market equilibrium.

•The terms supply and demand refer to the behavior of people......as they interact with one another in markets. • A market is a group of buyers and sellers of a particular good or service. • Buyers determine demand... • Sellers determine supply…

Competitive Market and other markets • Competitive market: a market with many buyers and sellers ; each has a negligible impact on the market price  Perfectly Competitive:  Homogeneous Products  Buyers and Sellers are Price Takers  Monopoly:  One Seller, controls price  Oligopoly:  Few Sellers, not aggressive competition  Monopolistic Competition:  Many Sellers, differentiated products

Meaning of Demand

Meaning and Definition of Demand • According to Benham: “The demand for anything, at a given price, is the amount of it, which will be bought per unit of time, at that price.” • According to Bobber, “By demand we mean the various quantities of a given commodity or service which consumers would buy in one market in a given period of time at various prices.” • Requisites: a. Desire for specific commodity. b. Sufficient resources to purchase the desired commodity. c. Willingness to spend the resources. d. Availability of the commodity at •. (i) Certain price (ii) Certain place (iii) Certain time.

Cont…. The word ‘demand’ consists of 4 main concepts: • It refers to both the ability to pay and a willingness to buy by the consumer (s). Demand is sometimes called effective demand. • Demand can be shown by a demand schedule which shows the maximum quantity demanded (willing & able to buy) at all prices. • Demand is a flow concept. Our willingness and ability to buy is subjected to a time period. At different times, we may have different demand schedules. Quantity Demanded : refers to the amount (quantity) of a good that buyers are willing to purchase at alternative prices for a given period.

Determinants of Demand • • • • • •

Product’s Own Price

•

Advertising Expenditure

Consumer Income Prices of Related Goods Tastes & Preferences Expectations Number of Consumers

Price Law of Demand – The law of demand states that, other things equal (ceteris paribus), the quantity demanded of a good falls when the price of the good rises.

The Law of Demand • Prof. Samuelson: “Law of demand states that people will buy more at lower price and buy less at higher prices, others thing remaining the same.” • Ferguson: “According to the law of demand, the quantity demanded varies inversely with price”. • Chief Characteristics: 1. Inverse relationship. 2. Price independent and demand dependent variable. 3. Income effect & substitution effect. •. Assumptions: •. No change in tastes and preference of the consumers. •. Consumer’s income must remain the same. •. The price of the related commodities should not change. •. The commodity should be a normal commodity

Income – As income increases, the demand for a normal good will increase. – As income increases, the demand for an inferior good will decrease.

Prices of Related Goods – Prices of Related Goods – When a fall in the price of one good reduces the demand for another good, the two goods are called substitutes. – When a fall in the price of one good increases the demand for another good, the two goods are called complements.

Others – Tastes & preferences – Expectations – Re-saleability – Advertising

The Demand Schedule and the Demand Curve – The demand schedule is a table that shows the relationship between the price of the good and the quantity demanded. – The demand curve is a graph of the relationship between the price of a good and the quantity demanded. – Ceteris Paribus: “Other thing being equal”

Demand Schedule Price of Ice-cream Cone Quantity of ($) cones Demanded 0.00

12

0.50

10

1.00

8

1.50

6

2.00

4

2.50

2

3.00

0

Figure Ram’s Demand Curve Price of Ice-Cream Cone

$3.00 2.50 2.00 1.50 1.00 0.50

0

2

4

6

8

10

12

Quantity of Ice-Cream Cones

Market Demand Schedule • Market demand is the sum of all individual demands at each possible price. • Graphically, individual demand curves are summed horizontally to obtain the market demand curve. • Assume the ice cream market has two buyers as follows…

Market demand as the Sum of Individual Demands Price of Icecream Cone ($)

Ram

0.00

12

0.50

10

6

16

1.00

8

5

13

1.50

6

4

10

2.00

4

3

7

2.50

2

2

4

3.00

0

1

1

Sita +

7

Market =

19

Shifts in the Demand Curve Price of Ice-Cream Cone

Increas e in demand

Decrease in demand

D2 D1 D3 Quantity of IceCream Cones

A Movement Along the Demand Curve Price of Cigarette s, per Pack.

C

A tax that raises the price of cigarettes results in a movements along the demand curve.

$4.00

A $2.00

D1

0

12

20

Number of Cigarettes Smoked per Day

Why demand curve slopes downwards? 1. Income effect 2. Substitution effect 3. Diminishing Marginal Utility

Law of Demand • Exceptions: • Inferior goods • Articles of snob appeal. (exception: Veblen goods, eg., diamonds) • Expectation regarding future prices (shares, industrial materials) • Emergencies • Change in fashion, habits, attitudes, etc.. • Importance: • Price determination. • To Finance Minister • To farmers • In the field of Planning.

Empirical Demand Function • Specification of the relationship includes two critical elements – Choosing the correct set of independent variables – Choosing appropriate functional form for the relationship

Choosing the Independent Variables Best guide to choosing Independent Variables is to turn to theory.

Qd = f ( P, M , PR , T , Pe , N ) Price expectations and tastes and preferences are often dropped due to the difficulty of measuring or estimating them.

Qd = f ( P, M , PR , N )

Choosing the Appropriate Functional Form • Choices we consider are – Linear: Q=a+bP+cM+dPR+eN – Log-linear: Q=aPbMc(PR)dNe

Linear Demand • Q=a+bP+cM+dPR+eN – Coefficient b yields the change in Q in response to a 1 unit increase in Price(b should be negative) – Coefficient c can be positive(normal) or negative(inferior). It yields the change in Q in response to a 1 unit increase in incoMe. – Coefficient d can be positive(substitutes) or negative(complements). It yields the change in Q in response to a 1 unit increase in the Price of a Related good. – Coefficient e should be positive and yields the change in Q in response to a 1 unit increase in Number of buyers( proxy is often population)

Elasticities for Linear Specification P ˆ ˆ E p =b Q M ˆ ˆ E M =c Q PR ˆ ˆ E PR =d Q

Own Price Elasticity

Income Elasticity

Cross Price Elasticity

Log-linear Demand • Q=aPbMc(PR)dNe • Converted into logs yields lnQ = ln a + b ln P + c ln M + d ln PR + e ln N • Elasticites are constant and equal to the estimated coefficients

The Individual’s Demand Curve Quantity of y

px

As the price of x falls...

…quantity of x demanded rises. px’ px’ ’ px’’’

U1 U2

x1 I = px’ + py

x2

x3 I = px’’ + py

U3

Quantity of x I = px’’’ + py

x

x’

x’’

x’’’

Quantity of x

Economic Models to Derive the Demand Function • Utility function – Gives the level of U ( x1 , x2 ) happiness for a give bundle of goods. Typically denoted xi-- quantity demanded for good i pi-- per unit price for good i M-- consumer’s income to be spent • Budget Constraint – The consumer will spend all of their incomex purchasing p + K + x pgoods = Mto consume. 1 1

N

N

The Basic Consumer Problem ) Go buy things to make yourself as happy as possible.

Select quantities of goods to maximize utility subject t the constraint that you cannot spend more than your income max

x1 , x2

s.t.

U ( x1 , x2 )

x1 p1 + x2 p2 = M

To solve this form the function.

L( x1 , x2 , λ ) = U ( x1 , x2 ) − λ ( x1 p1 + x2 p2 − M )

The Objective Function L( x1 , x2 , λ ) = U ( x1 , x2 ) − λ ( x1 p1 + x2 p2 − M ) • This function is called a Lagrangian. • The new variable λ is called the Lagrange multiplier.

• take derivatives with respect to each of the vari and set them equal to zero.x1 , x2 and λ

The First Order Conditions ∂L ( x1 , x2 , λ ) =0 ∂x1 ∂L ( x1 , x2 , λ ) =0 ∂x2 ∂L ( x1 , x2 , λ ) =0 ∂λ • Partial derivatives – derivative holding the other variables constant. • Solve this system of 3 equations

The Solutions x1 = x1 ( p1 , p2 , M ) x2 = x2 ( p1 , p2 , M )

Demand Functions – very useful in business.

• Not that important in Economic business applications. • Very important in other business applications.

Elasticity of demand • Definition: “Elasticity of demand is defined as the responsiveness of the quantity demanded of a good to changes in one of the variables on which demand depends.” • These variables are price of the commodity, prices of the related commodities, income of the consumer & other various factors on which demand depends. Thus, we have Price Elasticity, Cross Elasticity, Elasticity of Substitution & Income Elasticity. It is always price elasticity of demand which is referred to as elasticity of demand • A.Price Elasticity • Measures how much the quantity demanded of a good changes when its price changes. • Or • It may be defined as “Percentage Change in Quantity demanded over percentage change in price”

Factors affecting Elasticity of Demand 1. 2. 3. 4.

Availability of substitutes Postponement of consumption Proportion of expenditure (needles: inelastic; TV: elastic) Nature of the commodity (necessity vs. luxury; durability/reparability eg., shoes) 5. Different uses of the commodity (paper vs. ink) 6. Time period (elastic in the long term) 7. Change in income (necessaries: inelastic; milk and fruit for a rich man) 8. Habits 9. Joint demand 10.Distribution of income 11.Price level (very costly & very cheap goods: inelastic)

Price Elasticity •

Price Elasticity

•

Elastic Demand or more than 1 – When quantity demanded responds greatly to price changes

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Inelastic Demand or less than 1 – When quantity demanded responds little to price changes.

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Unitary Elastic – When quantity demanded responds equally to the price changes.

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Perfectly inelastic or 0 elastic demand

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Perfectly elastic or infinite elastic demand

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Economic factors determine the size of price elasticity for individual goods. Elasticity tends to be higher when the goods are luxuries, when substitutes are available and when consumer have more time to adjust their behavior.

Calculating Price Elasticity PED = % Change in Qty Demanded  % Change in Price Points to Remember: • We drop the minus sign from the numbers by treating all % changes as positive. That means all elasticity’s are positive, even though prices and quantities move in the opposite direction because of the law of downward sloping demand. • Definition of elasticity uses percentage changes in price and demand rather than actual changes. That means that a change in the units of measurement does not affect the elasticity. So whether we measure price in Rupees or paisa, the price elasticity stays the same.

Some business applications of Price Elasticity • • • • • •

Price discrimination Public utility pricing (electricity, railway) Joint supply (wool and mutton) Super markets Use of machines (lower cost of production for elastic) Factor pricing (workers producing inelastic demand products) • International trade (devalue when exports are price-elastic) • Shifting of tax burden (shift commodity tax when demand is inelastic) • Taxation policy

Elasticity & Revenue: • When demand is price inelastic, marginal revenue is negative and a price decrease reduces total revenue. • When demand is price elastic, marginal revenue is positive and a price decrease increases total revenue. • In the borderline case of unit elastic demand, marginal revenue is 0 and a price change leads to no change in the total revenue. B. Income Elasticity of Demand: Is the degree of responsiveness of quantity demanded of a good to a small change in the income of the consumer. • If the proportion of income spent on a good remains the same as income increases, then income elasticity for the good is equal to one. • If the proportion spent on a good increases, then the income elasticity for the good is greater than one. • If the proportion decreases as income rises, then income elasticity for the good is less than one.

Income elasticity  Types: • Zero • Negative • Positive (i) low (ii) unitary (iii) high  Empirical evidence suggests that income elasticity falls as income rises.  Income elasticity and business decisions 1. If ei is >0 but 1, sales will increase more rapidly than general economic growth . Corollary: in a growing economy while farmers suffer as their products have low income elasticity, industrialists gain as their products have high income elasticity.

Cross Elasticity: A change in the demand for one good in response to a change in the price of another good represents cross elasticity of demand of the former good for the latter good. • If two goods are perfect substitutes for each other cross elasticity is infinite and if the two goods are totally unrelated, cross elasticity between them is zero. • Goods between which cross elasticity is positive can be called Substitutes, the good between which the cross elasticity is negative are not always complementary as this is found when the income effect on the price change is very strong. 

Degrees of Elasticity of Demand • 1. Perfectly Elastic • 2. Perfectly Inelastic • 3. Unitary Elastic • 4. Relatively more elastic • 5. Relatively less elastic

1.

Perfectly Elastic

Y Ed = ∞ p

O

d

d1

X

2. Perfectly Inelastic Y p1

Ed = 0

p

O

d

X

3. Unitary Elastic Y p1

Ed = 1

p

O

d

d1

X

4. Relatively more Elastic

Y p1

Ed > 1

p

O

d

d1

X

5. Relatively less Elastic

Y p1

Ed < 1

p

O

d

d1

X

Figure 7.3 Elastic and inelastic demand Demand curves differ in their relative elasticity. Curve D1 is more elastic than curve D2, in the sense that consumers on curve D1 are more responsive to a given price change (P2 to P1) than are consumers on curve D2.

Figure 7.4 Changes in the elasticity coefficient The elasticity coefficient decreases as a firm moves down the demand curve. The upper half of a linear demand curve is elastic, meaning that the elasticity coefficient is greater than one. The lower half is inelastic, meaning that the elasticity coefficient is less than one. This means that the middle of the linear demand curve has an elasticity coefficient equal to one.

Methods of measurement of Elasticity 1.Percentage or Proportionate Method . Pe = Percentage change in demand or; . Percentage change in price .= Proportionate change in demand . Proportionate change in price .2. Total Outlay (Expenditure) Methods .TO=TQ * P ; where, .TO=total outlay; TQ=total quantity; P=price of the commodity .3. Geometric (Point) method – at any given point on the curve .Pe = lower segment of demand curve . upper segment of demand curve