Market Demand and Elasticity

Market Demand Curves

  

  The market demand is the total quantity of a good or service demanded by all potential

  buyers.

  

  The market demand curve is the relationship between the total quantity demanded of a good or service and its price, holding all other factors constant.

  

Construction of the Market Demand

Curve 

  The market demand curve is constructed by horizontally summing the demands of the

  individual consumers 

  Assume the market consists of only two buyers as shown in Figure 4.1

• ^{* –}

  At any given price, such as P , individual 1 _X ^*

• ^* demands X and individual 2 demands X .
_{1 2}

  (a) Individual 1 P _X X P* X*

  1 FIGURE 4.1: Constructing a Market Demand Curve from Individual Demand Curves

  (a) Individual 1 P _X X P* X*

  1 (b) Individual 2 X*

  2 FIGURE 4.1: Constructing a Market Demand Curve from Individual Demand Curves P _X

Construction of the Market Demand Curve

• –

  The total quantity demanded at the market at P

  ^*
_X is the sum of the two amounts: X ^* = X ^* ₁ + X ^* ₂ .

  

  The point X ^* , P ^* _X is one point on the market demand curve.

  

  The other points on the curve are similarly plotted.

  (a) Individual 1 P _X X P* X*

  1 (b) Individual 2 X*

  2 (c) Market Demand

  X D X*

FIGURE 4.1: Constructing a Market Demand

Curve from Individual Demand Curves

  P _X P _X

Shifts in the Market Demand Curve

  

  To discover how some event might shift a market demand curve, we must first find out how this event causes individual demand curves to shift and then compare the horizontal sum of these new demand curves with the old demand curve.

  

Shifts in the Market Demand Curve



  For example consider the two buyer case where both consumers regard X as a normal good.

  

  An increase in income for each consumer would shift their individual demand curves out so that the market demand curve, would also shift out

  

  This situation is shown in Figure 4.2

  (a) Individual 1 P _X X P* X*

  1 (b) Individual 2 X*

  2 (c) Market Demand

  X D X* FIGURE 4.2: Increases in Each individual’s Income Cause the Market Demand Curve to Shift Outward P _X P _X

  (a) Individual 1 P _X X P* X*

  1 (b) Individual 2 X*

  2 (c) Market Demand

  X D X* FIGURE 4.2: Increases in Each individual’s Income Cause the Market Demand Curve to Shift Outward P _X P _X X** X** X** D’

  1

  2

  

Shifts in the Market Demand Curve



  However, some events result in ambiguous outcomes.

• ^– If one consumer’s demand curve shifts out while another’s shifts in, the net effect depends on the size of the relative shifts.

  

  An increase in income for pizza lovers would

  increase the market demand for pizza so long as it is a normal good.

Shifts in the Market Demand Curve

  

  On the other hand, if the increase in income was for people who don’t like pizza, there would be no significant effect on the market demand curve for pizza.

  

  Changes in the prices of related goods, substitutes or complements, will also shift the individual and market demand curves.

Shifts in the Market Demand Curve

  

  If goods X and Y are substitutes, an increase in the price of Y will increase the demand for X.

  Similarly, a decrease in the price of Y will decrease the demand for X.

  

  If goods X and Y are complements, an increase in the price of Y will decrease the demand for X. A decrease in the price of Y will increase the demand for X.

A Word on Notation and Terms

  

  When looking at only one market, Q is used for the quantity of the good demanded, and P is used for its price.

  

  When drawing the demand curve, all non-price factors are assumed to not change.

  

  Movements along the curve are changes in quantity demanded, while shifts are changes in demand.

Elasticity

  

  Goods are often measured in different units (steak is measured in pounds while oranges are measured in dozens).

  

  It can be difficult to make simple comparisons between goods when trying to determine which is more responsive to changes in price.

Elasticity

   Elasticity is a measure of the percentage

  change in one variable brought about by a 1 percent change in some other variable.

  

  Since it is measured in percentages, the units cancel out so that it is a unit-less measure of responsiveness.

Price Elasticity of Demand

  

  The price elasticity of demand is the percentage change in the quantity demanded of a good in response to a 1 percent change in its price

  Percentage change in Q Price elasticity of demand e   _{Q , P} Percentage change in P

  Q 

  Q P Q 

e

_{Q , P}    P

   P Q

   P

Price Elasticity of Demand

  

  The price elasticity records how Q changes in percentage terms in response to a percentage change in P.

  

  Since, on a typical demand curve, P and Q move oppositely, e will be negative. _Q,P

  

  For example, if e = -2, a 1 percent increase _Q,P in price leads to a 2 percent decline in quantity.

Values of the Price Elasticity of Demand

  

  When e < -1, the quantity demanded is _Q,P relatively unresponsive to changes in price

  inelastic 

  When e = -1, a price increase causes a _Q,P proportional quantity decrease, and the curve is called unit elastic.

  

  When e > -1, a price increase causes more _Q,P than a proportional quantity decrease, and the curve is called elastic

TABLE 4.1: Terminology for the Ranges of e

  

Value of e at a Point Terminology for Curve

  on Demand Curve at This Point e Inelastic

  Q,P < -1 e Unit elastic

  Q,P = -1 e Elastic

  Q,P > -1

Price Elasticity and the Shape of the Demand Curve

  

  We often classify market demand curves by their elasticities

• ^– For example, the market demand curve for medical services is inelastic (nearly vertical) since there is little quantity response to changes in price. ^–

  

Alternatively, the market demand curve for a

single type of candy bar is very responsive to price change (nearly flat) and is very elastic.

Price Elasticity and the Substitution Effect

  

  Goods which have many close substitutes are subject to large substitution effects from a price change so their market demand curve is likely to be relatively elastic.

  

  Goods with few close substitutes, on the other hand, will likely be relatively inelastic.

Price Elasticity and the Substitution Effect

  

  There is also an income effect that will determine how responsive quantity demanded is to changes in price.

  

  However, since changes in the prices of

  most goods have a small effect on

  individuals’ real incomes, the income effect

  will likely not have as large an impact on elasticity as the substitution effect.

Price Elasticity and Time

  

  Some items can be quickly substituted for, such as a brand of breakfast cereal, others, such as heating fuel, may take several years.

  

  Thus, in some situations, it is important to make the distinction between the short-term and long-term elasticities of demand.

APPLICATION 4.2: Brand Loyalty

  

  Substitution due to price changes will likely take a longer time if individual’s develop

  spending habits.

  

  Such brand loyalties are rational since they reduce decision making costs.

  

  Over the long term, however, price differences may cause buyers to try other brands.

APPLICATION 4.2: Brand Loyalty

  

  It took several years, but by the 1970s the price differences between U.S. and Japanese cars eventually convinced Americans to buy the Japanese cars.

  

  Brand name Licensing, such as Coca-Cola sweatshirts and Mickey Mouse watches, makes products that were previously nearly perfect substitutes, now much less so.

Price Elasticity and Total Expenditures

  

  Total expenditures on a good are found by multiplying the good’s price (P) times the quantity purchased (Q).

  

  When demand is elastic, price increases will cause total expenditures to fall.

• ^– Total expenditures on the product decreases as the price goes up.

Price Elasticity and Total Expenditures

   For example suppose price elasticity = -1.5. ^– Suppose a family buys 100 pounds of chicken per year at a price of $2 per pound. The price elasticity of demand for chicken is -1.5. If the price of chicken increases to $2.20 (a 10% increase). What is the difference between new family’s expenditures on chicken and the old one? The family’s consumption of chicken falls to 85 pounds a year (a 15% decrease). Total expenditure on chicken will also fall, from $200 (100 pounds x $2 per pound) to $187 (85 pounds x $2.20 per pound). The difference is -

Price Elasticity and Total Expenditures

  

  Of course, when demand is inelastic and prices _– increase, total expenditures increase. _{Suppose that the price elasticity of demand for gasoline is -0.5. If the price of gasoline A family currently uses 1000 gallons of gasoline a year when the price is $1 per gallon; gasoline increase from $1000 (1000 gallons x $1/ gallon) to $1045 (950 gallons x $1.1/}

increases to $1.10 (10% increase). What happen to expenditure on gasoline? The

_gallon)

_{Consumption of gasoline falls to 950 gallons (5% decrease). Total expenditure on}

  

  With unit elasticity, total expenditures remain _– the same with a price change. _{direction with the quantity demanded. The movement in one direction by the price is fully offset by the movement in the other}

  TABLE 4.2: Relationship between Price Changes and Changes in Total Expenditure If Demand Is

In Response to an

  

Increase in Price,

Expenditures will

In Response to a Decrease in Price, Expenditures will

  Elastic Fall Rise Unit elastic Not change Not change Inelastic Rise Fall

APPLICATION 4.3: Volatile Farm Prices

  

  The demand for many basic agricultural products (wheat, corn, etc.) is relatively inelastic.

  

  Even modest changes in supply, brought about by weather patterns, can have large effects on crop prices.

  

Demand Curves and Price Elasticity



  The relationship between a particular demand curve and the price elasticity it exhibits can be complicated.

  

  For some curves, the elasticity remains constant everywhere, but for others it is different at every point.

  

  A more accurate way to describe it would be to say the elasticity is for current prices.

Linear Demand Curves and Price Elasticity

  

  The price elasticity of demand is always changing along a straight line demand curve.

• ^– Demand is elastic at prices above the midpoint price. ^–

  Demand is unit elastic at the midpoint price.

  ^–

  Demand is inelastic at prices below the midpoint price.

  

Numerical Example of Elasticity on

a Straight Line Demand Curve 

  Assume a straight-line demand curve for Walkman cassette tape players is

  Q = 100 - 2P

• ^– where Q is the quantity of players demanded per week and P is their price.

  

  This demand curve is illustrated in Figure 4.3 and Table 4.3 shows several price-quantity combinations.

FIGURE 4.3: Elasticity Varies along a Linear Demand Curve

  Price (dollars)

  50

  40

  30

  20

  10 20 405060 80 100 Quantity of tape players per week

  TABLE 4.3: Price, Quantity, and Total Expenditures on Walkmans for the Demand Function Q = 100 - 2P Price (P) Quantity (Q) Total Expenditures (P

  

Q)

  $50 $0

  40

  20 800

  30

  40 1,200

  25

  50 1,250

  20

  60 1,200

  10

  80 800 100

  

Numerical Example of Elasticity on

a Straight Line Demand Curve 

  For prices of $50 or more, nothing is bought so total expenditures are $0.

  

  As prices fall between $50 and $25, the midpoint, total expenditures increase.

  

  At the midpoint, total expenditures reach a maximum.

  

  As prices fall below $25, total expenditures also fall.

  

Elasticity of a Straight Line Demand

Curve 

  More generally, for a linear demand curve of the form Q = a - bP,

  Q 

  Q P Q  e

     Q , P

  P 

  P Q 

  P P e b .

     Q , P

  Q

A Unitary Elastic Curve

  

  Suppose the demand for tape players took the form

  1 , 200 Q

  

P

  The graph of this equation, shown in Figure 4.4,

• is a hyperbola. P·Q = $1,200 regardless of price so demand is
• unit elastic (-1) everywhere on the curve.

  

General Formula for the Elasticity

of a Hyperbola 

  If the demand curve takes the following form, the price elasticity of demand is equal to b everywhere on the curve.

  0) (b   b

  Q aP

FIGURE 4.4: A Unitary Elastic Demand Curve Price (dollars)

  60

  50

  40

  30

  20 20 24

  30

  40

  60 Quantity of tape players per week

Income Elasticity of Demand

  

  The income elasticity of demand equals the percentage change in the quantity demanded of a good in response to a 1 percent change in income.

  

  The formula is given by (where I represents income):

  Percentage change in Q e .

   Q ,

  I Percentage change in

  I

Income Elasticity of Demand

  

  For normal goods, e is positive because _Q,I increases in income lead to increases in purchases of the good.

   For inferior goods e is negative. _Q,I 

  If e > 1, the purchase of the good increases _Q,I more rapidly than income so the good might be called a luxury good.

APPLICATION 4.4: An Experiment in Health Insurance

  

  Most developed countries have some form of national health insurance. _–

  In the U.S. Medicare covers the elderly and Medicaid is available for many of the poor.

  

  Recently a number of comprehensive government health plans have been proposed.

The Moral Hazard Problem

  

  A “moral hazard” problem occurs because insurance misleadingly lowers the out-of- pocket expenses to patients, greatly increasing their demand for medical services.

  

  An important question, in considering implementing national health insurance is how large an increase is likely to develop?

The Rand Experiment

  

  The Rand Corporation conducted a government-funded large-scale experiment in four cities.

  

  People were assigned to different insurance plans that varied in the generosity of coverage they offered.

   Table 1 shows the results from the experiment.

The Rand Experiment

  

  A rough estimate of the elasticity of demand can be obtained by averaging the percentage changes across the various plans in Table 1

  % change in Q

  12  e .

  18     % change in P

  66 

Table 1: Results of the Rand Health Insurance Experiment Coinsurance rate Percent change in price Average total spending Percent change in quantity

  0.95 540.00

0.50 -47% 573.00 6.10%

  0.25 -50 617.00

  7.7 0.00 -100 750.00

  21.6 Average -66

  12

Low Elasticities for Hospital and Doctors’ Visits

  

  Using the estimate of -0.22 found in Table 4.4, and based on other studies suggests only a small increase in hospital and doctor visits would result from the lower prices provided by insurance.

  

  Alternatively, researchers have found greater elasticities (around -0.5) for dental care and outpatient mental health care.

Cross-Price Elasticity of Demand

  

  The cross-price elasticity of demand measures the percentage change in the quantity demanded of a good in response to a 1 percent change in the price of another good.

  Letting P’ be the price of another good,

  Percentage change in Q e .

   Q , P

  Percentage change in P'

Cross-Price Elasticity of Demand

  

  If the goods are substitutes, an increase in

  the price of one will cause buyers to

purchase more of the substitute, so the

  elasticity will be positive.

  

  If the goods are complements, an increase

  in the price of one will cause buyers to buy

less of that good and also less of the good

  they use with it, so the elasticity will be

  negative

Empirical Studies of Demand: Estimating Demand Curves

  

  Estimating a demand curve for a product is one of the more difficult but important problems in econometrics.

  

  Empirical studies are useful because they a provide a more precise estimate of the amount of change in quantity demanded that results due to a price change.

Problems Estimating Demand Curves

  

  The first problem is how to derive an estimate holding all other factors (the ceteris paribus

  assumption) constant.

  

  This problem is often solved, as discussed in the Appendix to Chapter 1, by the use of multiple regression analysis.

Problems Estimating Demand Curves

  

  The second problem deals with what is observed in the data. The data points represent quantity and price outcomes that are simultaneously determined by both the demand and the supply curves.

  

  The econometric problem is to “identify” from these equilibrium points the demand curve that generated them.

Some Elasticity Estimates

  

Table 4.4 gathers a number of estimated income and price elasticities of demand.

  

  Some things to note

• ^– All of the estimated price elasticities are less than zero as predicted by a negatively sloped demand curve. ^– Most of the price elasticity estimates are inelastic.

  

TABLE 4.4: Representative Price and

Income Elasticities of Demand Price Elasticity Income Elasticity

  Food

• 0.21 +0.28 Medical services -0.22 +0.22 Rental housing -0.18 +1.00 Owner-occupied housing -1.20 +1.20 Electricity -1.14 +0.61 Automobiles -1.20 +3.00

  Beer

• 0.26 +0.38 Wine
• 0.88 +0.97 Marijuana -1.50

  0.00 Cigarettes -0.35 +0.50 Abortions -0.81 +0.79 Transatlantic air travel -1.30 +1.40 Imports -0.58 +2.73 Money -0.40 +1.00

Some Elasticity Estimates

  

  The income elasticities of automobiles and transatlantic travel exceed 1 (luxuries).

  

  The high income elasticities are balanced by goods such as food and medical care which are less than 1 (necessities).

  

  There is no evidence of Giffen’s paradox in the table.

Some Cross-price Elasticity Estimates

  

Table 4.5 shows a few cross-price elasticity estimates

  

  All of the goods appear to be substitutes and have positive cross-price elasticities.

  

TABLE 4.5: Representative Cross-Price

Elasticities of Demand Demand for Effect of Price of Elasticity

  Estimate Butter Margarine

  1.53 Electricity Natural gas

  0.50 Coffee Tea

  0.15