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Market Demand. Chapter 5. Introduction. Demand for a commodity is differentiated from a want In terms of society’s willingness and ability to pay for satisfying the want This chapter determines total amount demanded for a commodity by all households Called market demand or aggregate demand

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market demand

Market Demand

Chapter 5

  • Demand for a commodity is differentiated from a want
    • In terms of society’s willingness and ability to pay for satisfying the want
  • This chapter determines total amount demanded for a commodity by all households
      • Called market demand or aggregate demand
        • Sum of individual household demands
          • Assuming individual household demands are independent of each other
  • Will explore network externalities
    • Independence assumption does not hold
  • Major determinants of market demand for a commodity are
    • Its own price
    • Price of related commodities
    • Households’ incomes
  • Elasticity of demand is a measure of influence each parameter has on market demand
  • We investigate own-price elasticity of demand
    • Classify market demand as elastic, unitary, or inelastic
      • Depending on its degree of responsiveness to a price change
  • Relating own-price elasticity to households’ total expenditures for a commodity
    • Demonstrate how this determines whether total expenditures for a commodity will increase, remain unchanged, or decline, given a price change
  • Define income elasticity of demand and elasticity of demand for the price of related commodities
    • Called cross-price elasticity
  • Applied economists are active in estimating elasticities for all determinants (parameters) of market demand
  • Knowledge of the influence these determinants provides information for firms’ decisions
  • Government policymakers also use estimates of elasticities
  • With reliable estimates of elasticities based on economic models
    • Economists can explain, predict, and control agents’ market behavior
market demand1
Market Demand
  • One arm of Marshallian cross
  • Conveys individual household preferences for a commodity given a budget constraint
  • Sum of all individual households’ demands for a single commodity
  • Consider only two households—Robinson, R, and Friday, F—and two commodities
    • xR1 and xF1 are household Robinson’s and household Friday’s demand for commodity x1, respectively
  • Both households face same per-unit prices for the two commodities
    • Each household is a price taker
  • Both households are bound by budget constraints
    • IR and IF represents income for Robinson and Friday, respectively
market demand2
Market Demand
  • Market demand, Q1, is sum of amounts demanded by the two households
  • Holding p2, IR, and IF constant, we obtain market demand curve for x1 in Figure 5.1
  • For a private good, market demand curve is horizontal summation of individual household demand curves
market demand3
Market Demand
  • At p*1 Robinson demands 5 units of Q1 and Friday demands 3
    • For a total market demand of 8 units
    • Varying price will result in other associated levels of market demand
      • Will trace out market demand curve for Q1
        • Will have a negative slope
          • For market demand to have a positive slope, a large portion of households would have to consider x1 a Giffen good
  • Assume market demand for a commodity is inversely related to its own price
  • Shifts in market demand will occur if there is a change in household preferences, income, price of another commodity, or population
  • As illustrated in Figure 5.2, market demand curve will shift outward for an increase in
    • Income
    • Population
    • Price of substitute commodities, or
    • A decrease in prices of complement commodities
network externalities
Network Externalities
  • Horizontal summation of households’ demand functions assumes individual demands are independent of each other
  • For some commodities, one household’s demand does depends on other households’ demands
    • Example of network externalities
      • Exist when a household’s demand is affected by other households’ consumption of the commodity
  • Positive network externalities result when
    • Value one household places on a commodity increases as other households purchase the item
  • Negative network externalities exist if household’s demand decreases as a result of other households’ actions
bandwagon effect
Bandwagon Effect
  • Specific type of positive network externality
  • Individual demand is influenced by number of other households consuming a commodity
  • The greater the number of households consuming a commodity
    • More desirable commodity becomes for an individual household
  • Key to marketing most toys and clothing is to create a bandwagon effect
  • Results in market demand curve shifting outward
    • Individual household demand increases in response to increased demand by numerous other households
market effect
Market Effect
  • If positive network externalities exist, summation of individual household demands does not take into account households’ increase in demand when other households increase their demand for the commodity
    • Will underestimate true market demand
      • Shown in Figure 5.3
  • Individual household demand curves are positively influenced by other households’ level of demand for commodity
    • Results in a further outward shift of individual household demand curves, and market demand curve
  • Instead of market demand being sum of 5 plus 3 units at p*1
    • Positive network externalities result in a market demand of 7 plus 6 units
market effect1
Market Effect
  • If negative network externalities exist
    • Summation of individual household demands will overestimate true market demand
      • Shown in Figure 5.4
        • Results in inward shift of individual household demand curves
          • With a corresponding inward shift in market demand curve
  • Market demand function provides a relationship between price and quantity demanded
    • Quantity demanded is inversely related to price
  • Of greater interest to firms and government policymakers is how responsive quantity demanded is to a change in price
  • Downward-sloping demand curve indicates
    • If a firm increases its price, quantity demanded will decline
      • Does not show magnitude of decline
  • To measure magnitude of responsiveness use derivative or slope of curve
    • The larger the partial derivative, the more responsive is y
units of measurement
Units Of Measurement
  • One problem in using derivative is units of measure
  • By changing units of measure—say from dollars to cents or pounds to kilograms
    • Cause magnitude of change or value of derivative to vary
      • For example, if y is measured in pounds, x in dollars, and ∂y/∂x = 2
        • Measurement is 2 pounds per dollar
          • For each $1 increase in x, y will increase by 2 units
        • However, if change scale used to measure y to ounces, then ∂y/∂x = 32
          • For each $1 increase in x, y will increase by 32 units
        • Just changing scale makes it appear that y is more responsive to a given change in x
unit free measure of responsiveness
Unit-free Measure Of Responsiveness
  • Prior failure to convert from English to metric system of measurement caused loss of Mars Climate Orbiter
  • To avoid making such errors in comparing responsiveness across different factors with different units of measurement in economics
    • Use a standardized derivative, elasticity
      • Removes scale effect
  • Derivative is standardized (converted into an elasticity)
    • By weighting it with levels of variables under consideration
      • Results in percentage change in y given a percentage change in x
        • Provides a unit-free measure of the responsiveness
      • Partial derivative is not as useful as elasticity measurement
logarithmic representation
Logarithmic Representation
  • As a percentage change measure, elasticity can be expressed in logarithmic form
price elasticity of demand
Price Elasticity Of Demand
  • For market quantity, Q is defined as
    • Q,p(∂Q/∂p)(p/Q) = ∂ ln Q/∂ ln p
  • Elasticity of demand indicates how Q changes (in percentage terms) in response to a percentage change in p
    • Ordinary good: ∂Q/∂p < 0
      • Implies Q,p < 0 given that p and Q are positive
        • Examples of demand elasticities are provided in Table 5.1
perfectly inelastic demand
Perfectly Inelastic Demand
  • A change in price results in no change in quantity demanded
    • Q,p = 0
    • Represented in Figure 5.5
      • Results in a vertical demand curve
        • At every price level quantity demanded is the same
          • Examples are difficult to find due to the lack of households with monomania preferences
          • For example, alcoholics and drug addicts would have highly inelastic demands over a broad range of quantity
perfectly elastic demand
Perfectly Elastic Demand
  • Smallest possible value of Q,p is for it to approach negative infinity
  • If Q,p = - demand is perfectly elastic
    • Very slight change in price corresponds to an infinitely large change in quantity demanded
      • Illustrated in Figure 5.6
  • Many examples of perfectly elastic demand curves
    • Whenever a firm takes its output price as given it is facing a perfectly elastic demand curve
      • For example, agriculture
classification of elasticity
Classification of Elasticity
  • Between elasticity limits from - to 0, elasticity may be classified in terms of its responsiveness
    • Q,p < -1, elastic, |∂Q/Q| > |∂p/p|
      • Absolute percentage change in quantity is greater than absolute percentage change in price
        • Quantity is relatively responsive to a price change
    • Q,p = -1, unitary, |∂Q/Q| = |∂p/p|
      • Absolute percentage change in quantity is equal to absolute percentage change in price
    • Q,p > -1, inelastic, |∂Q/Q| < |∂p/p|
      • Absolute percentage change in quantity is less than absolute percentage change in price
        • Quantity is relatively unresponsive to a price change
linear demand
Linear Demand
  • Linear demand curve will exhibit all three elasticity classifications
  • Consider linear demand function for commodity x1
    • x1 = 120 – 2p1
      • Plotted in Figure 5.7
    • Elasticity of demand represented as
      • 11 = (∂x1/∂p1)(p1/x1)
    • Size of elasticity coefficient increases in absolute value for movements up this linear demand curve
      • Because slope is remains constant while weight is increasing
        • At point B
          • 11 = (∂x1/∂p1)p1/x1 = -2(45/30) = -3, elastic
        • At D
          • 11 = (∂x1/∂p1)p1/x1 = -2(15/90) = -1/3, inelastic
        • At point C (A) [E] elasticity of demand is unitary (-) [0]
linear demand1
Linear Demand
  • General functional form for a linear market demand function
    • Q1 = a + bp1, b<0
      • Q1 denotes market demand for commodity 1
      • p1 is associated price per unit
      • Partial derivative is equal to constant b
        • Elasticity of demand is not constant along a linear demand curve
        • As p1/Q1 increases, demand curve becomes more elastic
        • In the limit, as Q1 approaches zero, elasticity of demand approaches negative infinity, perfectly elastic
        • p1 = 0 results in perfectly inelastic elasticity of demand
linear demand2
Linear Demand
  • A straight-line (linear) demand curve is certainly the easiest to draw (Figure 5.8)
    • However, such behavior is generally unrealistic
      • Because linear demand curve assumes (∂Q1/∂p1) = constant
        • Implies that a doubling of prices will have same effect on Q1 as a 5% increase
proportionate price changes
Proportionate Price Changes
  • Assuming households respond to proportionate rather than absolute changes in prices
  • May be more realistic to consider the demand function
    • Q1 = apb1, a > 0, b > 0 or
    • ln Q1 = ln a + b ln p1
      • Elasticity of demand is
        • 11 = (∂Q1/∂p1)(p1/Q1) = bap1b-1(p1/Q1) = b or
        • 11 = (∂ ln Q1/∂ ln p1) = b
          • Elasticity of this demand curve is constant along its entire length
          • Constant elasticity of demand curve, with b = -1 is illustrated in Figure 5.9
price elasticity and total revenue
Price Elasticity and Total Revenue
  • Valuable use of elasticity of demand
    • Predict what will happen to households’ total expenditures on a commodity or to producers’ total revenue when price changes
  • Total revenue (TR) and total expendituresare defined as price times quantity (p1Q1)
  • A change in price has two offsetting effects
    • Reduction in price has direct effect
      • Reduces total revenue for the commodity
      • Results in an increase in quantity sold
        • Increases total revenue
    • Considering these two opposing effects, total revenue from a commodity price change may rise, fall, or remain the same
      • Effect depends on how responsive quantity is to a change in price
        • Measured by elasticity of demand
price elasticity and total revenue1
Price Elasticity and Total Revenue
  • Relationship between total revenue and elasticity of demand may be established by differentiating total revenue (p1Q1) with respect to p1
  • Using product rule of differentiation, dividing both sides by Q1 and multiplying left-hand-side by p1/p1 yields total revenue elasticity
    • TR, p = 1 + 11
      • Measures percentage change in total revenue for a percentage change in price
      • Sign depends on whether 11 is > or < -1
        • If 11 > -1, demand is inelastic and TR,p > 0
          • Price and total revenue move in same direction
        • If 11 < -1, demand is elastic, and TR,p < 0
          • An increase in p1 is associated with a decrease in total revenue
        • If elasticity of demand is unitary, Q,p = -1, then TR,p = 0
price elasticity and total revenue2
Price Elasticity And Total Revenue
  • If elasticity of demand is elastic
    • Quantity demanded will increase by a larger percentage than price decreases
      • Total revenue will increase with a price decline
  • Opposite occurs when demand is inelastic
    • A price decline results in total revenue declining
      • Because quantity demanded increases by a smaller percentage than price decreases
  • In elastic portion of demand curve
    • Price and total revenue move in opposite directions
  • In inelastic portion
    • Price and TR move in same direction
price elasticity and the price consumption curve
Price Elasticity and the Price Consumption Curve
  • Setting p2 as numeraire price, p2 = 1
    • Then p1x1 + x2 = I
  • Solving for total revenue (expenditures) for x1 yields
    • p1x1 = I – x2
    • On vertical axis in Figure 5.7, at p1 = $45,
      • Income I is initially allocated between total expenditures for x2, x2, and total expenditure on x1, I - x2
    • Decreasing p1 from $45 to $30 results in a decline in total expenditure for x2 and an increase in total expenditure for x1
      • Movement from B to C in indifference space results in a negatively sloping price consumption curve
price elasticity and the price consumption curve1
Price Elasticity and the Price Consumption Curve
  • Declining price consumption curve is associated with an increase in total expenditures on x1
    • Indicating elastic demand
  • Negatively sloping portion of price consumption curve is associated with elastic portion of demand curve
  • Positively sloping price consumption curve is associated with inelastic portion of demand curve
    • Decreasing p1 from $30 to $15 results in total expenditures for x2 increasing and total expenditures for x1 declining
    • Indicating inelastic demand
  • If price consumption curve has a zero slope, unitary elasticity exists
price elasticity and the price consumption curve2
Price Elasticity and the Price Consumption Curve
  • Slope of price consumption curve is determined by magnitude of income and substitution effects
    • Total effect of a price change is sum of these two effects
    • Closeness of substitutes for a commodity directly influences substitution effect
      • The more closely related substitutes are to the commodity, the larger will be the substitution effect
      • A relatively large substitution effect will decrease slope of price consumption curve
        • Will make demand curve more elastic
      • If a commodity has a close substitute and if price of substitute remains constant
        • A rise in price of commodity will divert households’ expenditures away from product toward substitute
price elasticity and the price consumption curve3
Price Elasticity and the Price Consumption Curve
  • Other important determinants of slope of price consumption curve
    • Proportion of income allocated for a commodity
      • And whether commodity is normal or inferior
    • The smaller the proportion of income allocated for a commodity, the larger the slope of price consumption curve
      • The more inelastic the demand
  • Income effect is relatively small for a commodity requiring a small fraction of income
    • Results in a more inelastic demand
price elasticity and the price consumption curve4
Price Elasticity and the Price Consumption Curve
  • An inferior commodity will tend to result in a positively sloping price consumption curve
    • Inelastic demand curve
    • If inferior nature of a commodity results in a Giffen good, result is
      • Backward-bending price consumption curve
      • Positively sloping demand curve
  • A final major determinant of demand elasticity is time allowed for adjusting to a price change
    • Elasticities of demand tend to become more elastic as time for adjustment lengthens
      • The longer the time interval after a price change, the easier it may become for households to substitute other commodities
income elasticity of demand
Income Elasticity Of Demand
  • Relationship between change in quantity demanded and change in income may be represented by the slope of an Engel curve
  • Weighting this slope with income divided by quantity results in income elasticity
    • ηQ = (∂Q/∂I)(I/Q)
    • Measures percentage change in quantity to a percentage change in income
      • Classified as follows
cross price elasticity of demand
Cross-Price Elasticity of Demand
  • Demand for a commodity such as an automobile will depend on its own price and income and
    • Prices of other related commodities
  • Measure responsiveness of demand to a price change in a related commodity by cross-price elasticity
  • Cross-price elasticity of demand for commodities x1 and x2
    • When Q1 is a gross substitute for Q2
      • 12= (∂Q1/∂p2)(p2/Q1) = ∂ ln Q1/∂ ln p2> 0
    • When Q1 is a gross complement for Q2
      • 12= (∂Q1/∂p2)(p2/Q1) = ∂ ln Q1/∂ ln p2< 0
    • Cross-price elasticity can be either positive or negative
      • Depending on whether Q1 is a gross substitute or gross complement for Q2
slutsky equation in elasticities
Slutsky Equation in Elasticities
  • Slutsky equation from Chapter 4
  • Substitution elasticity
  • Indicates how demand for x1 responds to proportional compensated price changes
slutsky equation in elasticities1
Slutsky Equation in Elasticities
  • Slutsky equation in elasticity form
  • Where α1 = p1x1/I is proportion of income spent on x1
    • Indicates how price elasticity of demand can be disaggregated into substitution and income components
      • Relative size of income component depends on proportion of total expenditures devoted to commodity in question
        • Given a normal good, the larger the income elasticity and proportion of income spent on the commodity, the more elastic is demand
      • Income effect will be reinforced by substitution effect
        • Larger the substitution effect, the more elastic is demand