©2005, Southwestern Slides by Pamela L. Hall Western Washington University Market Demand Chapter 5

2 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  Sum of individual household demands  Assuming individual household demands are independent of each other Will explore network externalities  Independence assumption does not hold

3 Introduction 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

4 Introduction 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

5 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 x R 1 and x F 1 are household Robinson’s and household Friday’s demand for commodity x 1, 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 I R and I F represents income for Robinson and Friday, respectively

6 Market Demand Market demand, Q 1, is sum of amounts demanded by the two households  Holding p 2, I R, and I F constant, we obtain market demand curve for x 1 in Figure 5.1  For a private good, market demand curve is horizontal summation of individual household demand curves

7 Figure 5.1 Market demand for commodity Q1 …

8 Market Demand At p* 1 Robinson demands 5 units of Q 1 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 Q 1  Will have a negative slope  For market demand to have a positive slope, a large portion of households would have to consider x 1 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

9 Figure 5.2 Shift in market demand

10 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

11 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

12 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

13 Figure 5.3 Market demand for commodity Q1 …

14 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

15 Figure 5.4 Market demand for commodity Q1 …

16 Elasticity 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

17 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

18 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

19 Logarithmic Representation As a percentage change measure, elasticity can be expressed in logarithmic form

20 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

21 Table 5.1 Estimates of price elasticities of demand

22 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

23 Figure 5.5 Perfectly inelastic demand curve

24 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

25 Figure 5.6 Perfectly elastic demand curve

26 Classification of Elasticity Between elasticity limits from -  to 0, elasticity may be classified in terms of its responsiveness   Q,p |∂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

27 Linear Demand Linear demand curve will exhibit all three elasticity classifications Consider linear demand function for commodity x 1  x 1 = 120 – 2p 1 Plotted in Figure 5.7  Elasticity of demand represented as  11 = (∂x 1 /∂p 1 )(p 1 /x 1 )  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 = (∂x 1 /∂p 1 )p 1 /x 1 = -2(45/30) = -3, elastic  At D   11 = (∂x 1 /∂p 1 )p 1 /x 1 = -2(15/90) = -1/3, inelastic  At point C (A) [E] elasticity of demand is unitary (-  ) [0]

28 Figure 5.7 Linear demand curve …

29 Linear Demand General functional form for a linear market demand function  Q 1 = a + bp 1, b<0 Q 1 denotes market demand for commodity 1 p 1 is associated price per unit Partial derivative is equal to constant b  Elasticity of demand is not constant along a linear demand curve  As p 1 /Q 1 increases, demand curve becomes more elastic  In the limit, as Q 1 approaches zero, elasticity of demand approaches negative infinity, perfectly elastic  p 1 = 0 results in perfectly inelastic elasticity of demand

30 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 (∂Q 1 /∂p 1 ) = constant  Implies that a doubling of prices will have same effect on Q 1 as a 5% increase

31 Figure 5.8 Linear demand curve

32 Proportionate Price Changes Assuming households respond to proportionate rather than absolute changes in prices May be more realistic to consider the demand function  Q 1 = ap b 1, a > 0, b > 0 or  ln Q 1 = ln a + b ln p 1 Elasticity of demand is   11 = (∂Q 1 /∂p 1 )(p 1 /Q 1 ) = bap 1 b -1 (p 1 /Q 1 ) = b or   11 = (∂ ln Q 1 /∂ ln p 1 ) = 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

33 Figure 5.9 Constant unitary elasticity of demand …

34 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 expenditures are defined as price times quantity (p 1 Q 1 ) 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

35 Price Elasticity and Total Revenue Relationship between total revenue and elasticity of demand may be established by differentiating total revenue (p 1 Q 1 ) with respect to p 1 Using product rule of differentiation, dividing both sides by Q 1 and multiplying left-hand-side by p 1 /p 1 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 p 1 is associated with a decrease in total revenue  If elasticity of demand is unitary,  Q,p = -1, then  TR,p = 0

36 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

37 Table 5.2 Response of total revenue to a price change

38 Figure 5.10 Elasticity of demand and total revenue …

39 Price Elasticity and the Price Consumption Curve Setting p 2 as numeraire price, p 2 = 1  Then p 1 x 1 + x 2 = I Solving for total revenue (expenditures) for x 1 yields  p 1 x 1 = I – x 2  On vertical axis in Figure 5.7, at p 1 = $45, Income I is initially allocated between total expenditures for x 2, x 2 , and total expenditure on x 1, I - x 2   Decreasing p 1 from $45 to $30 results in a decline in total expenditure for x 2 and an increase in total expenditure for x 1 Movement from B to C in indifference space results in a negatively sloping price consumption curve

40 Price Elasticity and the Price Consumption Curve Declining price consumption curve is associated with an increase in total expenditures on x 1  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 p 1 from $30 to $15 results in total expenditures for x 2 increasing and total expenditures for x 1 declining  Indicating inelastic demand If price consumption curve has a zero slope, unitary elasticity exists

41 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

42 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

43 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

44 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  η Q = (∂Q/∂I)(I/Q)  Measures percentage change in quantity to a percentage change in income Classified as follows

45 Table 5.3 Estimated income elasticities

46 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 x 1 and x 2  When Q 1 is a gross substitute for Q 2  12 = (∂Q 1 /∂p 2 )(p 2 /Q 1 ) = ∂ ln Q 1 /∂ ln p 2 > 0  When Q 1 is a gross complement for Q 2  12 = (∂Q 1 /∂p 2 )(p 2 /Q 1 ) = ∂ ln Q 1 /∂ ln p 2 < 0  Cross-price elasticity can be either positive or negative Depending on whether Q 1 is a gross substitute or gross complement for Q 2

47 Table 5.4 Estimated cross-price elasticities of demand …

48 Slutsky Equation in Elasticities Slutsky equation from Chapter 4 Substitution elasticity Indicates how demand for x 1 responds to proportional compensated price changes

49 Slutsky Equation in Elasticities Slutsky equation in elasticity form  Where α 1 = p 1 x 1 /I is proportion of income spent on x 1 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