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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 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 • Sum of individual household demands • Assuming individual household demands are independent of each other • Will explore network externalities • Independence assumption does not hold
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
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
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 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 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 • 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 • 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 • 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 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
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
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 • 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 • As a percentage change measure, elasticity can be expressed in logarithmic form
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 • 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 • 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 • 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 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 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 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 • 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 • 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 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 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 • 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 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 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 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 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 • 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 • 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 from Chapter 4 • Substitution elasticity • Indicates how demand for x1 responds to proportional compensated price changes
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
