Elasticity And Demand MANAGERIAL ECONOMICS Foundations of Business Analysis and Strategy 12th Christopher R. Thomas & S. Charles Maurice https://meet.google.com/qof-vsat-wpu EDITION THE PRICE ELASTICITY OF DEMAND • its purpose is to measure the consumer responsiveness to a price change; • The percentage change in quantity demanded, divided by the percentage change in price; • E is always a negative number because P and Q are inversely related. • calculated for movements along a given demand curve (or function) as price changes and all other factors affecting quantity demanded are held constant. • measure of how sensitive quantity demanded is to changes in price. THE PRICE ELASTICITY OF DEMAND • Example: THE PRICE ELASTICITY OF DEMAND Predicting the Percentage Change in Quantity Demanded • Example #1: Predicting the Percentage Change in Price • Example #2: PRICE ELASTICITY AND TOTAL REVENUE • the price of the commodity times quantity demanded • The total amount paid to producers for a good or service Price Elasticity and Changes in Total Revenue Price Effect • effect on total revenue of changing price, holding output constant. • the quantity sold does not remain constant; it moves in the opposite direction of price • the increase in quantity, by itself, would increase total revenue if the price of the product remained constant. PRICE ELASTICITY AND TOTAL REVENUE • the price of the commodity times quantity demanded • The total amount paid to producers for a good or service Price Elasticity and Changes in Total Revenue Quantity Effect • effect on total revenue of changing the quantity sold, for a given price level PRICE ELASTICITY AND TOTAL REVENUE • Example #1: a. Current Price: $18 Per DVD b. Weekly Sales: 600 DVDs a. Current Price: $16 Per DVD b. Weekly Sales: 800 DVDs FACTORS AFFECTING PRICE ELASTICITY OF DEMAND Availability of Substitutes • The better the substitutes for a given good or service, the more elastic the demand for that good or service. • The definition of the market for a good greatly affects the number of substitutes and thus the good’s price elasticity of demand. Percentage of Consumer’s Budget • All other things equal, we would expect the price elasticity to be directly related to the percentage of consumers’ budgets spent on the good. Time Period of Adjustment • The length of the time period used in measuring the price elasticity affects the magnitude of price elasticity. CALCULATING PRICE ELASTICITY OF DEMAND Computing Elasticity a. it is convenient to avoid computing percentage changes by using a simpler formula Thus, • price elasticity can be calculated by multiplying the slope of demand times the ratio of price divided by quantity b. can be measured either (1) over an interval (or arc) along demand or (2) at a specific point on the demand curve CALCULATING PRICE ELASTICITY OF DEMAND Computation of Elasticity over an Interval or Arc a. it is when elasticity is calculated over an interval of a demand curve (either a linear or a curvilinear demand) b. Computation is slope of demand multiplied by the ratio of the average values of P divided by Q CALCULATING PRICE ELASTICITY OF DEMAND Computation of Elasticity at a Point a. it is a measurement of demand elasticity calculated at a point on a demand curve rather than over an interval. b. Computation is accomplished by: • multiplying the slope of demand (computed at the point of Point Elasticity When Demand Is Linear measure) • by the ratio P/Q (computed using the values of P and Q at the point of measure) CALCULATING PRICE ELASTICITY OF DEMAND Point Elasticity When Demand Is Linear where P and Q are the values of price and quantity at the point of measure. CALCULATING PRICE ELASTICITY OF DEMAND Point Elasticity When Demand Is Curvilinear • This formula can be used for computing point elasticity simply by substituting the slope of the curved demand at the point of measure for the value of slope of demand • This can be accomplished by measuring the slope of the tangent line at the point of measure. • As it turns out, the alternative formula E = P/(PA) for computing point elasticity on linear demands can also be used for computing point elasticities on curvilinear demands. To do so, the price-intercept of the tangent line T serves as the value of A in the formula. CALCULATING PRICE ELASTICITY OF DEMAND Elasticity (Generally) Varies along a Demand Curve Demand Is Linear a. Even though the absolute rate at which quantity demanded changes as price changes (∆Q/∆P) remains constant, the proportional rate of change in Q as P changes (%∆Q/%∆P) varies along a linear demand curve. b. Moving along a linear demand does not cause the term (∆Q/∆P) to change, but elasticity does vary because the ratio P/Q changes. Moving down demand, by reducing price and selling more output, causes the term P/Q to decrease which reduces the absolute value of E. c. moving up a linear demand, by increasing price and selling less output, causes P/Q and |E| to increase CALCULATING PRICE ELASTICITY OF DEMAND Elasticity (Generally) Varies along a Demand Curve Demand Is Curved a. both the slope and the ratio P/Q vary continuously along demand b. elasticity generally varies along curvilinear demands, but there is no general rule about the relation between price and elasticity as there is for linear demand c. Exception: • • • When demand takes the form Q = aPb, the elasticity is constant along the demand curve and equal to b. no calculation of elasticity is required, and the price elasticity is simply the value of the exponent on price, b The absolute value of b can be greater than, less than, or equal to 1, so that this form of demand can be elastic, inelastic, or unitary elastic at all points on the demand curve. CALCULATING PRICE ELASTICITY OF DEMAND Elasticity (Generally) Varies along a Demand Curve Demand Is Curved a. Example: • Q = aPb, with the values of a and b equal to 100,000 and -1.5, respectively. Notice that price elasticity equals -1.5 at both points U and V where prices are $20 and $40, respectively. Clearly, you never need to compute the price elasticity of demand for this kind of demand curve because E is the value of the exponent on price (b). MARGINAL REVENUE, DEMAND, AND PRICE ELASTICITY The addition to total revenue Marginal Revenue attributable to selling one additional unit of output; the slope of total (MR) revenue. Because this measures the rate of change in total revenue as quantity changes, MR is the slope of the TR curve. related to the way changes in price and output affect total revenue along a demand curve MARGINAL REVENUE, DEMAND, AND PRICE ELASTICITY Demand Schedule For A Product Demand Schedule Price X Quantity MARGINAL REVENUE, DEMAND, AND PRICE ELASTICITY Inframarginal Units those units that could have been sold at a higher price had the firm not lowered price to sell the marginal unit. Example: 2nd unit of output sells for $3.50 marginal revenue ≠ $3.50 price on the first unit = $4 “Because price must fall in order to sell additional units, marginal revenue must be less than price at every other level of sales (output)” MARGINAL REVENUE, DEMAND, AND PRICE ELASTICITY MARGINAL REVENUE, DEMAND, AND PRICE ELASTICITY When demand is linear, marginal revenue is linear and lies halfway between demand and the vertical (price) axis This implies that marginal revenue must be twice as steep as demand, and demand and marginal revenue share the same intercept on the vertical axis Linear demand equation: Q = a’ + bP a’ = a + cM + dPR MARGINAL REVENUE, DEMAND, AND PRICE ELASTICITY When demand is linear, Inverse demand equation: • where A = -a’/b and B = 1/b. Since a’ is always positive and b is always negative (by the law of demand), it follows that A is always positive and B is always negative: A > 0 and B < 0. MARGINAL REVENUE, DEMAND, AND PRICE ELASTICITY Marginal Revenue and Price Elasticity MARGINAL REVENUE, DEMAND, AND PRICE ELASTICITY Marginal Revenue and Price Elasticity the relation between marginal revenue, price, and price elasticity, for linear or curvilinear demands • • E = price elasticity of demand P = product price OTHER DEMAND ELASTICITIE Income Elasticity • measure of the responsiveness of quantity demanded to changes in income, holding all other variables in the general demand function constant. Cross-price Elasticity • measure of the responsiveness of quantity demanded to changes in the price of a related good, when all the other variables in the general demand function remain constant. OTHER DEMAND ELASTICITIE Income Elasticity • measure of the responsiveness of quantity demanded to changes in income, holding all other variables in the general demand function constant. • the percentage change in quantity demanded divided by the percentage change in income, holding all other variables in the general demand function constant, including the good’s own price EM depends on the sign of ∆Q/∆ M; which may be positive (if the good is normal) or negative (if the good is inferior) • can be measured either over an interval or at a point on the general demand curve. OTHER DEMAND ELASTICITIE Income Elasticity • can be measured either over an interval or at a point on the general demand curve. interval measure of income elasticity: point measure of income elasticity: Q = a + bP + cM + dPR OTHER DEMAND ELASTICITIE Income Elasticity • Example: expects average household income in Fulton County to increase = $45,000 to $50,000 (Ave. = 47,500.00) constant average price = $30,000 per car Sales = 800 to 1,400 units per month. The income elasticity of demand in Panel A, which will be shown in the next slide, is: OTHER DEMAND ELASTICITIE Income Elasticity OTHER DEMAND ELASTICITIE Cross-price Elasticity • measure of the responsiveness of quantity demanded to changes in the price of a related good, when all the other variables in the general demand function remain constant. If the rise in the price of one good causes the quantity purchased of another good to fall, the goods are complements purchased of another good to fall, the goods are complements If there is no change in the quantity purchased of the other good, the two goods are independent SUMMARY • PRICE ELASTICITY OF DEMAND, E, measures responsiveness or sensitivity of consumers to changes in the price of a good by taking the ratio of the percentage change in quantity demanded to the percentage change in the price of the good: E = %∆Qd/% ∆ P. The larger the absolute value of E, the more sensitive buyers will be to a change in price. Demand is elastic when |E|>1, demand is inelastic when |E|<1, and demand is unitary elastic when |E| = 1. If price elasticity is known, the percentage change in quantity demanded can be predicted for a given percentage change in price: %∆Qd = %=∆P X E. And the percentage change in price required for a given change in quantity demanded can be predicted when E is known: %∆P = %∆Qd ÷ E. SUMMARY • The effect of changing price on total revenue is determined by the price elasticity of demand. When demand is elastic (inelastic), the quantity (price) effect dominates. TOTAL REVENUE always moves in the same direction as the variable, price or quantity, having the dominant effect. When demand is unitary elastic, neither effect dominates, and changes in price leave total revenue unchanged. SUMMARY • Several FACTORS affect the elasticity of demand for a good: (1) the better and more numerous the substitutes for a good, the more elastic is the demand for the good; (2) the greater the percentage of the consumers’ budgets spent on the good, the more elastic is demand; and (3) the longer the time period consumers have to adjust to price changes, the more responsive they will be and the more elastic is demand. SUMMARY • When calculating E over an INTERVAL OF DEMAND, use the interval or arc elasticity formula: multiply slope of demand, ∆Q/∆P, times the ratio Average P/Average Q. When calculating E at a POINT ON DEMAND, multiply the slope of demand, computed at the point of measure, times the ratio P/Q, computed using the values of P and Q at the point of measure. When demand is LINEAR, Q= a’ + bP, the point elasticity can be computed using either of two equivalent formulas: E=b(P/Q) or E=P/(P-A), where P and Q are the values of price and quantity demanded at the point of measure along demand, and A (=-a’/b) is the price-intercept of demand. For CURVILINEAR DEMAND FUNCTIONS, the point elasticity is computed using the formula E=P/(P-A) and A is the price-intercept of the tangent line extended from the point on demand to cross the price axis. In general, E varies along a demand curve, and for linear demand curves, price and |E| vary directly: the higher (lower) the price, the more (less) elastic is demand. SUMMARY • MARGINAL REVENUE, MR, is the change in total revenue per unit change in output. Marginal revenue is 0 when total revenue is maximized. When INVERSE DEMAND IS LINEAR, P=A + BQ, MR is also linear, intersects the vertical (price) axis at the same point demand does, and is twice as steep as the inverse demand function: MR=A+2BQ. When MR is positive (negative), total revenue increases (decreases) as quantity increases, and demand is elastic (inelastic). When MR is 0, the price elasticity of demand is unitary and total revenue is maximized. For ANY DEMAND CURVE, when demand is elastic (inelastic), MR is positive (negative). When demand is unitary elastic, MR is 0. For all demand curves, MR=P[1 + (1/E)]. SUMMARY • INCOME ELASTICITY, EM, measures the responsiveness of quantity demanded to changes in income, holding the price of the good and all other demand determinants constant: EM=%∆Qd/%∆M. Income elasticity is positive (negative) if the good is normal (inferior). CROSS-PRICE ELASTICITY, EXY, measures the responsiveness of quantity demanded of good X to changes in the price of related good Y, holding the price of good X and all other demand determinants for good X constant: EXY=%∆QX/%∆PY. Cross-price elasticity is positive (negative) when the two goods are substitutes (complements).
