The Concept of Elasticity Managerial Economics Demand Analysis The Concept of Elasticity and its Applications Ch. 3 Traditional economic theory “explains” economic phenomena and makes “what if” or conditional predictions Managerial economics “describes” the economic forces what shape the internal and external economic environments and It “prescribes rules for managerial decision-making that further the goal of the firm What’s the goal of the firm?

The concept of elasticity The sensitivity (degree of responsiveness) of sales (demand) to a change in one of the demand-affecting variables, say, price

The Importance of Elasticity The firm needs to know the effect of a change in any of the determinants of demand (price, advertising, income, competitors’ prices, etc.) that affects the demand for a product in order to: Meet sales target Gain market share Maximize profit These are the right answer to the wrong question. If the question was: What are the means effective in achieving the objective of the firm, then these are the correct answers. But the question is not about the means but rather about the fundamental objective of the firm. Do not make Type III error – asking the wrong question. Type I error – wrongly convict an innocent person; Type II error – failure to convict a guilty person

The Price Elasticity of Demand … measures the responsiveness of the quantity demanded to a change in the price of the product, holding constant the values of all other variables in the demand function. In mathematical term, %in Q Ep = --------------- , ceteris paribus %  in P

The Arc Price Elasticity of Demand How can the percentage changes in Q and P be calculated in order to derive the price elasticity of demand? Q --------------- (Q1 + Q2)/2 Ep = ------------------ P -------------- (P1 + P2)/2

Drive the Demand Curve of the following information: (Q = 40,000,000 - 2,500P) Price 16,000 P2=12,500 B P1=12,000 A Q 0 8,750,000 40,000,000 10,000,000

How sensitive are consumers to a change in the avg How sensitive are consumers to a change in the avg. price of automobiles? We calculate the arc price elasticity of demand between A and B as: 10,000,000-8,750,000 ------------------------------ [10,000,000+8,750,000]/2 Ep = -------------------------------- = - 3.267 12,000 - 12,500 ----------------------- [12,000 + 12,500]/2

Interpretation Between points A and B (or between the price range from $12,000 to $12,500), a one-percent increase in the average price of cars will bring about, on average, a reduction of sales by 3.267%, ceteris paribus. Because the price elasticity of demand is calculated between two points on a given demand curve, it is called the arc price elasticity of demand.

Classification of The Price Elasticity of Demand For decision-making purposes, three specific ranges of price elasticity of demand have been identified. Using the absolute value of the price elasticity of demand, the three ranges are: 1) |Ep| > 1, the demand is said to be elastic. 2) |Ep| < 1, the demand is said to be inelastic. 3) |Ep| = 1, we have unitary elasticity.

Caveat Elasticity measure depends on the price at which it is measured. It is not generally a constant (because the demand curve is not likely to be a straight line).

The Point Price Elasticity of Demand It measures the price elasticity of demand at a given price or a particular point on the demand curve. Q P ep = (-----)(----) P Q

Calculation of the point elasticity using the demand for automobile equation Q = -2,500P + 1,000I + 0.05Pop - 1,000,000i + 0.05A Supposing that: P = $12,000, I1 = $23,500, Pop = 230,000,000, i = 10, and A = $300,000,000 Other things being equal, if P1 = $12,000, Q1 = 10,000,000. The point price elasticity is: Q P ep = (-----) (---) P Q = (-2,500)(12,000/10,000,000) = - 3

Point price elasticity (cont.) What's the point elasticity of demand at P2 = $12,500? At this price, Q = 8,750,000. Hence, Q P ep = (-----) (---) P Q = (-2,500)(12,500/8,750,000) = - 3.571

Two versions of the elasticity of demand – Point vs. Arc Price 16,000 ep= -3.571 Ep= -3.267 12,500 ep= -3.0 12,000 Q 8,750,000 10,000,000

From Concept to Applications We began with a definition of the elasticity of demand based on, %in Q Ep = --------------- %  in P If we know the price elasticity of demand (Ep), the formula will let us answer a number of "what if" questions.

Examples (1) How great a price reduction is necessary to increase sales by 10%? (2) What will be the impact on sales of a 5% price increase? (3) Given marginal cost and price elasticity information, what is the profit-maximizing price?

The price increase needed to reduce gasoline consumption by 1% Supposing that the elasticity of demand for gasoline is -0.5, how much prices must go up to reduce gasoline use by 1%? - 0.01 - 0.5 = ---------- , %P %P = (-0.01/-0.5) = + 0.02 or 2%

Price elasticity of demand and Total Revenue - Still Another Application If |Ep | > 1, i.e., elastic demand, P, TR decreases If |Ep | < 1, i.e., inelastic demand, P, TR increases If |Ep | = 1, i.e., unitary elasticity, P, TR remains unchanged.

Lessons: (1) The first lessons in business: Never lower your price in the inelastic range of the demand curve. Such a price decrease would reduce total revenue and might at the same time increase average production cost. (2) When the demand is inelastic, raise the price to increase revenue and, possibly, profit. (3) When demand is elastic, price increases should be avoided.

Lessons But should we always cut price when the demand is elastic? Even over the range where demand is elastic, a firm will not necessarily find it profitable to cut prices; the profitability of such an action depends on whether the marginal revenues generated by the price reduction exceed the marginal cost of the added production.

Another Example: Optimal Pricing Step 1 – Using the relationship between MR and Ep established in McGuigan/Moyer/Harris, Ch. 3, p. 90 Given, TR = PQ, للفهم فقط TR  (PQ) MR = ------- = --------- Q  Q Q P = P(-----) + Q (-----) Q Q Q P 1 = P (1 + ----- -----) = P ( 1 + ----) P Q ep

Optimal Pricing Optimal Price is when MC = MR i.e., MC = P (1 + 1/ep) That is, the profit-maximizing price is determined by MC and ep

Determinants of Price Elasticity of Demand Starter Questions : (1) If the demand for gasoline is inelastic, why is it that sales at a particular gas station will drop off when it raises prices? (2) What explains the fact that the demand for some products is more sensitive to price than the demand for other products?

The determinants are: The availability of substitute goods The extent to which a good is considered to be a necessity The proportion of income spent on the product The cost of searching for lower prices The degree to which price signals quality Time

Differentiation Strategy and Elasticity If your strategy is to differentiate your product (a costly activity), you need low elasticity (inelastic demand) to enable the higher price. If you are attempting a low-cost/price leadership strategy, high elasticity is the key. (You need to convince customers that your products are good substitutes for the leading brands.)

Other Elasticities The income elasticity of demand provides a measure of the responsiveness of demand to changes in income, holding constant the effect of all other variables. The "arc" income elasticity is: Q ------------ Q1 + Q2 EI = --------------- I ---------- I1 + I2

Arc Income Elasticity Illustrated The Demand for Automobiles: Q = -2,500P + 1,000I + 0.05Pop - 1,000,000i + 0.05A Supposing that: P = $12,000, I1 = $23,500, Pop = 230,000,000, i = 10, and A = $300,000,000 Then, Q1 = 10,000,000. But if income rises to I2 = $24,000, sales forecast is raised by 500,000 to Q2 =10,500,000. This implies an income elasticity of: 500,000 -------------------------------- 10,000,000+10,500,000 EI = ----------------------------------- = 2.317 500 ------------------------------- 23,500+24,000

Point income elasticity: Q I eI = ----- ----- I Q At I1 = $23,500, 23,500 eI = (1,000) ( ----------------) = 2.35 10,000,000 and at I2 = $24,000, 24,000 eI = (1,000) ( ---------------) = 2.29 10,500,000

Examples of Income Elasticities Description Income Elasticity Examples ----------------------------------------------------------------------------------- Inferior goods EI < 0 Basic foodstuffs, (Countercyclical) generic products, bus rides, etc. Noncyclical normal 0 < EI < 1 Cigarettes, liquor, goods soaps, movies, health care etc. Cyclical normal EI > 1 New cars, houses, goods travel,capital equipment, etc. ------------------------------------------------------------------------------------------

Cross-Price Elasticity of Demand A change in the price of Coca Cola influences the sales of Pepsi. We use the concept of cross-price elasticity of demand to measure the relationship between the price of Coca Cola and the volume of sales of Pepsi.

The Arc Cross Elasticity of Demand Supposing that product x and y are related, and that, Qx = a0 + a1Px + a2I + a3Py The arc cross-price elasticity is: Qx -------------- Qx1 + Qx2 EPy = ------------------- Py ------------- Py1 + Py2

The point cross-price elasticity Qx Py e py = ( -----)(----) Py Qx

Some Uses of Cross-Price Elasticity According to an FTC Report by Michael Ward, AT&T’s cross price elasticity of demand for long distance services is 9.06 If MCI and other competitors reduced their prices by 4 percent, what would happen to the demand for AT&T services?

Answer AT&T’s demand would fall by 36.24 percent!

Antitrust and Cross Elasticities of Demand Cross elasticity of demand is used in industrial organization to measure the interrelations among industries. The case of DuPont and its Cellophane.