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ELASTICITY

ELASTICITY. Elasticity is the concept economists use to describe the steepness or flatness of curves or functions. In general, elasticity measures the responsiveness of one variable to changes in another variable. PRICE ELASTICITY OF DEMAND.

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ELASTICITY

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  1. ELASTICITY • Elasticity is the concept economists use to describe the steepness or flatness of curves or functions. • In general, elasticity measures the responsiveness of one variable to changes in another variable. Elasticity

  2. PRICE ELASTICITY OF DEMAND • Measures the responsiveness of quantity demanded to changes in a good’s own price. • The price elasticity of demand is the percent change in quantity demanded divided by the percent change in price that caused the change in quantity demanded. Elasticity

  3. FACTS ABOUT ELASTICITY • It’s always a ratio of percentage changes. • That means it is a pure number -- there are no units of measurement on elasticity. • Price elasticity of demand is computed along a demand curve. Elasticity is not the same as slope. Elasticity

  4. LOTS OF ELASTICITIES! • THERE ARE LOTS OF WAYS TO COMPUTE ELASTICITIES. SO BEWARE! THE DEVIL IS IN THE DETAILS. • MOST OF THE AMBIGUITY IS DUE TO THE MANY WAYS YOU CAN COMPUTE A PERCENTAGE CHANGE. BE ALERT HERE. IT’S NOT DIFFICULT, BUT CARE IS NEEDED. Elasticity

  5. pE = $2.50 What’s the percent increase in price here because of the shift in supply? S' price S pE = $2 D Q QE CIGARETTE MARKET Elasticity

  6. IS IT: • A) [.5/2.00] times 100? • B) [.5/2.50] times 100? • C) [.5/2.25] times 100? • D) Something else? Elasticity

  7. From time to time economists have used ALL of these measures of percentage change -- • including the “Something else”! • Notice that the numerical values of the percentage change in price is different for each case: Go to hidden slide Elasticity

  8. Economists usually use the “midpoint” formula (option C), above) to compute elasticity in cases like this in order to eliminate the ambiguity that arises if we don’t know whether price increased or decreased. Elasticity

  9. Using the Midpoint Formula Elasticity = % change in p = times 100. % change in p = For the prices $2 and $2.50, the % change in p is approx. 22.22 percent. Elasticity

  10. What’s the percent change in Q due to the shift in supply? S' price S pE’ = $2.50 pE = $2 D Q (millions) QE’ = 7 QE = 10 CIGARETTE MARKET Elasticity

  11. Use the midpoint formula again. • Elasticity = • % change in Q = • % change in Q = • For the quantities of 10 and 7, the % change in Q is approx. -35.3 percent. (3/8.5 times 100) Elasticity

  12. NOW COMPUTE ELASTICITY • % change in p = 22.22 percent • % change in Q = -35.3 percent E = -35.3 / 22.22 = -1.6 (approx.) Elasticity

  13. But you can do the other options as well: • A) If you use the low price, and its corresponding quantity, as the base values, then elasticity = 1.2 • B) If you use the high price, and its corresponding quantity, as the base values, then elasticity = 2.1 (approx.) • C) And the midpoint formula gave 1.6 (approx.) • SAME PROBLEM...DIFFERENT ANSWERS!!! Elasticity

  14. Compute elasticity between prices of $9 and $8. MORE ELASTICITY COMPUTATIONS QUANTITY PRICE P 0 10 14 1 9 12 2 8 10 3 7 8 4 6 6 5 5 4 6 4 2 7 3 Q 0 8 2 0 2 4 6 8 10 12 14 9 1 10 0 Elasticity

  15. USE THE MIDPOINT FORMULA. The % change in Q = The % change in P = Therefore elasticity = Go to hidden slide Elasticity

  16. Compute elasticity between prices of $3 and $2. Now we try different prices QUANTITY PRICE 0 10 P 1 9 14 2 8 12 3 7 10 4 6 8 6 5 5 4 6 4 2 7 3 Q 0 8 2 0 2 4 6 8 10 12 14 9 1 10 0 Elasticity

  17. The % change in Q = The % change in P = Therefore elasticity = Go to hidden slide Elasticity

  18. E = -5.67 E = -.33 ELASTICITY IS NOT SLOPE! QUANTITY PRICE Note that elasticity is different at the two points even though the slope is the same. (Slope = -1) P 0 10 14 1 9 12 2 8 10 3 7 8 4 6 6 5 5 4 6 4 2 7 3 Q 0 8 2 0 2 4 6 8 10 12 14 9 1 10 0 Elasticity

  19. TERMS TO LEARN • Demand is ELASTIC when the numerical value of elasticity is greater than 1. • Demand is INELASTIC when the numerical value of elasticity is less than 1. • Demand is UNIT ELASTIC when the numerical value of elasticity equals 1. • NOTE: Numerical value here means “absolute value.” Elasticity

  20. Demand is elastic here. Demand is inelastic here. LIKE THIS! P QUANTITY PRICE 14 0 10 12 1 9 10 2 8 8 3 7 6 4 6 4 5 5 2 6 4 Q 0 7 3 0 2 4 6 8 10 12 14 8 2 9 1 10 0 Elasticity

  21. A FINAL ELASTICITY MEASURE • POINT ELASTICITY OF DEMAND • If you know or can see the demand curve for a good (you don’t know just two points), you can compute “point elasticity of demand” at a single point on the demand curve. • Here’s the idea: Elasticity

  22. The % change in price can be written as: • P)/Pbase times 100 • The % change in quantity can be written as: • Q)/Qbase times 100 • So elasticity is: (Q)/ (P)) ( Pbase / Qbase) Elasticity

  23. So elasticity is Q)/ (P) multiplied by the ratio of base price to base quantity. • Point elasticity uses this formula to compute the elasticity of demand AT A POINT on a demand curve. Elasticity

  24. EXAMPLE P Elasticity at a price of $3 is .90. 6 $3 D Q 10 18 Elasticity

  25. There is an important relationship between what happens to consumers’ spending on a good and elasticity when there is a change in price. • Spending on a good = P Q. • Because demand curves are negatively sloped, a reduction in P causes Q to rise and the net effect on PQ is uncertain, and depends on the elasticity of demand. Elasticity

  26. Demand is elastic here. At P = $9, spending is $9 (= 1 times $9). At P = $8, spending is $16 ( = 2 times $8). When price fell from $9 to $8, spending rose. Q must have increased by a larger percent than P decreased. So... QUANTITY PRICE 0 10 P 1 9 14 2 8 12 3 7 10 4 6 8 5 5 6 6 4 4 7 3 2 8 2 0 Q 9 1 0 2 4 6 8 10 12 14 10 0 Elasticity

  27. Demand is inelastic here. At P = $3, spending is $21 (= 7 times $3). At P = $2, spending is $16 ( = 8 times $2). When price fell from $3 to $2, spending fell. Q must have increased by a smaller percent than P decreased. So... QUANTITY PRICE P 0 10 14 1 9 12 2 8 10 3 7 8 4 6 6 5 5 4 6 4 2 7 3 0 8 2 Q 0 2 4 6 8 10 12 14 9 1 10 0 Elasticity

  28. There is an easy way to tell whether demand is elastic or inelastic between any two prices. • If, when price falls, total spending increases, demand is elastic. • If, when price falls, total spending decreases, demand is inelastic. Elasticity

  29. But total spending is easy to see using a demand curve graph: P QUANTITY PRICE 14 0 10 12 1 9 The shaded area is P times Q or total spending when P = $9. 10 2 8 8 3 7 6 4 6 4 5 5 6 4 2 7 3 0 Q 0 2 4 6 8 10 12 14 8 2 9 1 10 0 Elasticity

  30. P 14 PRICE QUANTITY 12 The shaded area is P times Q or total spending when P = $8. 0 10 10 1 9 8 2 8 6 3 7 4 4 6 2 5 5 0 Q 6 4 0 2 4 6 8 10 12 14 7 3 8 2 9 1 10 0 Elasticity

  31. = loss in TR due to fall in P = gain in TR due to rise in Q P 14 QUANTITY PRICE 12 0 10 10 1 9 Total spending is higher at the price of $8 than it was at the price of $9. 8 2 8 6 3 7 4 4 6 2 5 5 6 4 0 Q 0 2 4 6 8 10 12 14 7 3 8 2 9 1 10 0 Elasticity

  32. P 14 QUANTITY PRICE 12 0 10 The shaded area is total spending (total revenue of sellers) when P = $3. 1 9 10 2 8 8 3 7 6 4 6 4 5 5 2 6 4 0 7 3 Q 0 2 4 6 8 10 12 14 8 2 9 1 10 0 Elasticity

  33. P QUANTITY PRICE 14 0 10 12 1 9 Total revenue of sellers (total spending by buyers) falls when price falls from $3 to $2. 10 2 8 8 3 7 6 4 6 4 5 5 2 6 4 7 3 0 Q 0 2 4 6 8 10 12 14 8 2 9 1 10 0 Elasticity

  34. relatively more elastic at p* relatively more inelastic at p* Here’s a convenient way to think of the relative elasticity of demand curves. p p* Q Q* Elasticity

  35. Examples of elasticity • Doctors through the AMA restrict the supply of physicians. How does this affect the incomes of doctors as a group? • A labor union negotiates a higher wage. How does this affect the incomes of affected workers as a group? • MSU decides to raise the price of football tickets. How is income from the sale of tickets affected? • Airlines propose to raise fares by 10%. Will the boost increase revenues? Elasticity

  36. MORE ... • MSU is considering raising tuition by 7%. Will the increase in tuition raise revenues of MSU? • CATA recently raised bus fares in the Lansing area. Will this increase CATA’s total receipts? Elasticity

  37. The answers to all of these questions depend on the elasticity of demand for the good in question. Be sure you understand how and why! Elasticity

  38. DETERMINANTS OF DEMAND ELASTICITY • The more substitutes there are available for a good, the more elastic the demand for it will tend to be. [Related to the idea of necessities and luxuries. Necessities tend to have few substitutes.] • The longer the time period involved, the more elastic the demand will tend to be. • The higher the fraction of income spent on the good, the more elastic the demand will tend to be. Elasticity

  39. OTHER ELASTICITY MEASURES • In principle, you can compute the elasticity between any two variables. • Income elasticity of demand • Cross price elasticity of demand • Elasticity of supply Elasticity

  40. Each of these concepts has the expected definition. For example, income elasticity of demand is the percent change in quantity demand divided by a percent change income: • EINCOME = • Income elasticity of demand will be positive for normal goods, negative for inferior ones. Elasticity

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