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ELASTICITY

ELASTICITY. Wk 7. Responsiveness of changes in quantity demanded to a change in price of the product. It is measured by the formula: percentage change in quantity demanded/percentage change in price.

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ELASTICITY

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  1. ELASTICITY Wk 7

  2. Responsiveness of changes in quantity demanded to a change in price of the product. • It is measured by the formula: percentage change in quantity demanded/percentage change in price. • For example, if the price of butter is reduced by 10% and the demand increases by 20%, the price elasticity of demand is 2.

  3. Goods with a price elasticity of less than 1 are said to be inelastic. • Goods with a price elasticity greater than 1 are said to be elastic. • A firm wishing to increase revenue (price x quantity) should increase the price of its products if demand is inelastic. • This is because the percentage fall in quantity demanded will be less than the percentage increase in price. • Conversely, a firm with an elastic demand for its products should reduce price to increase revenue.

  4. The Price Elasticity of Demand (commonly known as just price elasticity) measures the rate of response of quantity demanded due to a price change. • The formula for the Price Elasticity of Demand (PEoD) is: PEoD = (% Change in Quantity Demanded)/(% Change in Price)

  5. Calculating the Price Elasticity of Demand • You may be asked the question "Given the following data, calculate the price elasticity of demand when the price changes from $9.00 to $10.00”. • First we'll need to find the data we need. • We know that the original price is $9 and the new price is $10, so we have Price(OLD)=$9 and Price(NEW)=$10. • From the chart we see that the quantity demanded when the price is $9 is 150 and when the price is $10 is 110.

  6. Since we're going from $9 to $10, we have QDemand(OLD)=150 and QDemand(NEW)=110, where "QDemand" is short for "Quantity Demanded". So we have: • Price(OLD)=9Price(NEW)=10QDemand(OLD)=150QDemand(NEW)=110

  7. To calculate the price elasticity, we need to know what the percentage change in quantity demand is and what the percentage change in price is. • It's best to calculate these one at a time. • Calculating the Percentage Change in Quantity Demanded • The formula used to calculate the percentage change in quantity demanded is: [QDemand(NEW) - QDemand(OLD)] / QDemand(OLD)

  8. By filling in the values we wrote down, we get: • [110 - 150] / 150 = (-40/150) = -0.2667 • We note that % Change in Quantity Demanded = -0.2667 (We leave this in decimal terms. • In percentage terms this would be -26.67%). • Now we need to calculate the percentage change in price.

  9. Calculating the Percentage Change in Price • Similar to before, the formula used to calculate the percentage change in price is: [Price(NEW) - Price(OLD)] / Price(OLD) • By filling in the values we wrote down, we get: • [10 - 9] / 9 = (1/9) = 0.1111 • We have both the percentage change in quantity demand and the percentage change in price, so we can calculate the price elasticity of demand.

  10. Final Step of Calculating the Price Elasticity of Demand • We go back to our formula of: PEoD = (% Change in Quantity Demanded)/(% Change in Price) • We can now fill in the two percentages in this equation using the figures we calculated earlier. • PEoD = (-0.2667)/(0.1111) = -2.4005

  11. When we analyze price elasticities we're concerned with their absolute value, so we ignore the negative value. • We conclude that the price elasticity of demand when the price increases from $9 to $10 is 2.4005.

  12. How Do We Interpret the Price Elasticity of Demand? • A good economist is not just interested in calculating numbers. • The number is a means to an end; in the case of price elasticity of demand it is used to see how sensitive the demand for a good is to a price change. • The higher the price elasticity, the more sensitive consumers are to price changes.

  13. A very high price elasticity suggests that when the price of a good goes up, consumers will buy a great deal less of it and when the price of that good goes down, consumers will buy a great deal more. • A very low price elasticity implies just the opposite, that changes in price have little influence on demand.

  14. Often an assignment or a test will ask you a follow up question such as "Is the good price elastic or inelastic between $9 and $10". • To answer that question, you use the following rule of thumb: • If PEoD > 1 then Demand is Price Elastic (Demand is sensitive to price changes) • If PEoD = 1 then Demand is Unit Elastic • If PEoD < 1 then Demand is Price Inelastic (Demand is not sensitive to price changes)

  15. Recall that we always ignore the negative sign when analyzing price elasticity, so PEoD is always positive. • In the case of our good, we calculated the price elasticity of demand to be 2.4005, so our good is price elastic and thus demand is very sensitive to price changes.

  16. Price elasticity of supply:Data • Price Quantity Demanded Quantity Supplied $7 200 50 $8 180 90 $9 150 150 $10 110 210 $11 60 250

  17. PEoS = (% Change in Quantity Supplied)/(% Change in Price The Price Elasticity of Supply measures the rate of response of quantity demand due to a price change. If you've already read The Price Elasticity of Demand and understand it, you may want to just skim this section, as the calculations are similar.

  18. PEoS = (% Change in Quantity Supplied)/(% Change in Price. • Calculating the Price Elasticity of Supply • You may be asked "Given the following data, calculate the price elasticity of supply when the price changes from $9.00 to $10.00" Using the chart on the bottom of the page, I'll walk you through answering this question.

  19. First we need to find the data we need. We know that the original price is $9 and the new price is $10, so we have Price(OLD)=$9 and Price(NEW)=$10. • From the chart we see that the quantity supplied (make sure to look at the supply data, not the demand data) when the price is $9 is 150 and when the price is $10 is 110. • Since we're going from $9 to $10, we have QSupply(OLD)=150 and QSupply(NEW)=210, where "QSupply" is short for "Quantity Supplied".

  20. Price(OLD)=9Price(NEW)=10QSupply(OLD)=150QSupply(NEW)=210 • To calculate the price elasticity, we need to know what the percentage change in quantity supply is and what the percentage change in price is. • It's best to calculate these one at a time.

  21. Calculating the Percentage Change in Quantity Supply • The formula used to calculate the percentage change in quantity supplied is: [QSupply(NEW) - QSupply(OLD)] / QSupply(OLD) • By filling in the values we wrote down, we get: • [210 - 150] / 150 = (60/150) = 0.4 • So we note that % Change in Quantity Supplied = 0.4 (This is in decimal terms. • In percentage terms it would be 40%). • Now we need to calculate the percentage change in price.

  22. Calculating the Percentage Change in Price • Similar to before, the formula used to calculate the percentage change in price is: [Price(NEW) - Price(OLD)] / Price(OLD) • By filling in the values we wrote down, we get: • [10 - 9] / 9 = (1/9) = 0.1111 • We have both the percentage change in quantity supplied and the percentage change in price, so we can calculate the price elasticity of supply. • Final Step of Calculating the Price Elasticity of Supply

  23. We go back to our formula of: PEoS = (% Change in Quantity Supplied)/(% Change in Price) • We now fill in the two percentages in this equation using the figures we calculated. • PEoD = (0.4)/(0.1111) = 3.6 • When we analyze priceelasticities we're concerned with the absolute value, but here that is not an issue since we have a positive value. We conclude that the price elasticity of supply when the price increases from $9 to $10 is 3.6.

  24. How Do We Interpret the Price Elasticity of Supply? • The price elasticity of supply is used to see how sensitive the supply of a good is to a price change. • The higher the price elasticity, the more sensitive producers and sellers are to price changes. • A very high price elasticity suggests that when the price of a good goes up, sellers will supply a great deal less of the good and when the price of that good goes down, sellers will supply a great deal more. • A very low price elasticity implies just the opposite, that changes in price have little influence on supply.

  25. Often you'll have the follow up question "Is the good price elastic or inelastic between $9 and $10". To answer that, use the following rule of thumb: • If PEoS > 1 then Supply is Price Elastic (Supply is sensitive to price changes) • If PEoS = 1 then Supply is Unit Elastic • If PEoS < 1 then Supply is Price Inelastic (Supply is not sensitive to price changes)

  26. Recall that we always ignore the negative sign when analyzing price elasticity, so PEoS is always positive. • In our case, we calculated the price elasticity of supply to be 3.6, so our good is price elastic and thus supply is very sensitive to price changes.

  27. Income Elasticity of Demand • The Income Elasticity of Demand measures the rate of response of quantity demand due to a raise (or lowering) in a consumers income. The formula for the Income Elasticity of Demand (IEoD) is given by: IEoD = (% Change in Quantity Demanded)/(% Change in Income) • Calculating the Income Elasticity of Demand

  28. Data • Income Quantity Demanded • $20,000 60 • $30,000 110 • $40,000 150 • $50,000 180 • $60,000 200

  29. On an assignment or a test, you might be asked "Given the following data, calculate the income elasticity of demand when a consumer's income changes from $40,000 to $50,000". • The first thing we'll do is find the data we need. We know that the original income is $40,000 and the new price is $50,000 so we have Income(OLD)=$40,000 and Income(NEW)=$50,000.

  30. From the chart we see that the quantity demanded when income is $40,000 is 150 and when the price is $50,000 is 180. • Since we're going from $40,000 to $50,000 we have QDemand(OLD)=150 and QDemand(NEW)=180, where "QDemand" is short for "Quantity Demanded". • So you should have these four figures written down: • Income(OLD)=40,000Income(NEW)=50,000QDemand(OLD)=150QDemand(NEW)=180

  31. To calculate the price elasticity, we need to know what the percentage change in quantity demand is and what the percentage change in price is. It's best to calculate these one at a time. • Calculating the Percentage Change in Quantity Demanded • The formula used to calculate the percentage change in quantity demanded is: [QDemand(NEW) - QDemand(OLD)] / QDemand(OLD) • By filling in the values we wrote down, we get: • [180 - 150] / 150 = (30/150) = 0.2

  32. So we note that % Change in Quantity Demanded = 0.2 (We leave this in decimal terms. In percentage terms this would be 20%) and we save this figure for later. Now we need to calculate the percentage change in price. • Calculating the Percentage Change in Income • Similar to before, the formula used to calculate the percentage change in income is: [Income(NEW) - Income(OLD)] / Income(OLD) • By filling in the values we wrote down, we get: • [50,000 - 40,000] / 40,000 = (10,000/40,000) = 0.25

  33. We have both the percentage change in quantity demand and the percentage change in income, so we can calculate the income elasticity of demand. • Final Step of Calculating the Income Elasticity of Demand • We go back to our formula of: IEoD = (% Change in Quantity Demanded)/(% Change in Income) • We can now fill in the two percentages in this equation using the figures we calculated earlier. • IEoD = (0.20)/(0.25) = 0.8

  34. Unlike price elasticities, we do care about negative values, so do not drop the negative sign if you get one. Here we have a positive price elasticity, and we conclude that the income elasticity of demand when income increases from $40,000 to $50,000 is 0.8.

  35. How Do We Interpret the Income Elasticity of Demand? • Income elasticity of demand is used to see how sensitive the demand for a good is to an income change. • The higher the income elasticity, the more sensitive demand for a good is to income changes. • A very high income elasticity suggests that when a consumer's income goes up, consumers will buy a great deal more of that good. • A very low price elasticity implies just the opposite, that changes in a consumer's income has little influence on demand. • Often an assignment or a test will ask you the follow up question "Is the good a luxury good, a normal good, or an inferior good between the income range of $40,000 and $50,000?" To answer that use the following rule of thumb:

  36. If IEoD > 1 then the good is a Luxury Good and Income Elastic • If IEoD < 1 and IEOD > 0 then the good is a Normal Good and Income Inelastic • If IEoD < 0 then the good is an Inferior Good and Negative Income Inelastic • In our case, we calculated the income elasticity of demand to be 0.8 so our good is income inelastic and a normal good and thus demand is not very sensitive to income changes.

  37. Cross-Price Elasticity of Demand • The Cross-Price Elasticity of Demand measures the rate of response of quantity demanded of one good, due to a price change of another good. • If two goods are substitutes, we should expect to see consumers purchase more of one good when the price of its substitute increases. • Similarly if the two goods are complements, we should see a price rise in one good cause the demand for both goods to fall.

  38. O R • The cross elasticity of demand and cross price elasticity of demand measures the responsiveness of the demand of a good to a change in the price of another good. • It is measured as the percentage change in demand for the first good that occurs in response to a percentage change in price of the second good. For example, if, in response to a 10% increase in the price of fuel, the demand of new cars that are fuel inefficient decreased by 20%, the cross elasticity of demand would be −20%/10% = −2.

  39. The formula used to calculate the coefficient cross elasticity of demand is

  40. CPEoD = (% Change in Quantity Demand for Good X)/(% Change in Price for Good Y) • Calculating the Cross-Price Elasticity of Demand • You're given the question: "With the following data, calculate the cross-price elasticity of demand for good X when the price of good Y changes from $9.00 to $10.00." Using the chart on the bottom of the page, we'll answer this question.

  41. We know that the original price of Y is $9 and the new price of Y is $10, so we have Price(OLD)=$9 and Price(NEW)=$10. • From the chart we see that the quantity demanded of X when the price of Y is $9 is 150 and when the price is $10 is 190. • Since we're going from $9 to $10, we have QDemand(OLD)=150 and QDemand(NEW)=190. You should have these four figures written down:

  42. Price(OLD)=9Price(NEW)=10QDemand(OLD)=150QDemand(NEW)=190 • To calculate the cross-price elasticity, we need to calculate the percentage change in quantity demanded and the percentage change in price. We'll calculate these one at a time. • Calculating the Percentage Change in Quantity Demanded of Good X • The formula used to calculate the percentage change in quantity demanded is: [QDemand(NEW) - QDemand(OLD)] / QDemand(OLD)

  43. [190 - 150] / 150 = (40/150) = 0.2667 • So we note that % Change in Quantity Demanded = 0.2667 (This in decimal terms. In percentage terms this would be 26.67%). • Calculating the Percentage Change in Price of Good Y • The formula used to calculate the percentage change in price is: [Price(NEW) - Price(OLD)] / Price(OLD) • We fill in the values and get: • [10 - 9] / 9 = (1/9) = 0.1111

  44. We have our percentage changes, so we can complete the final step of calculating the cross-price elasticity of demand. • Final Step of Calculating the Cross-Price Elasticity of Demand • We go back to our formula of: CPEoD = (% Change in Quantity Demanded of Good X)/(% Change in Price of Good Y) • We can now get this value by using the figures we calculated earlier. • CPEoD = (0.2667)/(0.1111) = 2.4005 • We conclude that the cross-price elasticity of demand for X when the price of Y increases from $9 to $10 is 2.4005.

  45. How Do We Interpret the Cross-Price Elasticity of Demand? • The cross-price elasticity of demand is used to see how sensitive the demand for a good is to a price change of another good. • A high positive cross-price elasticity tells us that if the price of one good goes up, the demand for the other good goes up as well. • A negative tells us just the opposite, that an increase in the price of one good causes a drop in the demand for the other good. • A small value (either negative or positive) tells us that there is little relation between the two goods. • Often an assignment or a test will ask you a follow up question such as "Are the two goods complements or substitutes?". • To answer that question, you use the following rule of thumb:

  46. If CPEoD > 0 then the two goods are substitutes • If CPEoD =0 then the two goods are independent (no relationship between the two goods • If CPEoD < 0 then the two goods are complements • In the case of our good, we calculated the cross-price elasticity of demand to be 2.4005, so our two goods are substitutes when the price of good Y is between $9 and $10.

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