Elasticity - A Quantitative Approach The rst elasticity tutorial took a qualitative approach to elasticity. The idea conveyed was: Elasticity = Responsiveness The elasticity of Q with respect to P is the responsiveness of Q to changes in P. Q is the quantity demanded. P is the price per unit. Elasticity has a quantitative meaning, too. Elasticity is a specic way of measuring responsiveness. Suppose P changes, and Q changes as a result. The elasticity of Q with respect to P is the relative change in Q divided by the corresponding relative change in P. You can also say: The elasticity of Q with respect to P is the percentage change in Q divided by the corresponding percentage change in P. For example, if the price of something goes up by 1% and sales fall by 2%, the elasticity of quantity demanded with respect to price is -2%/1% = -2. Don't neglect the minus sign. For demand, the elasticity number is negative, because price and quantity move in opposite directions. You can write the elasticity formula this way: (Change in Q)+(Level' of Q) Elasticity = W The numerator of this fraction is the change in Q relative to the level of Q. The denominator of the fraction is the change in P relative to the level of P. The elasticity concept can be applied to other things besides Quantity and Price. You can use the concept whenever changing one thing makes something else change. For example, some researchers have estimated the elasticity of population health status with respect to the population's medical care expenditure. This elasticity is the percentage difference in health status divided by the percentage difference in medical care expenditure. (This elasticity usually comes out small, by the way.) In this example, health status goes in the place of Q and medical care spending goes in the place of P. In the formula, you can consider Q and P as placeholders for anything that changes in response to changes in something else. There's a shorter way to say "the elasticity of Q with respect to P." You can say "the P elasticity of Q," as in "the price elasticity of demand" or "the income elasticity of demand." Here's the formula again for the P elasticity of Q: (Change in Q)+(Level of Q) Elasticity = (Change in P)+(Leuel of P) Let's try to apply this. Suppose that a medical practice nds that when the price of a certain test is is $10, the quantity demanded is 100 tests per month, while if the price is $30, the quantity demanded is only 60 tests per month. What's the price elasticity of demand? Let's take this one step at a time, because I have some points to make. The rst point is that, when you gure the changes in Q and P, you do both in the same direction of time. Let's call the $10 price and 100 quantity the "before" situation, and the $30 price and 60 quantity the "after" situation. To be consistent, you have to calculate all changes as "after\" minus "before" or "before" minus "after." Let's calculate all changes as "after" minus "before." What is the change in Q, "after" minus \"before"? (The "after" quantity is 60. The "before" quantity is 100.) Question 2 1 pts Now for the "levels" in the elasticity formula. What number do you think you should use for the level of Q in the numerator of the fraction? 0 100 060 Q I'm not sure. Here is the formula again: (Change in Q)+(Level' of Q) Elasticity = W You have a choice of what level of Q should go into the formula. There is no one right answer. The phrase "level of Q" is ambiguous. You could use the "before" level of Q, which is 100 in our example. You could use the "after" level of Q, which is 60 in our example. You could use something in between. Whichever you use, be consistent between the top of the fraction and the bottom. If you use the "before" level of Q in the top, use the "before" level of P in the bottom. If the change in Q is small relative to the levels of Q, it doesn't matter much which Q you use for the level of Q. The elasticity comes out about the same regardless. If you want a middle choice use the "arc elasticity." It uses values halfway between \"before" and "after." Let's show that. Here's the denition of arc elasticity: (Change in Q)+(Auerage of Q5) AI'C ElaSilCl Iy = (Change in P)+(Average of PS) To get the average of the Q's, add them and divide by 2. The same goes for the average of the P's. Let's use that in the calculation. The data again are: If the price is $10, demanded quantity is 100 tests per month. If the price is $30, demanded quantity is 60 tests per month. What is the average of the Q5? Z Question 4 So the (Change in Q) + (Average of Q5) is what? (Type a decimal number, not a percent) E That's the numerator of the Arc Elasticity fraction. Next, we calculate the denominator. Repeating the data: If the price is $10, demanded quantity is 100 tests per month. If the price changes to $30, demanded quantity is 60 tests per month. This is our arc elasticity fraction so far: 0.5 Arc Elasticity = 'W Tackling the denominator, what is the change in P, "after" minus "before"? Question 6 And the average of the P5? 50, (Change in P} + (Average of P3) is: Question 8 Last step: Based on the above fraction, what is the arc elasticity? Elastic and Inelastic The terms "elastic" and "inelastic" can be given a precise meaning in terms of the number that comes out of the elasticity fraction. The divider between elastic and inelastic demand is -1. (For elasticities where you expect a positive relationship between Q and P, such as for elasticities of supply, the divider is +1.) If the demand elasticity is more negative than -1, the demand is elastic. If the demand elasticity is between -1 and 0, the demand is inelastic. I avoided saying "higher" and "lower" in the above denition, because economists say that the elasticity of demand is "high" when it's a big negative number. They say that the elasticity of demand is \"low" when it's a small negative number, meaning close to 0. The elasticity of demand for oil is low. The elasticity of demand for cubic zirconia (imitation diamond) is high. Question 9 1 pts In our example, we got a price elasticity of demand of -0.5. Is this elastic or inelastic demand? 0 Elastic demand 0 Inelastic demand When Does Raising Your Price Bring In More Money? For demand, there's a relationship between the elasticity and what happens to total revenue from customers when you change your price: If demand is elastic (if the elasticity is more negative than -1] then if the price goes up, the total amount customers spend goes down. If demand is inelastic (if the elasticity is between -1 and 0) then if the price goes up, the total amount customers spend goes up. If you have unitary elasticity (if the elasticity of demand is exactly -1) then if the price goes up, the total amount customers spend stays the same. Let's see how this works in our example. Question 10 1 p At a price of $10, you sell 100 tests per month. What is the total revenue (Price time Quantity) When the price is $30, you do 60 tests per month. What is that total revenue? Question 12 1 pts 50, raising the price from $10 to $30 does what to total revenue? 0 Revenue goes up 0 Revenue goes down Question 13 1 pts Our calculated elasticity was 0.5, which we called "inelastic" because its absolute value was less than 1. Is this consistent with the idea that revenue goes up when price goes up? 0 Yes ONO