Elasticity Summary - Online Tutor, Practice Problems & Exam Prep

Understanding price elasticity of demand and supply is crucial for analyzing market behavior. The formula for price elasticity is given by ${\%}^2\left(\mathrm{Qd}\right)/{\%}^2\left(P\right)$. An elasticity greater than 1 indicates elastic demand, while less than 1 indicates inelastic demand. Additionally, income elasticity and cross-price elasticity help determine normal goods and substitutes. Understanding these concepts aids in maximizing revenue and recognizing market equilibrium.

Elasticity Summary

Alright guys, I hope you're excited for this video. This is where I took everything we've learned so far and I put it all onto one page and we just got a ton of information all crammed in here, so let's check it out. So here we go. I've got it nice and organized for you. We're going to start with our price elasticities of demand and supply. So, we got our titles there and then I've got your formulas right next to it. Right? I've got those super shorthand. I think you should feel comfortable with reading that by now. We've got percentage change in quantity demanded divided by percentage change in price there, right? So, that's going to be your formula that you should use and then I've got all the different ways you can end up with an answer, right. You're going to be able to analyze your answers based on this column. You're going to get an answer above 1. Boom. You know it's elastic. You can't forget it there. And here I made a note, absolute value. Right? So for both of these, price elasticity of demand and price elasticity of supply, it's always going to be positive numbers, right? Always positive numbers, we use the absolute value, don't worry about negative and positive. And here on the right, I've got the steps that we've been using, right? That step by step process to subtract, to add, and remember these steps worked for all of our elasticities that we've worked on so far. The only thing you had to note was what were our 2 variables, right? For price elasticity of demand and supply, we had quantities and price, right? Quantity demanded or quantity supplied and price on the denominator. Same steps, right? Income, right. So that's why I kind of italicized these is just because those are our 2 variables. I left it as the one for elasticity of demand just because it's the most common one, but you should be comfortable substituting that for income or across price, right? Whatever it is, just use your two variables from the problem. So there you have your price elasticity of demand and supply so you can kinda see how related they are, and then down here we've got our income elasticity of demand and our cross price elasticity of demand, right? The other 2 that we did and they've got some similarities too. So first, just like before I gave you your formulas, percentage change in quantity demanded over percentage change in income or for cross price, percentage change in quantity demanded of good X, right, the first good divided percentage change in price of the other good. And then in the next box I've got how we're going to analyze these, right. When you get your answer, your elasticity, this is how you're going to analyze whether it's a normal good or substitute complement, whatever we're working with. We've got it all there and I made a quick note here, right, for these 2, the sign does matter. We got to keep the positive or the negative so we're going to have to pay attention to that and that's why I've got the step 6 here. This is where after we've solved our subtraction, addition, midpoint method stuff, we need to make sure that we check the signs of quantity and the sign of price or income, right. So there we go. We kind of have everything about the midpoint method and all our different elasticities in one place, and since we had some extra space on the page, I went ahead and gave you even a little more information here in the bottom. Remember when we talked about the straight line demand curve and where there was a point where we maximize revenue? Boom, we got it right here. To the left of that middle point is going to be elastic, to the right of that middle point is inelastic, at that point we're unit elastic and that's where we maximize revenue, and we've got a little information about total revenue over here and what happens with different price changes, right? If price goes up and total revenue goes up, then we've got inelastic demand just like the other cases there, right? So we've kind of got everything from the chapter on one page here. You guys should feel pretty comfortable to use this while you're studying and then you'll ace it once you get to the test. Cool, let's do a couple more practice problems before we wrap up elasticity.

A linear, downward-sloping demand curve is

• A. Inelastic
• B. Unit Elastic
• C. Elastic
• D. Inelastic at some points, and elastic at others

An increase in the supply of a good will increase the total revenue producers receive if:

• A. The demand curve is inelastic
• B. The demand curve is elastic
• C. The supply curve is inelastic
• D. The supply curve is elastic

A life-saving machine without any close substitutes will tend to have:

• A. A small price elasticity of demand
• B. A large price elasticity of demand
• C. A small price elasticity of supply
• D. A large price elasticity of supply

Here’s what students ask on this topic:

What is the formula for calculating price elasticity of demand?

The formula for calculating price elasticity of demand (PED) is given by:

$\frac{\%∆Q{d}_{}}{\%∆P}$

Where $\%∆Q{d}_{}$ is the percentage change in quantity demanded and $\%∆P$ is the percentage change in price. This formula helps determine how sensitive the quantity demanded of a good is to a change in its price.

How do you interpret the value of price elasticity of demand?

The value of price elasticity of demand (PED) indicates how responsive the quantity demanded is to a change in price. If PED > 1, demand is elastic, meaning consumers are highly responsive to price changes. If PED < 1, demand is inelastic, meaning consumers are less responsive to price changes. If PED = 1, demand is unit elastic, meaning the percentage change in quantity demanded is equal to the percentage change in price.

What is the difference between price elasticity of demand and price elasticity of supply?

Price elasticity of demand (PED) measures how much the quantity demanded of a good responds to a change in its price, while price elasticity of supply (PES) measures how much the quantity supplied of a good responds to a change in its price. Both use similar formulas, but PED focuses on consumer behavior, and PES focuses on producer behavior.

How do you calculate income elasticity of demand?

Income elasticity of demand (YED) is calculated using the formula:

$\frac{\%∆Q{d}_{}}{\%∆I}$

Where $\%∆Q{d}_{}$ is the percentage change in quantity demanded and $\%∆I$ is the percentage change in income. This helps determine whether a good is a normal good (positive YED) or an inferior good (negative YED).

What is cross-price elasticity of demand and how is it calculated?

Cross-price elasticity of demand (XED) measures how the quantity demanded of one good responds to a change in the price of another good. It is calculated using the formula:

$\frac{\%∆Q{d}_X}{\%∆P{Y}_{}}$

Where $\%∆Q{d}_X$ is the percentage change in quantity demanded of good X and $\%∆P{Y}_{}$ is the percentage change in price of good Y. A positive XED indicates substitute goods, while a negative XED indicates complementary goods.