How to Solve Elasticity Problems in Economics - YouTube

All right this video is going to go over how to solve elasticity problems and economics

The example you're looking at in front of you right now is for the price elasticity of demand

You'll see we have percent change in [quantity] over

percent change in price, and if you get confused over which goes on top you can remember this little trick a

Quarter-Pounder [I] know it's kind of lame

But if you think about McDonald's and the quarter pounders you'll always get these straight

So this example looks at the price elasticity of demand

We have this percent change in Q which is just our ending quantity minus our beginning quantity

Over average quantity our end price minus our beginning price over average price

if we want to look at

the income elasticity of demand

we're just going to have our percent change in Q as

It's affected [by] income

So percent change in Q over percent change in income and that's our income elasticity of demand

Our cross price elasticity of demand is just going to be our percent change in Q again

Over our percent change in P but the difference here is [that] this

Quantity is for good J. And the change in price is for good

I so they are different goods. Maybe hamburgers

quantity of Hamburgers and price of Hotdogs that sort of thing

All right, so for the first example. [we] have price changing from $5 to $10

Increasing $5 and quantity changing from 30 to 20 so a decrease in 10 units

What is the price elasticity of demand?

Well, we know before

From before that it's the percent change in quantity over the percent change in price

Quarter Pounders remember but now we have to find the percent change in quantity and the percent change in price

So first let's do the percent change in quantity

percent change in Quantity

We take our ending quantity or 20 minus our beginning quantity of 30

Then we have to find what our [average] quantity is

so 20 Plus 30

divided by 2

this gives us negative 10 over 20 plus 30 is 50 divided by 2

or 25

and this can also be written as if we divide it by 2.5 as

4/10 Or We divide each [of] those by 2 can get 2/5?

Now we need to find the percent change in price

So we're going to use the similar method we'll start off with our ending dollar amount of 10

subtract our initial Dollar amount of 5

divided by the average

10 Plus 5 divided by 2

So here we get 5 dollars is the difference 10 minus 5

10 plus 5 is 15 divided by 2 gives us

7.5 and

[those] are all dollars these are all dollars and that gives us

[2] thirds

so our percent change in price is 2/3 our

percent change in Quantity

Forgot those there is negative 2 over 5

so when we add

Those to where they go and our price elasticity of demand formula

Our numerator is going to be negative 2 point or negative 2 over 5 our

Denominator is going to be 2/3

Using that invert and multiply rule. We can take this denominator and flip it and

multiply it by the numerator

So we get negative

2/5

Times 3 Halves [and]

So that's going to give us negative 6

over 10

or

negative [three] over [five] if we divide both these by two and

That's just going to be negative point six second example

What happens if they give you the price elasticity of demand and they want you to find the percent change in something?

So here we have the price elasticity of demand is equal to negative 0.5

And the price changes from [20] to [$10] so here the price goes down

first let's find the percent change in

p

So that's going to be equal [to] 10

Minus 20 over the average here is 15

so we get 10 over 15 and

Then we set that up in our equation and solve for Q so

we have Q in

The numerator percent change in Q our percent change in P in the denominator

10 over 15, and so that's going to be equal [to]

negative 1.5, our price elasticity of demand

So now what we need to do is solve for this percent change in Q so what we can do here is

flip this guy over

Or we can just multiply both sides by 10 over 15, so we get percent

change in Q equals negative one point five

times

our 10 over 15

What is 10 over 15 times 1.5?

This is the same as [2/3] so [2/3] times 1.5. Is going to give us negative

[1]

So our percent change in quantity is going to be equal to negative one

So if we have a price elasticity of demand of negative [1.5] a price change from 20 to 10

What's our percent change in Q our percent change in Q is going to be negative [one]?