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]?