Price elasticity of demand example question where you have
to solve for the percent change in quantity or price instead of the elasticity
measure. Imagine an elasticity question that gives you the elasticity and then
asks you to calculate the percent change in either quantity or price given the
percent change in the other term. For example, you are told that the price elasticity
of demand for apples is -2 and that
quantity demanded of applies increases from 100 apples to 250 apples.
What would the corresponding change in price have to be to accommodate this
change in quantity demanded?
First we have to set up our standard price elasticity of
demand formula or equation:
Price elasticity of Demand = The percent change in quantity
demanded/the percent change in price
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| Price elasticity of demand Equation |
Using this equation from our examples above we will plug the
-2 value into the equation as well as the percent change in quantity demanded
is found by taking the difference between 100 and 250 apples and then dividing
by the average (,1000+2,500)/2 --an example of the midpoints theorem in action--
which gives us 1,750. The result is 1,500 divided by 1,750 which is 6/7. Once
we plug these values into the price elasticity of demand formula above we will
get:
-2 = 6/7 / Percent
change in price.
If we multiply both sides of the equation by percent change
in price and divide both sides by -2 we end up with:
Percent change in price = -6/14
We can see that the change in price necessary to change the
quantity demanded by 1,500 units would be a -6/14 change in price or a roughly
43% decrease in the price level for apples.
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| Exploring the price elasticity of demand for apples |
The trick to solving this type of elasticity problem is to
remember the price elasticity of demand formula and plugging in all of the
information that you have available and then performing some algebra to get the
value that you are missing. For example, if you need to solve for the percent
change in price, you should set up your elasticity formula to look like:
Elasticity = X/Percent change in price
You can then multiply both sides by the percent change in
price and then solve for X to get your answer.
Similarly, if the problem asks you to find the percent
change in price, you can set up the elasticity equation to look like:
Elasticity = Percent change in quantity demanded/X
You then must multiply both sides by X and divide both sides
by the elasticity measure in order to solve for X.
Let's consider another example where the elasticity measure
is -3 and the percent change in price is equal to -16% (meaning that price
falls by 16%). Using the methods discussed earlier in this post we know that we
have to plug this information into our elasticity formula to find out what the
percent change in quantity will be. This gives us the following elasticity
formula:
-3 = X / -16%
First, we know that a price elasticity of demand measure of
-3 is highly elastic so we would expect the corresponding percent change in quantity
demanded to be much larger than the percent change in price of 16%. In fact,
when we multiply both sides by -16% we end up with X equals to 48% which means
that our quantity demanded will increase by almost 50% given a much lower
percent change in price. This confirms that the price elasticity of demand
measure for the good is very elastic and responsive to associated changes in
price level.
