Extra Practice Problems for Elasticity

Price Elasticity of Demand: Midpoint Method – Percentage change in demand/percentage change in price
Price Elasticity of Demand: Midpoint Method – Percentage change in demand/percentage change in price

1. Given the following demand schedule:

PRICE QUANTITY REVENUE
15 10
10 55
5 100

a) Fill in the revenue column; without doing any further computations, is the demand curve elastic or inelastic? Why?

b) Compute the coefficient of elasticity between a price of $5 and of $15 using the midpoint formula.

2. Company ElastiPad produces tablets competing with the iPad. Six months into the release of their new product, elastoPad, they reduced the price from $200 to $100 to test the market and their theory that they could improve revenues by making the change. It was a huge success! At $200 demand for their elastoPad was 20,000 units, but with the reduced price of $100 demand topped 60,000 units! At $200 revenue was $4 million, whereas at $100 revenue reached $6 million. Using the above midpoint formula, determine if the price change was elastic or inelastic. Show your work.

3.

PRICE ELASTICITY OF SUPPLY EXAMPLE PROBLEM

Given the following data for the supply and demand of movie tickets, calculate the price elasticity of supply when the price changes from $9.00 to $10.00.

We know that the original price is $9 and the new price is $10, so we have Price (Old) =$9 and Price (New) = $10. From the chart we see that the quantity supplied, when the price is $9 is 75 and when the price is $10 is 105.

4.

Answer Key

Total Revenue Column: 150, 550, 500

1a. since revenue increased when price declines, demand will be elastic

1b. The percentage change in quantity, using the midpoint formula is: (100 – 10) / 55 = 90/55 = 1.636.

The coefficient of elasticity is the percentage change in quantity divided by the percentage change in price, or – 90/55 = – 1.636. Since this is greater than 1 demand is elastic over this range, as we expected from the increase in revenue.

2.

E =
[(60,000 – 20,000) / [(60,000 + 20,000)/2]]
————————————————————
[($200 – $100)/[($200 + $100)/2]]

E = (40,000/40,000) / (100/150)

E = 1 / .67

E = 1.49: This product is considered elastic because E > 1

3.

Price (Old) = $9
Price (New) = $10
Quantity Supplied (Old) = 75
Quantity Supplied (New) = 105

To calculate the price elasticity of supply for movie tickets, we need to know what the percentage change in quantity supplied is and what the percentage change in price is.

CALCULATING THE PERCENTAGE CHANGE IN QUANTITY SUPPLY

The formula used to calculate the percentage change in quantity supplied is:

[Quantity Supplied (New) –Quantity Supplied (Old)] /Quantity Supplied (Old))

[105 – 75] / 75 = (30/75) = 0.4

So we note that % Change in Quantity Supplied = 0.4

Now we need to calculate the percentage change in price.

CALCULATING THE PERCENTAGE CHANGE IN PRICE

The formula used to calculate the percentage change in price is:

[Price (New) – Price (Old)] /Price (Old))

By filling in the values we wrote down, we get:

[10 – 9] / 9 = (1/9) = 0.1111

We have both the percentage change in quantity supplied and the percentage change in price, so we can calculate the price elasticity of supply.

CALCULATING THE PRICE ELASTICITY OF SUPPLY

PES = (% Change in Quantity Supplied)/(% Change in Price)

We now fill in the two percentages in this equation using the figures we calculated.

PEoD = (0.4)/(0.1111) = 3.6

We get that the price elasticity of supply when the price increases from $9 to $10 is 3.6. So for movie tickets, the price is elastic and thus supply is very sensitive to price changes.

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