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# Price Elasticity of Supply

## A Primer on the Price Elasticity of Supply

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The Price Elasticity of Supply measures the rate of response of quantity demand due to a price change. If you've already read The Price Elasticity of Demand and understand it, you may want to just skim this section, as the calculations are similar. (Your course may use the more complicated Arc Price Elasticity of Supply formula. If so you'll need to see the article on Arc Elasticity) We calculate the Price Elasticity of Supply by the formula:

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

### Calculating the Price Elasticity of Supply

You may be asked "Given the following data, calculate the price elasticity of supply when the price changes from \$9.00 to \$10.00" Using the chart on the bottom of the page, I'll walk you through answering this question.

First we need to find the data we need. 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 (make sure to look at the supply data, not the demand data) when the price is \$9 is 150 and when the price is \$10 is 110. Since we're going from \$9 to \$10, we have QSupply(OLD)=150 and QSupply(NEW)=210, where "QSupply" is short for "Quantity Supplied". So we have:

Price(OLD)=9
Price(NEW)=10
QSupply(OLD)=150
QSupply(NEW)=210

To calculate the price elasticity, we need to know what the percentage change in quantity supply is and what the percentage change in price is. It's best to calculate these one at a time.

### Calculating the Percentage Change in Quantity Supply

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

[QSupply(NEW) - QSupply(OLD)] / QSupply(OLD)

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

[210 - 150] / 150 = (60/150) = 0.4

So we note that % Change in Quantity Supplied = 0.4 (This is in decimal terms. In percentage terms it would be 40%). Now we need to calculate the percentage change in price.

### Calculating the Percentage Change in Price

Similar to before, 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.

### Final Step of Calculating the Price Elasticity of Supply

We go back to our formula of:

PEoS = (% 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

When we analyze price elasticities we're concerned with the absolute value, but here that is not an issue since we have a positive value. We conclude that the price elasticity of supply when the price increases from \$9 to \$10 is 3.6.

### How Do We Interpret the Price Elasticity of Supply?

The price elasticity of supply is used to see how sensitive the supply of a good is to a price change. The higher the price elasticity, the more sensitive producers and sellers are to price changes. A very high price elasticity suggests that when the price of a good goes up, sellers will supply a great deal less of the good and when the price of that good goes down, sellers will supply a great deal more. A very low price elasticity implies just the opposite, that changes in price have little influence on supply.

Often you'll have the follow up question "Is the good price elastic or inelastic between \$9 and \$10". To answer that, use the following rule of thumb:

• If PEoS > 1 then Supply is Price Elastic (Supply is sensitive to price changes)

• If PEoS = 1 then Supply is Unit Elastic

• If PEoS < 1 then Supply is Price Inelastic (Supply is not sensitive to price changes)
Recall that we always ignore the negative sign when analyzing price elasticity, so PEoS is always positive. In our case, we calculated the price elasticity of supply to be 3.6, so our good is price elastic and thus supply is very sensitive to price changes.

## Data

 Price Quantity Demanded Quantity Supplied \$7 200 50 \$8 180 90 \$9 150 150 \$10 110 210 \$11 60 250
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