# Elasticity of supply

The Price Elasticity of Supply measures the rate of response of quantity demand due to a price change. If you've already read Elasticity of Demand and understand it, you may want to just skim this section, as the calculations are similar.

Definitions

— According to Lipsey, "Elasticity of supply is the ratio of percentage change in quantity supplied over the percentage change in price."

— In the words of Prof. Bilas, "Elasticity of supply is defined as the percentage change in quantity supplied divided by percentage change in price."

Price elasticity of supply measures the relationship between change in quantity supplied and a change in price. The formula for price elasticity of supply is:

### Supply Analysis • ∆Q =change in the demand.(difference in demand)

• ∆P=change in the price.(difference in the price)

• P1=initial price. (first price/ old price)

• Q1=initial demand. (first demand/ old demand)

The value of elasticity of supply is positive, because an increase in price is likely to increase the quantity supplied to the market and vice versa.

### 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 Q Supply(OLD)=150 and Q Supply(NEW)=210, where "Q Supply" 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.

### Five Types of Elasticities of Supply:

1. Unit Elastic Supply: When change in price of X brings about exactly proportionate change in its quantity supplied then supply is unit elastic i.e. elasticity of supply is equal to one, e.g. if price rises by 10% and supply expands by 10% then, change in the quantity supplied the supply is relatively inelastic or elasticity of supply is less than one.

Es = % change in Quantity Supplied of X

% change in price of X

2. Relatively Elastic Supply: When change in price brings about more than proportionate change in the quantity supplied, then supply is relatively elastic or elasticity of supply is greater than one.

3. Perfectly Inelastic Supply: When a change in price has no effect on the quantity supplied then supply is perfectly inelastic or the elasticity of supply is zero.

4. Perfectly Elastic Supply: When a negligible change in price brings about an infinite change in the quantity supplied, then supply is said to be perfectly elastic or elasticity of supply is infinity.

All the five types of Elasticities of supply can be shown by different slopes of the supply curve. Fig. (1) Shows the supply is unit elastic because change in price from OP to OP1 brings about exactly proportionate change in the quantity supplied of commodity X viz., from OM to OM1. In this case Es = 1. Fig (2) shows that supply is relatively inelastic because change in price of from OP to OP1 brings about less than proportionate change in quantity supplied of X. in this case Es < 1.

Fig (3) shows that supply is relatively elastic because change in price of X from OP to OP1 brings about more than proportionate change in quantity supplied of X. in this case Es > 1.

Fig (4) shows that supply is perfectly inelastic because change in price of X from OP to OP1 has absolutely no effect on quantity supplied of X. in this case Es = 0. Thus, if the supply curve is vertical, i.e. parallel to Y-axis it represents perfectly inelastic supply.  Fig (5) shows that supply is perfectly elastic because a small change in price of X brings about infinite change in supply. Thus, if the supply curve is horizontal or parallel to X- axis it represents perfectly elastic supply.

Hence, the five different types of elasticities of supply can be shown by five different slopes of supply curve.