Price Elasticity of Supply: Calculation and Determinants

Introduction

Welcome to our final lesson in the module on elasticity. Having thoroughly explored the demand side—how consumers react to changes in price, income, and the prices of related goods—we now pivot to the supply side. This lesson introduces the price elasticity of supply (PES), a concept that measures the responsiveness of producers' quantity supplied to a change in the market price of their product.

Just as price elasticity of demand is crucial for understanding consumer behavior and pricing strategy, price elasticity of supply is essential for analysing how quickly and effectively a market can respond to new conditions. By the end of this lesson, you will be able to calculate the price elasticity of supply using various methods and identify the key factors that determine whether supply is elastic or inelastic.

Defining and Interpreting Price Elasticity of Supply

Price elasticity of supply (PES) measures the percentage change in quantity supplied resulting from a one percent change in price. The formula is a direct counterpart to the one for price elasticity of demand:

E_{S} = \frac{Percentage Change in Quantity Supplied}{Percentage Change in Price} = \frac{%Δ Q _{S}}{%Δ P}

A critical distinction from price elasticity of demand is that PES is almost always a positive number. This is a direct consequence of the law of supply: as the price of a good rises, producers are willing to supply more of it. Both the numerator ( $%Δ Q_{S}$ ) and the denominator ( $%Δ P$ ) will move in the same direction, yielding a positive result.

To begin, let's watch a video that provides a clear overview of the concept and its interpretation.

Y1 12) Price Elasticity of Supply (PES)

The video "Y1 12) Price Elasticity of Supply (PES)" by EconplusDal offers a great introduction to the topic.

Please watch the first two segments. The first part, the definition, introduces the formula and explains why the value is always positive. The second part, the interpretation, explains how to classify supply based on the numerical value of PES.

As the video explains, we interpret the value of PES as follows:

Elastic Supply ( $E_{S} > 1$ ): Quantity supplied is highly responsive to price changes. A given percentage change in price leads to a larger percentage change in quantity supplied.
Inelastic Supply ( $E_{S} < 1$ ): Quantity supplied is not very responsive to price changes. A given percentage change in price leads to a smaller percentage change in quantity supplied.
Unit Elastic Supply ( $E_{S} = 1$ ): The percentage change in quantity supplied is equal to the percentage change in price.

There are also two theoretical extremes:

Perfectly Inelastic Supply ( $E_{S} = 0$ ): Quantity supplied is fixed and does not change regardless of the price. The supply curve is vertical. Think of the supply of stadium seats for a specific event.
Perfectly Elastic Supply ( $E_{S} = \infty$ ): Producers are willing to supply any amount at a specific price, but nothing at a lower price. The supply curve is horizontal.

Graphically, a steeper supply curve represents a more inelastic supply, while a flatter, more shallow curve indicates a more elastic supply.

Calculating Price Elasticity of Supply

As with demand elasticities, your CB2 exam will require you to calculate PES from both discrete data points and supply functions. Your quantitative background will be a significant asset here.

1. The Midpoint (Arc) Method

When you are given two price-quantity combinations, the most accurate way to calculate elasticity is the midpoint method. This ensures the result is the same regardless of whether the price is increasing or decreasing.

The formula is:

E_{S} = \frac{( Q _{S 2} - Q _{S 1} )}{( Q _{S 1} + Q _{S 2} ) /2} \div \frac{( P _{2} - P _{1} )}{( P _{1} + P _{2} ) /2}

The following video provides a very clear, step-by-step demonstration of this calculation method.

Midpoint Method: Price Elasticity of Supply

The video "Midpoint Method: Price Elasticity of Supply" by Economics in Many Lessons focuses entirely on this calculation.

Watch the video in its entirety. It provides three distinct examples: Problem 1: Calculating an inelastic supply (E_S = 0.8). Problem 2: Calculating a highly elastic supply (E_S = 8.8). Problem 3: Calculating unit elastic supply (E_S = 1). Pay close attention to the three-step process the presenter uses: calculating the percentage change in quantity, the percentage change in price, and then finding their ratio.

Let's test this with an example shown in a spreadsheet.

An Excel spreadsheet showing the calculation of Price Elasticity of Supply using the midpoint method.

Let's verify the calculation shown in the image:

Initial Supply ( $S_{0}$ ): 200,000
Final Supply ( $S_{1}$ ): 180,000
Initial Price ( $P_{0}$ ): $4
Final Price ( $P_{1}$ ): $3

The formula used in the spreadsheet is: $E_{S} = \frac{( S _{1} - S _{0} )}{( S _{1} + S _{0} )} \div \frac{( P _{1} - P _{0} )}{( P _{1} + P _{0} )}$ . This is a simplified version of the midpoint formula where the /2 terms cancel out.

E_{S} = \frac{( 180000 - 200000 )}{( 180000 + 200000 )} \div \frac{( 3 - 4 )}{( 3 + 4 )}

E_{S} = \frac{- 20000}{380000} \div \frac{- 1}{7} \approx - 0.0526 \div - 0.1429 \approx 0.368

The result of 0.37 is correct, indicating an inelastic supply.

2. The Point Method for Supply Functions

When you have a linear supply function, such as $Q_{S} = c + d P$ , you can calculate the point elasticity of supply. This is analogous to the point elasticity of demand and leverages calculus.

The formula is:

E_{S} = \frac{d Q _{S}}{d P} \cdot \frac{P}{Q _{S}}

For a linear supply function $Q_{S} = c + d P$ , the derivative $\frac{d Q _{S}}{d P}$ is simply the coefficient $d$ .

The following reading from MIT OpenCourseWare provides a formal treatment of this method.

[PDF] Market Definition, Elasticities and Surpluses

This document offers a rigorous, mathematical approach to elasticity.

Please read the sections on price elasticity of supply. Start with section 2.3.4 for the formal definition. Then, move to section 3.2, which explains point elasticity for a linear supply curve and provides a worked example showing how elasticity changes at different points on the same curve.

Challenge: Deriving the Supply Curve from Elasticity

A more advanced problem, which your background makes you well-suited for, involves working backward: deriving the supply curve equation when given an equilibrium point and the elasticity at that point.

[PDF] Market Definition, Elasticities and Surpluses

This is a continuation of the previous reading.

Study the example under section 3.5. This section demonstrates how to use the point elasticity formula to solve for the coefficients of a linear supply function. The logic of rearranging the formula to find the slope d and then solving for the intercept c is a powerful application of the concept.

Practice Problem (Exam Style)

Let's work through a calculation problem from your CB2 exam materials.

CB2 Booklet 1 - PDFCOFFEE.COM

This booklet contains past exam questions. We will focus on a specific calculation.

Locate Question 2 on page 42. We are interested in part (ii): price elasticity of supply of Good Y. The table provides the following data for Good Y: Point 1: Price = 60, Quantity Supplied = 100 Point 2: Price = 65, Quantity Supplied = 110 Now, find the solution to Question 2 on page 56. The solution calculates PES using the "original method" (simple percentage changes) rather than the midpoint method. Let's calculate it ourselves using both methods to compare. Original Method (as in the solution): E_S = \frac{\%\Delta Q_S}{\%\Delta P} = \frac{(110-100)/100}{(65-60)/60} = \frac{0.1}{0.0833} = +1.2 Midpoint Method: E_S = \frac{(110-100)}{(100+110)/2} \div \frac{(65-60)}{(60+65)/2} = \frac{10}{105} \div \frac{5}{62.5} E_S \approx 0.0952 \div 0.08 = +1.19 In this case, both methods give a very similar result. Since E_S > 1, the supply of Good Y is elastic.

Factors Affecting Price Elasticity of Supply

Now that you're comfortable with the calculations, we'll address the second part of the learning outcome: what determines whether supply is elastic or inelastic?

Y1 12) Price Elasticity of Supply (PES)

We return to the EconplusDal video, which has an excellent segment on the determinants of PES.

Watch the segment from this timestamp. The video uses the mnemonic "PSSST" to help remember the key factors.

Here is a summary of the factors discussed in the video:

Production Lag / Time Period: This is the most significant determinant.
- Short Run: Supply is typically inelastic. It's difficult for firms to change production levels quickly because some factors of production (like factory size) are fixed.
- Long Run: Supply becomes more elastic. Firms have enough time to adjust all factors of production—they can build new factories, train more workers, or even enter/exit the industry.
Stocks (Inventories): If a firm has a large stockpile of finished goods, it can respond to a price increase almost instantly by selling its inventory. This makes supply highly elastic. Conversely, if there are no stocks, supply is more inelastic.
Spare Capacity: A firm operating below its maximum possible output has spare capacity. It can easily increase production without incurring large costs, making supply more elastic. A firm already at full capacity will find it difficult and costly to increase output, making supply inelastic.
Substitutability of Factors of Production (Factor Mobility): This refers to how easily a firm can switch its resources (labour, capital) to produce a different good. If factors are highly mobile, the firm can quickly shift to producing the more profitable good, making its supply elastic. For example, a farmer who can easily switch from growing wheat to growing corn has an elastic supply of each.
Time Period (Revisited as the overriding factor): The time horizon influences all other factors. In the long run, firms can overcome production lags, build up stocks, create spare capacity, and find ways to make their factors of production more substitutable. Therefore, supply is almost always more elastic in the long run than in the short run.

Conclusion

This lesson completes our exploration of elasticity, a fundamental tool in economic analysis. You have learned how to measure the responsiveness of suppliers to price changes, a concept symmetric to the price elasticity of demand.

Key Takeaways:

Price Elasticity of Supply (PES) measures the responsiveness of quantity supplied to a change in price. Its value is positive due to the law of supply.
Supply is elastic if $E_{S} > 1$ , inelastic if $E_{S} < 1$ , and unit elastic if $E_{S} = 1$ .
PES can be calculated using the midpoint method for discrete points or the point method ( $E_{S} = \frac{d Q _{S}}{d P} \cdot \frac{P}{Q _{S}}$ ) for supply functions.
The primary determinant of PES is the time period, with supply being significantly more elastic in the long run. Other key factors include the availability of stocks, spare capacity, and the mobility of factors of production.

You are now equipped to analyse both sides of the market with the full toolkit of elasticity. In our next module, we will delve deeper into the demand side by examining the theory of consumer choice, starting with how economists model utility and satisfaction.

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