Elasticities (Price, Income, Cross)

Introduction

Ever found yourself wondering why demand for certain products plummets after even a small price hike, while other products seem to keep selling no matter how pricey they get? Welcome to the concept of elasticity—one of those fundamental ideas in economics that can sometimes feel, well, a bit abstract at first. I recall the first time I wrestled with this topic in graduate school. I was running a small pop-up coffee stand on weekends and wanted to figure out why a small increase in the latte price caused a huge drop in sales, yet raising the price of muffins by 50 cents didn’t faze customers much. That real-world puzzle took me right into elasticity, and discovering the reasons was a total “aha!” moment.

In investment and financial analysis, understanding elasticity helps you predict how demand or supply will react to changes in price or consumer income. This is especially relevant when you consider revenue projections, cost structures, and even macroeconomic cycles. If you’re looking at equities in the retail sector, for instance, knowledge of elasticity can help you analyze how well a firm’s products might withstand price fluctuations or an economic downturn that affects consumer income.

Below, we’ll discuss the major types of elasticity—Price Elasticity of Demand, Price Elasticity of Supply, Income Elasticity of Demand, and Cross-Price Elasticity of Demand—and how each can be interpreted and applied.

We’ll keep the discussion approachable but also tie everything back to real-world applications, as well as highlight some typical pitfalls that Level I candidates (and yes, even more experienced professionals) sometimes encounter.

Price Elasticity of Demand

Price Elasticity of Demand (PED) measures how sensitive the quantity demanded of a good or service is to changes in its price. Formally, the PED is:

where \(Q_d\) is the quantity demanded and \(P\) is the price of the good.

• Elastic Demand: |PED| > 1
• Inelastic Demand: |PED| < 1
• Unit Elastic: |PED| = 1

An “elastic demand” means a small percentage change in price results in a larger percentage change in quantity demanded. Think about items like branded cereals: if you bump the price up by just a bit, some shoppers switch to cheaper brands instantly. Conversely, products such as life-saving medications typically have “inelastic demand,” because even if the price changes, the demand changes by a smaller percentage (people need those medications regardless of cost).

Main Determinants of Price Elasticity of Demand

• Availability of Substitutes: The more substitute products available, the more elastic the demand.
• Necessity vs. Luxury: Necessities tend to be less price-sensitive, while luxury items can be highly elastic.
• Time Horizon: Demand becomes more elastic over time as consumers adjust their consumption patterns.
• Share of Consumer Budget: Goods that form a large portion of one’s budget (like housing) tend to have more elastic demand.

Price Elasticity of Demand and Total Revenue

One classic use of PED is examining its relationship with total revenue (TR), defined as:

• When demand is elastic, an increase in price reduces total revenue (and a decrease in price can increase total revenue).
• When demand is inelastic, an increase in price can increase total revenue, because the drop in quantity demanded is relatively small.

Here’s a small flowchart capturing the interplay between price changes, quantity demanded, and total revenue under different elasticities:

    flowchart LR
	A["Price <br/>Increases"] --> B["Quantity <br/>Demanded Falls"]
	B["Quantity <br/>Demanded Falls"] --> C["Impact <br/>on Revenue <br/>Depends on <br/>Demand Elasticity"]
	C["Impact <br/>on Revenue <br/>Depends on <br/>Demand Elasticity"] --> D["If Demand is <br/>Elastic: Total <br/>Revenue <br/>Decreases"]
	C["Impact <br/>on Revenue <br/>Depends on <br/>Demand Elasticity"] --> E["If Demand is <br/>Inelastic: Total <br/>Revenue <br/>Increases"]

This interplay is critical for corporate pricing strategies. Analyzing the demand elasticity of the goods or services that a firm sells can help a manager decide whether to raise or lower prices to maximize revenue.

Price Elasticity of Supply

Price Elasticity of Supply (PES) measures how quickly producers respond to a change in price by adjusting the quantity they supply. Formally:

where \(Q_s\) is the quantity supplied.

Some goods or services—like digital products—can be scaled up quickly at relatively low cost. That often results in highly elastic supply since a small increase in price might spur a large increase in quantity supplied (e.g., streaming services or e-books). But if you’re talking about farmland or specialized rare microchips, supply can remain relatively inelastic in the short run because you just can’t crank out more farmland or specialized manufacturing capacity overnight.

Determinants of Price Elasticity of Supply

• Production Timeframe: For many goods, supply becomes more elastic over the long run.
• Ease of Storing Inventory: Goods that can be stored easily can have more elastic supply in the short run.
• Availability of Production Inputs: If inputs are readily available and factor markets are flexible, supply can adjust more readily to price changes.

Understanding PES is especially important for industries like commodities (e.g., oil). We often talk about “supply shocks,” where supply is slow to adjust to big swings in global demand, leading to large price fluctuations.

Income Elasticity of Demand

Income Elasticity of Demand (YED) helps us understand how changes in consumer income affect demand. The formula is:

If YED is greater than zero, the good is typically considered “normal” (demand increases as income rises). If YED is less than zero, the good is “inferior,” meaning demand goes down as people’s incomes go up (they opt for higher-quality options).

Normal vs. Inferior Goods

• Normal Goods (YED > 0): Luxury cars, gourmet meals, or high-end fashion. Demand increases faster than income if the good is a luxury (YED > 1).
• Inferior Goods (YED < 0): Basic staples or cheaper substitutes like store-brand groceries. As income increases, demand for these goods might drop.

In a portfolio management context, analyzing a company’s product line in relation to the economic cycle can be insightful. For instance, during recessions, some consumers cut back on high-end goods and switch to lower-priced alternatives. Income elasticity helps you anticipate which companies might face strong headwinds (e.g., luxury brands) and which might stay stable or even see demand rise (e.g., discount retailers offering budget-friendly items).

Cross-Price Elasticity of Demand

Cross-Price Elasticity of Demand (XED) measures the responsiveness of demand for one good (say, Good A) to a change in the price of another good (say, Good B). The formula is:

• Substitutes (XED > 0): If the price of one good goes up, demand for its substitute increases. A rise in the price of coffee might increase the demand for tea, assuming consumers see them as fairly interchangeable sources of caffeine.
• Complements (XED < 0): If the price of one good goes up, demand for its complement decreases. Think about printers and ink cartridges: if printer prices rise significantly, fewer people might buy printers—and, by extension, fewer ink cartridges.

This concept comes up in multi-product firms and in analyzing broader industry trends. A beverage company, for example, might assess how changes in soda prices influence the demand for bottled water or energy drinks.

Elasticity Categories at a Glance

Let’s summarize the categories of elasticity with a quick table:

Real-World Applications and Insights

• Pricing Strategy: If a firm identifies that the demand for its flagship product is highly elastic, raising prices could be risky for revenue. Conversely, knowledge of inelastic demand might allow modest price increases without significantly hurting sales.
• Forecasting Demand Shifts: Investment analysts often project how demand might change if consumers’ incomes rise or if competing products shift in price.
• Policy and Taxation: Governments rely on elasticity to forecast the effects of taxes or subsidies on the overall market. For instance, a tax on cigarettes (where demand is inelastic) may not drastically reduce smoking but can increase government revenue.
• Complementary Product Lines: Firms might set prices for printers cheaply knowing that the inelastic demand for ink cartridges (a complementary product) will generate profits later.

Common Missteps and Pitfalls

• Confusing Direction of Causality: Remember that XED looks at how changes in Good B’s price affect Good A’s demand, not the other way around.
• Misinterpreting Sign: A negative sign often indicates how quantity moves in the opposite direction of price. Keep an eye on whether the question is about complements vs. substitutes, or normal vs. inferior goods.
• Overlooking Time Horizons: A commodity can be inelastic in the short run but becomes more elastic in the long run as alternatives or new technology appear.

Linking Elasticities to Other Topics

Earlier in this chapter, we covered how markets can experience surpluses or shortages (Section 1.2) and how consumer and producer surplus arises (Section 1.3). Elasticity underpins these concepts:

• In Surplus or Shortage Scenarios: Highly elastic supply or demand might quickly eliminate a surplus/shortage as prices adjust.
• In Calculating Surpluses: The shape of the demand or supply curve (linked to elasticity) determines how changes in price shift the distribution of consumer and producer surplus.

Moreover, as you progress into advanced areas like macroeconomic forecasting (discussed further in Chapter 3), elasticity insights can come in handy. During recessionary phases, for example, goods with high income elasticity might see a significant drop in demand, influencing business cycle analysis.

Exam Tips and Best Practices

1. Know Your Formulas: Elasticity formulas are straightforward but watch out for the negative sign in price elasticity of demand. Typically, we talk about PED in absolute value terms.
2. Practice Interpreting Numerical Values: Be comfortable deciding whether a good is elastic, inelastic, or unit elastic—especially with borderline cases.
3. Watch for Extremes: Perfectly inelastic demand means quantity demanded doesn’t change at all when price changes (vertical demand curve). Perfectly elastic demand means quantity demanded changes dramatically at a specific price (horizontal demand curve).
4. Understand Real-World Scenarios: Command an example or two in your mind for each elasticity concept—this will help you in scenario-based questions.

References

• Sloman, J. (2013). “Economics.” Pearson.
• Samuelson, P. A., & Nordhaus, W. D. (2010). “Economics.” McGraw-Hill.
• Investopedia: Elasticity

Test Your Knowledge: Price, Income, and Cross-Elasticities Quiz