cfa study session #4: economics: elasticity

Following quantitative methods comes an entire 500 page book devoted exclusively to economics. Separated into 3 sections, the economics portion of the CFA exam focuses on microeconomics, macroeconomics, and monetary & fiscal policy. This blog post will deal specifically with the first section: microeconomics, which includes price elasticity, market theory, and the organization of production & output.

We start with understanding the "price elasticity of demand," which simply measures the responsiveness of the quantity demanded of a product relative to changes in the price for that same product. This degree of responsiveness determines how elastic the products is, that is, whether it is elastic (very responsive), inelastic (not responsive), or unit elastic (when change in demand equals change in price). The equation is:

elasticity of demand = *% change in quantity demanded / % change in price
* % change is calculated by dividing the difference between the starting and ending values by an average of the starting and ending values (rather than dividing by the beginning value, which is more common when calculating % changes) to get a more accurate elasticity ratio.

Intuitively we know that some products, such as oil, are highly inelastic. In other words, the world will always demand oil regardless of the price, as evidenced when a barrel of oil reached an all-time peak of $147.27 on July 11, 2008. In contrast, a product such as a t-shirt is very elastic. Unless it's a Ralph Lauren polo t-shirt, most people consider one t-shirt to be very similar to any other, and therefore will purchase from whichever manufacturer has the lowest price. Elasticity isn't always a foregone conclusion, and it can change over time. For example, when Apple launched the iPod they successfully differentiated their mp3 from their competitors, turning an otherwise elastic commodity into an inelastic "must-have" brand. By developing a strong brand image and brand loyalty, Apple was able to charge a premium by changing the elasticity for their iPod.

Products tend to be elastic when there a large number of substitutes available. For example, an increase in the price of hamburgers will lead to a decrease in their consumption, because hamburgers have an elastic demand curve, and an concomitant increase in consumption of hot dogs (all other things being equal), because hot dogs are consider a viable substitute for hamburgers. There is no accounting for taste! This example sets the stage for the next step in understanding elasticity, which is calculating "cross elasticity" to determine the responsiveness of demand relative to price based on more than one product, such as hamburgers and hot dogs.

Using the above example, we can calculate whether two different products are substitutes (positive cross elasticity) or compliments (negative cross elasticity). If the price of hamburgers doubles from $2 to $4 each, and this results in an increase in hot dogs consumed from 8 to 14, then we can calculate that the two products are substitutes, because resulting cross elasticity ratio is positive .817, calculated as follows:

= (8-14)/11 / (4-2)/3
= 5.45% / 6.67%
cross elasticity = .817

The higher the number, the more magnified the difference in quantity demanded in one good relative to an incremental change in price of the substitute good. And of course the same holds true working in reverse for compliment goods, such as soda and hotdogs, which we would expect to have a negative cross elasticity.

Besides measuring the elasticity of demand, and cross elasticity, we can similarly calculate "income elasticity" by dividing the % change in quantity demanded of a product by a % change in income. In other words, when we earn more money we are more likely to purchase "luxury" products (i.e. steak and lobster), which have high elasticity, and less likeley to purchase inelastic "inferior" products (i.e. potatoes and rice). In this case a negative ratio indicates an inferior good, and a positive ratio indicates a luxury good, which is highly responsive to changes in income and therefore very elastic.

Elasticity of supply operates along similar lines as it does for demand. We calculate supply elasticity by dividing the % change in quantity supplied by the % change in price. The degree of responsiveness of supply to price often depends on the number of substitutes available, and whether the time-frame for making a supply decision is momentary, short-term, or long-term in nature.

Beyond asking you to calculate elasticity, a typical question may involve understanding the effect of elasticity on demand and revenue. For example, "For a particular company's product, the % change in quantity demanded is smaller than the % change in price that caused the change in quantity demanded. If the company increased the price of that product, total revenue from sales of that product would most likely:
A. increase and demand in elastic
B. decrease and demand is elastic
C. increase and demand is inelastic

The answer is C. We must first determine whether or not the product is elastic or inelastic before we can determine its effect on quantity demanded and ultimately revenue. The question tells us that price has little effect on quantity demanded (in fact, it's smaller!). If a product is inelastic then people will continue to buy it even if the price goes up (like the price of oil). Therefore, even if the same amount of product is sold, but the price they are charging has increased, then by definition the total revenue must also increase.