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Chapter 5: Elasticity and Its Application

Chapter Objectives Little Picture: learning how price changes affect the quantity of goods and services

sold in markets (i.e., elasticity).

Big Picture: learning about elasticity to obtain a better understanding of

microeconomics, i.e., what forces determine the price (and market quantity) of a good

or service.

This chapter is the most mathematical that you will encounter this term. (Chapters

13-17 are more graphical and geometric than mathematical, so by the time we reach

them, make sure you are ready for a good bit of spatial analysis. Be sure to read

chapter 2's appendix, "Graphing: A Brief Review" if you haven't already. If you have

read it, reviewing the points on which you are weakest and practicing drawing graphs

with pen and paper won't hurt either. For example, graph your utility, telephone, or

other bills over the months of the year to view any obvious or not-too-obvious

relationships between the time of the year and spending. And so on.)

Please read this chapter carefully. The good news is that in this chapter we return to

studying the demand and supply sides of the market individually. There are no shifts

of curves or more than one curve to deal with at a time. However, as mentioned

above, there is some math: arithmetic and dividing fractions. These calculations are

made for observing how a change in a variable such as price or income affects the

quantity demanded, supplied, or both in a market. This concept is known as

elasticity. It is of great interest to business owners or decision makers (from

proprietors to CEOs) to investors to anyone else who is interested in knowing the

extent to which product sales will be affected by changes in variables such as product

price or consumer incomes.

Truth be told, elasticity was a concept stolen by economists from the discipline of

physics. In Newtonian mechanics, the concept is used to describe the extent to which

"rigid" bodies can have their dimensions altered by pulling, pushing, twisting, or

compression. In microeconomics, the extent to which the quantity of goods and

services sold can be pulled or pushed by a price change is of interest. For example,

price elasticity of demand is concerned with observing how much of a product

consumers purchase in response to a change in the product’s price. On the supply side

of the market, elasticity refers to how much suppliers alter the quantity of a product

they supply to the market in response to a change in the product’s price.

(Other elasticities such as income and cross-price elasticity of demand are

important, especially if you decide to enter a business field such as market research

where consumer demand patterns are closely scrutinized. However, given that it's

usually enough of a task for beginning students to understand price elasticity of

demand, we will examine other elasticities besides price, but not in great detail).

price elasticity of demand (simple formula) = % change in quantity demanded

% change in price

The way to read the fraction on the right side of the equation above is, "a percentage

change in quantity demanded caused by a percentage change in price." This is a good

way of emphasizing the relationship between price and quantity--quantity changes in

response to price. Notice the exact variables involved in the ratio as well: percentage

change, not just “change” or “quantity demanded” divided by price.

Remembering the law of demand ("price and quantity are inversely related") and that

on the demand side of the market there is a negative relationship between price and

quantity, we would expect the above formula to always produce a number that is

negative (-) in value. We will follow the convention mentioned by Mankiw of

dropping the minus sign.

After the simple version of elasticity is examined, the midpoint method is introduced

and advertised by Mankiw as a "better way to calculate percentage changes and

elasticities." (I leave it to you to answer as a discussion issue as to why it is

better.) The midpoint formula at the end of section 5-1c looks frightening enough and

you can read Mankiw's adequate explanation. However, in terms of dividing one

fraction by another (red/blue in the formula immediately below), for the purposes of

memorization an easier version of the midpoint formula is:

price elasticity of demand (midpoint formula) = Q2-Q1

Average of Q2 and Q1

P2-P1

Average of P2 and P1

Remember: "Quantity over price, second minus first. Both over their

averages." (You already know that an average of two numbers is adding the two

numbers and dividing by the number two. This gets us a slightly less scary-looking

equation with no "double-nested" fractions!)

Let's work an example from Figure 1, graph (d).

For the numbers provided in this graph of a price increase from $4 to $5:

P1= 4

P2=5

Q1=100

Q2=50

Avg. of Q2 and Q1= 50 + 100 = 150/2 = 75

Avg. of P2 and P1= 5 + 4 = 9/2 = 4.5

Here is the calculation using the simpler version of the midpoint formula:

50-100

75 = -0.67 = -3.05 = 3.05

(dropping the minus sign)

5-4 0.22

4.5

Compare this to the answer produced using the simple formula:

= % change in quantity demanded

% change in price

= -67 = -3.0455 = 3.05

+22

In this example, the answers from the two formulas are equal (3.05). Practice these,

as they will reappear on the next exam. By the way, in case you're wondering, the

technical name for the numerical result of these formulas (3.05 in the two examples

above) is the elasticity coefficient. [Mankiw dances around naming it, and math

majors who take the class always ask what the variable symbol is (sometimes the

Greek letter nu, sometimes epsilon) and its technical name. They know no one in

their right mind--even an economist--would represent a variable symbolically with the

phrase "price elasticity of demand!"]

Take a look at the other four graphs (a, b, c, and e) in Figure 1 besides graph

(d). Remember, if the absolute value (value without the minus sign) of the price

elasticity coefficient is:

< 1, then demand is inelastic

> 1, then demand is elastic

= 1, then demand is unit elastic

For the elasticity coefficient 3.05 calculated above, since 3.05 > 1, demand is

elastic. As you'll see later in Figure 5, the same applies for price elasticity of supply,

although there's no issue of a minus sign attaching to the coefficient because from the

law of supply, quantity supplied and price are positively related.

By the way, here's a helpful little mnemonic (memory device) for remembering the

relationship between the value of the elasticity coefficient and what type of elasticity

prevails. Remember the abbreviation "i.e." (id est, from Latin which means "that

is"). Jot down i.e. and put a number 1 between the "i" and the "e" so you get

"i. 1 e." Viewed as if sitting on a number line, this should help you remember that any

elasticity-coefficient value of less than one is a value that is inelastic ("i.") and any

elasticity coefficient value greater than one ("e.") is elastic (1 is the boundary between

inelastic and elastic).

Total Revenue and the Price Elasticity of Demand Here's the second tricky area of the material in this chapter: total revenue (price times

quantity or P*Q) depends on price elasticity and changes in relation to it. If demand

is inelastic, an increase in price causes an increase in total revenue. If demand is

elastic, an increase in price causes a decrease in total revenue.

Before ending, let's summarize all the relationships we've covered so far in one table:

Type of

Demand

Elasticity

Coefficient

Value

Price and Total Revenue

inelastic < 1 move in same direction

elastic > 1 move in opposite direction

unit elastic = 1 total revenue doesn't change when

price changes

Discussion Topics (topics requiring examples are marked with an asterisk *)

Please copy these topics exactly as written--shortening them can cause you to

omit follow-up questions and thus lose points.

1. determinants of price elasticity of demand (choose one of the four and provide

an example for it)*

2. price elasticity of demand (provide a numerical example using either the simple

or midpoint formula)*

3. What purpose does the midpoint method serve?

4. elasticity coefficient*

5. Variety of Demand Curves (Figure 1--describe one of the five with its elasticity

value, then provide a verbal example)*

6. In the seven elasticities from the real world, which of the named goods are

elastic? Which are inelastic?

7. three general rules describing the relationship between total revenue and the

price elasticity of demand (choose one, provide a numerical example)*

8. Using income elasticity of demand, how does one recognize an inferior good?

9. cross-price elasticity of demand*

10. price elasticity of supply*

11. Name and explain a key determinant of price elasticity of supply in most

markets (provide a numerical example)*

12. Summarize how the price elasticity of supply is computed and provide a

numerical example*

13. Variety of Supply Curves (Figure 5--describe one of the five with its elasticity

value, then provide a verbal example)*

14. Explain how price elasticity of supply can vary along a supply curve and

provide an example*

15. How can good news for farming be bad news for farmers?

16. Why did OPEC fail to keep the price of oil high?

17. Does drug interdiction increase or decrease drug-related crime?