ELASTICITY OF DEMAND AND SUPPLY

"Elasticity" measures the "change relationship" of 2 variables not in an absolute numeric way but in a "percentage" ("proportional" - "relative") way. The measure of "elasticity" takes the standard measure of "slope" and converts it into a percentage calculation by dividing each change in a variable by its "base."

Slope has the general formula (in x and y):

Elasticity has the general formula (in x and y):

Terminology:

1. The general concept is called "elasticity of demand" (and "elasticity of supply")
2. Particular categories (under elasticity of demand) are:
   • price elasticity of demand (sometimes called "own price elasticity of demand")
     • The percentage change in quantity demanded brought about by a one percent change in the good’s own price: (% change in Q_d)/(% change in P)
   • income elasticity of demand
     • The percentage change in quantity demanded brought about by a one percent change in income: (% change in Q_d)/(% change in I)
   • cross price elasticity of demand (or just "cross elasticity of demand")
     • The percentage change in quantity demanded (of good x) brought about by a one percent change in the price of a related good (y): 
               (% change in Q^x_d)/(% change in P^y)
       
       (Notice that all categories have the effect on "quantity demanded" (or Q_d) of a change in one of the variables, from our original Ch. 4 list, which affect demand
3. Within categories we have 3 cases (price elasticity of demand to illustrate):
   • price inelastic demand (price elasticity coefficient E_p< 1)
   • unit price elasticity demand (price elasticity coefficient E_p = 1)
   • price elastic demand (price elasticity coefficient E_p > 1)

Observations:

Elasticity is a dimensionless measure: it is a percentage divided by a percentage.

Just the value is stated: for example, "price elasticity of demand of 2.0"

The minus sign is ignored for purposes of interpretation

Price elasticity of demand changes value along a straight-line demand function

Look at an example:

	P	Q	TR (= P x Q)
Initial values	6	12	72
Case # 1	8	11	88	price inelastic demand
				(Ep < 1)
Case # 2	8	9	72	unit price elastic demand
				(Ep = 1)
Case # 3	8	8	64	price elastic demand
				(Ep >1)

Comment:

The demand curve is inverse. A price increase always leads to a quantity decrease (and vice versa), so that there are opposite influences on Total Revenue (TR=P x Q). The question is, which change (the price change or the quantity change) predominates? This is the question which elasticity asks.

• If when price is raised, the price change predominates over the quantity change, TR will rise. (E_p < 1). And vice versa.
• If when price is raised, the quantity change and the price change are relatively (percentage) the same, they are mutually offsetting, and TR will not change. (E_p = 1). And vice versa.
• If when price is raised, the quantity change predominates over the price change, TR will fall. (E_p >1). And vice versa.

The definition and the formula for price elasticity of demand are:

1. So if the fraction E_P < 1, that means:
   % change in quantity demanded < % change in price and quantity demanded is relatively insensitive to a price change, and demand is said to be price inelastic. 
2. But if the fraction E_P >1, that means:
   % change in quantity demanded > % change in price and quantity demanded is relatively sensitive to a price change, and demand is said to be price elastic.
3. Of course if E_P = 1, 
   % change in quantity demanded = % change in price and demand is said to be unit price elastic

Since with price-inelastic demand, E_P < 1, % change in quantity demanded < % change in price, it stands to reason that an INCREASE in price leads to a INCREASE in Total Revenue AND a DECREASE in price leads to an DECREASE in Total Revenue

While with price-elastic demand, E_P > 1, % change in quantity demanded > % change in price, it stands to reason that an INCREASE in price leads to a DECREASE in Total Revenue AND a DECREASE in price leads to an INCREASE in Total Revenue 

The factors which are said to affect the relative price elasticity of demand can be remembered as follows:

The greater is the:

1. Passage of time
2. Availability of substitutes
3. Percentage the item represents in the budget

then the greater will be the degree of price elasticity of demand.

Therefore, an item with many substitutes, or which represents a major expenditure, will tend to have an elasticity coefficient E_P greater than one, in which a given percentage price change will produce a larger percentage change in the quantity demanded.

In the case of having many substitutes, consumers "don’t have to put up with a price increase"; while with an item representing a major portion of a person’s budget such as a consumer durable good, the price increase will be very evident to the consumer and may make the consumer think twice about buying it.

Of course, with additional time, demand also becomes more price elastic, that is, consumers are more sensitive to price increases in the long run than in the short run, because they have more time to adjust their consumption habits to conserve the now-higher-priced good.

Class Notes | Clint Johnson |  Economics & Finance | Departments & Majors
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