Price Elasticity of Demand and Supply
Reading: Chapter 5 of Tucker
Overview:
Price Elasticity of Demand: The price elasticity of demand formula measures consumer responsiveness to a change in price.
Calculating Price Elasticity of Demand: Ratio of the percentage change in the quantity demanded of a product to a percentage change in its price.
The general CONCEPTUAL formula for price elasticity of demand:
Ed = percentage change in quantity demanded/percentage change in price
Ed is the elasticity coefficient
The elasticity coefficient represents the percentage change in quantity demanded for each one percent change in price.
Normally we calculate a percentage change as follows: (new value - old value)/(old value). The problem is that if we use this formula for calculating percentage change, we will get a different number for percentage change for an increase than for a decrease.
Example: Suppose that in year 1 a stock sells for $10 per share, in year 2 the price falls to $5 per share, and in year 3 the price returns to $10 per share. What was the percentage change from year 1 to year 2?
-50%.
What was the percentage change from year 2 to year 3?
+100%.
If an unscrupulous stock tout simply took the average of each year's performance of the stock, the average would be:
100-50/2 = 25%!
Wow, let's buy that stock!
Since we get a different percentage change depending on the base value we use, this method is considered to be inadequate for calculating elasticities. We want to get a single elasticity number for a segment of a demand curve, regardless of whether prices are rising or falling.
The midpoint between the two base points is used to solve this issue. To compute the midpoint, the change in quantity demanded is divided by average quantity demanded and the change in price is divided by the average price.
Midpoints formula for CALCULATING price elasticity of demand:
Ed =
(Q2 - Q1)/Qaverage
Divided by:
(P2 - P1)/Paverage
Where:
Q1 is the first quantity demanded
Q2 is the second quantity demanded
Qaverage is the average of Q1 and Q2
P1 is the first price
P2 is the second price
Paverage is the average of P1 and P2
Use the formula above to recalculate the average of each year's stock performance above and see how it provides a more accurate picture of the stock's true performance....
Note that we always take the absolute value of Ed to make it positive and easier to work with.
Comparing Elasticity Coefficients
There are 5 possible results obtained from the midpoints formula. Refer to Exhibit 3 in Tucker.
Elastic demand: condition in which the percentage change in quantity demanded is greater than the percentage change in price. Demand is elastic when the elasticity coefficient is greater than 1.
When demand is elastic, a decrease in price will result in an increase in total revenue.
Total revenue = price multiplied by quantity demanded.
What are some examples of goods or services that have elastic demand?
Inelastic demand: condition in which the percentage change in quantity demanded is less than the percentage change in price. Demand is inelastic when the elasticity coefficient is less than 1.
When demand is inelastic, a decrease in price will result in a decrease in total revenue.
What are some examples of goods or services that have inelastic demand?
Unitary elastic demand: condition in which the percentage change in quantity demanded is equal to the percentage change in price. In this case, the elasticity coefficient is 1.
The total amount of money spent on a good or service does not vary with change in price. Therefore, total revenue will remain the same at any price.
In this extreme case, at a given price, buyers are willing to buy as much of a good or service as a seller is willing to sell. At higher prices, buyers will buy nothing. The demand curve is perfectly horizontal.
In this other extreme case, at any price, demand is always the same. The demand curve is perfectly horizontal.
Why use the complicated midpoints formula? Why not just use the slope of the demand curve to measure consumer responsiveness to a change in price?
Example: Suppose I buy 2 lbs. of coffee each month when coffee costs $5, and 1 lb of coffee each month when coffee costs $7.50. What is the (absolute value of the) slope of the demand curve connecting these two (p,q) combinations? 2.50/1 = 2.5. This suggests that my coffee demand is price-elastic (in other words, that I am quite sensitive to price). Now measure coffee in ounces, where there are 16 ounces per pound. What is the slope of the demand curve connecting these two (p,q) combinations? 2.50/16 = 0.15625. This suggests that my coffee demand is price-inelastic (in other words, that I am quite insensitive to price).
Now use the midpoints formula and show yourself that different units of measure (pounds, ounces) do not affect my elasticity of demand.
Price elasticity changes along a downward-sloping straight-line demand curve from elastic to unitary elastic and finally to inelastic. Total revenue changes depending on price elasticity. Refer to Exhibit 4.
|
Price Elasticity of Demand |
Elasticity Coefficient |
Price |
Total Revenue |
|
Elastic |
Ed > 1 |
Increase |
Decrease |
|
Elastic |
Ed > 1 |
Decrease |
Increase |
|
Unitary elastic |
Ed = 1 |
Increase or decrease |
No change |
|
Inelastic |
Ed < 1 |
Increase |
Increase |
|
Inelastic |
Ed < 1 |
Decrease |
Decrease |
Determinants of Price Elasticity
There are three main factors that determine whether a good or service's price is elastic, unitary elastic, or inelastic.
The availability of substitutes causes the demand for goods and services to be elastic. If a substitute of similar quality and price to the original is available, consumers will switch to that product if the price of the original rises.
The text lists automobiles and chinaware as two examples of products that have elastic demand because they have many substitutes. Others?
If no substitute is available, the price of a good or service is inelastic. What are some examples of goods and services with few substitutes?
The price elasticity of goods and services is directly related to the percentage on one's budget spent on the good or service. If the purchase represents only a small portion of a person's budget, a change in price will generally not affect demand. If, however, the purchase represents a large portion of a person's budget, a change in price may cause the person to look for substitutes or go without.
Price elasticity of demand can often be divided into short-term and long-term categories.
In the short-term, demand may be inelastic. Over the long-term, demand may become elastic. Explain.
Other Elasticity Measures (For all other elasticity measures we care about the sign (+,-) and thus we do NOT take absolute value)
The general CONCEPTUAL formula is:
Ey = percentage change in quantity demanded/ percentage change in income
where Ey is the income elasticity demand coefficient.
Note: We can calculate income elasticity of demand using the midpoints formula.
For a normal good or service, income elasticity of demand is positive. For an inferior good or service, income elasticity of demand is negative. Contrast a normal good or service with an inferior good or service to illustrate this point.
The general CONCEPTUAL formula is:
Ec = percentage change in quantity demanded of one good/percentage change in price of another good
where Ec is the cross-elasticity coefficient.
Note: We can calculate cross elasticity of demand using the midpoints formula.
Two goods or services are substitutes when Ec > 0 , or a positive value. The larger the positive coefficient, the greater the substitutability between goods.
Two goods or services are compliments when Ec < 0, or a negative value. The large the negative coefficient, the greater the complementary relationship.
The formula is:
Es = percentage change in quantity supplied/percentage change in price
where Es is the price elasticity of supply.
Note: We can calculate price elasticity of supply using the midpoints formula.
Supply is:
Price Elasticity and the Impact of Taxation
Price elasticity affects how the burden of taxation is spread among sellers and consumers.
Tax incidence: the share of tax ultimately paid by consumers and sellers.
If the demand curve slopes downward and the supply curve slopes upward, sellers cannot raise the price by the full amount of the tax. Sellers and consumers share the burden of paying the tax.
If demand is perfectly inelastic, however, demand remains unchanged regardless of price. In this case, sellers increase the price by the amount of the tax and consumers pay the entire tax.
If the government imposed an excise tax of 10 percent on all blue Honda Civics sold in Humboldt County, who do you think would bear the largest burden of the tax--consumers or producers? Why?
If the government imposed an excise tax of 10 percent on all automobiles sold in the U.S., who do you think would bear the largest burden of the tax--consumers or producers? Why?