Problem 1 :Yesterday, the price of envelopes was $3 a box, and Julie was willing to buy 10 boxes. Today, the price has gone up to $3.75 a box, and Julie is now willing to buy 8 boxes. Is Julie's demand for envelopes elastic or inelastic? What is Julie's elasticity of demand?
Problem 2 :If Neil's elasticity of demand for hot dogs is constantly 0.9, and he buys 4 hot dogs when the price is $1.50 per hot dog, how many will he buy when the price is $1.00 per hot dog?
Problem 3 :Which of the following goods are likely to have elastic demand, and which are likely to have inelastic demand?
Home heating oil
Pepsi
Chocolate
Water
Heart medication
Oriental rugs
Problem 4 :If supply is unit elastic and demand is inelastic, a shift in which curve would affect quantity more? Price more?
Problem 5 :Katherine advertises to sell cookies for $4 a dozen. She sells 50 dozen, and decides that she can charge more. She raises the price to $6 a dozen and sells 40 dozen. What is the elasticity of demand? Assuming that the elasticity of demand is constant, how many would she sell if the price were $10 a box?
1. To find Julie's elasticity of demand, we need to divide the percent change in quantity by the percent change in price.
% Change in Quantity = (8 - 10)/(10) = -0.20 = -20%
% Change in Price = (3.75 - 3.00)/(3.00) = 0.25 = 25%
Elasticity = |(-20%)/(25%)| = |-0.8| = 0.8
Her elasticity of demand is the absolute value of -0.8, or 0.8. Julie's elasticity of demand is inelastic, since it is less than 1.
2. This time, we are using elasticity to find quantity, instead of the other way around. We will use the same formula, plug in what we know, and solve from there.
Elasticity =
And, in the case of John, %Change in Quantity = (X – 4)/4
Therefore :
Elasticity = 0.9 = |((X – 4)/4)/(% Change in Price)|
% Change in Price = (1.00 - 1.50)/(1.50) = -33%
0.9 = |(X – 4)/4)/(-33%)|
|((X - 4)/4)| = 0.3
0.3 = (X - 4)/4
X = 5.2
Since Neil probably can't buy fractions of hot dogs, it looks like he will buy 5 hot dogs when the price drops to $1.00 per hot dog.
3. Elastic demand: Pepsi, chocolate, and Oriental rugs
Inelastic demand: Home heating oil, water, and heart medication
4. Shifting the demand curve would affect quantity more, and shifting the supply curve would affect price more.
5. To find the elasticity of demand, we need to divide the percent change in quantity by the percent change in price.
% Change in Quantity = (40 - 50)/(50) = -0.20 = -20%
% Change in Price = (6.00 - 4.00)/(4.00) = 0.50 = 50%
Elasticity = |(-20%)/(50%)| = |-0.4| = 0.4
The elasticity of demand is 0.4 (elastic).
To find the quantity when the price is $10 a box, we use the same formula:
Elasticity = 0.4 = |(% Change in Quantity)/(% Change in Price)|
% Change in Price = (10.00 - 4.00)/(4.00) = 1.5 = 150%
Remember that before taking the absolute value, elasticity was -0.4, so use -0.4 to calculate the changes in quantity, or you will end up with a big increase in consumption, instead of a decrease!
-0.4 = |(% Change in Quantity)/(150%)|
|(%Change in Quantity)| = -60% = -0.6
-0.6 = (X - 50)/50
X = 20
The new demand at $10 a dozen will be 20 dozen cookies.
Question: Do you think the price elasticity of demand for Ford sport-utility vehicles (SUVs) will
increase, decrease, or remain the same when each of the following events occurs? Explain your
answer.
a. Other car manufacturers, such as General Motors, decide to make and sell SUVs.
b. SUVs produced in foreign countries are banned from the American market.
c. Due to ad campaigns, Americans believe that SUVs are much safer than ordinary passenger cars.
d. The time period over which you measure the elasticity lengthens. During that longer time, new
models such as four-wheel-drive cargo vans appear.
Answer to Question:
a. The price elasticity of demand for Ford SUVs will increase because more substitutes are available.
b. The price elasticity of demand for Ford SUVs will decrease because fewer substitutes are available.
c. The price elasticity of demand for Ford SUVs will decrease because other cars are viewed as less of
a substitute.
d. The price elasticity of demand for Ford SUVs will increase over time because more substitutes (such
as four-wheel-drive cargo vans) become available.
Question: What can you conclude about the price elasticity of demand in each of the following
statements?
a. “The pizza delivery business in this town is very competitive. I’d lose half my customers if I raised the
price by as little as 10%.”
b. “I owned both of the two Jerry Garcia autographed lithographs in existence. I sold one on eBay for a
high price. But when I sold the second one, the price dropped by 80%.”
c. “My economics professor has chosen to use the Krugman/Wells textbook for this class. I have no Practice Questions and Answers from Lesson I-7: Elasticity
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choice but to buy this book.”
d. “I always spend a total of exactly $10 per week on coffee.”
Answer to Question:
a. This statement says that a 10% increase in price reduces the quantity demanded by 50%. That
is, the price elasticity of demand is
-50%/10% = -5
So demand is elastic.
b. The fact that it was necessary for price to drop by 80% in order to sell one more unit (an increase in
quantity of 67%, using the midpoint method) indicates that the demand for Jerry Garcia autographed
lithographs is inelastic.
c. There is no substitute available, so demand is inelastic. (Although, over time, as more used
Krugman/Wells textbooks become available, the price elasticity of demand will increase.)
d. Demand is unit-elastic: no matter what the price of coffee is, the total revenue to the producer (which
is my total expenditure on coffee) remains the same.
Practice Problems on Elasticity
1. Anna owns the Sweet Alps Chocolate store. She charges $10 per pound for her hand made chocolate. You, the economist, have calculated the elasticity of demand for chocolate in her town to be 2.5. If she wants to increase her total revenue, what advice will you give her and why? Be able to explain your answer.
2. If the cross elasticity of demand between peanut butter and milk is -1.11, then are peanut butter and milk substitutes or complements? Be able to explain your answer.
3. A 10 percent increase in income brings about a 15 percent decrease in the demand for a good. What is the income elasticity of demand and is the good a normal good or an inferior good? Be able to explain your answer.
4. If the price of a good increases by 8% and the quantity demanded decreases by 12%, what is the price elasticity of demand? Is it elastic, inelastic or unitary elastic?
5. Discount stores sell relatively elastic goods.Ceteris paribus, explain why selling at a relatively low price is profitable for them?
ANSWERS
1. Anna should lower her price. Her price elasticity of demand for chocolate is elastic (greater than one) and therefore, when she lowers her price she will sell a lot more chocolate. The greater quantity sold will make up for her lower price, increasing her total revenue. In other words, she is selling at a lower price but making up for it in volume of sales.
2. Peanut butter and milk are complements because a negative cross price elasticity of demand means that as the price of milk goes up, the demand for peanut butter goes down. This would indicate that when the price of milk goes up, we buy less milk and we are also buying less peanut butter (so we must buy these together -- they are complements).
3. -15%/10% = -.15/.10 = -1.5. Remember the elasticity is always read as the absolute value or a positive number, so it is 1.5 (elastic, or greater than one). The good is an inferior good because the sign is negative, indicating that an increase in income will bring a decrease in the demand for the good.
4. -12%/8% = -.12/.08 = -1.5. Again, drop the negative sign, so the elasticity is 1.5. This means it is elastic (greater than one).
5. It is profitable because with elastic goods, dropping the price lower can bring them a lot more business. Therefore, at the low prices they can sell a large volume of goods, making up for the lower prices and bringing in more revenue (P x Q).