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Foundations of Economic Analysis
Homework #3
Stratton
Name _________Key________
Objective: to provide practice and assessment of your understanding of Elasticity. (Hint: you may
want to work out your answers on another sheet of paper and transfer your work to this one to
avoid submitting a messy worksheet.) {See HW03_Elast for graphs}
Instructions: For each term, write a short definition in your own words and explain the
significance of the term in the space provided or attach additional sheets if necessary. Each
numbered question is worth 2 points – total 42 points.
Definitions:
1.
Elasticity of demand – A measure of how responsive the quantity demanded is to a
change in the price of a commodity. Measured as the percentage change in quantity
demanded divided by the percentage change in price. Allows us to estimate magnitudes
of changes in the quantity demanded as the price changes.
2.
Income elasticity of demand – A measure of how responsive the quantity demanded is to
a change in consumer income. Measured as the percentage change in quantity demanded
divided by the percentage change in income. It is used to identify normal and inferior
goods.
3.
Elasticity of supply – A measure of how responsive the quantity supplied is to a change
in the price of a commodity. Measured as the percentage change in quantity supplied
divided by the percentage change in price. Allows us to estimate magnitudes of changes
in the quantity supplied as the price changes.
4.
Cross-price elasticity of demand – A measure of how responsive the quantity demanded
of one commodity (A) is to a change in the price of a second commodity (B). Measured
as the percentage change in quantity of A demanded divided by the percentage change in
the price of B. Use to determine if two goods are complements, substitutes or unrelated in
consumption.
5.
Marginal revenue – The additional revenue (sales receipts) associated with the sale of one
additional unit of a commodity. Measured as TR / Q Used to determine if revenues
x
increase or decrease with a change in output and to determine the profit maximizing
output.
6.
Average revenue – Average revenue is the price of the commodity. It is calculated as
total revenue divided by the quantity sold. TR / Qx Is the same as price or the product for
non-discriminating firms.
7.
Inelastic demand – Demand is considered inelastic (at a specific price) if the absolute
value of the own price elasticity of demand is less than unity. That is, if the percentage
change in quantity demanded is less than the percentage change in price. Or that it is
relatively unresponsive to changes in price. As price is increased revenue also increases
along an inelastic demand curve.
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8.
Perfectly inelastic demand – Demand is considered perfectly inelastic quantity demanded
is independent of the price. That is, if the quantity demanded is the same at all prices or if
the demand curve is vertical. Very few examples, though it is important as a limiting
case.
9.
Luxury good – A good is considered a luxury if its income elasticity of demand is
positive and greater than one. Thus, as one’s income increases a larger part of one’s
budget is devoted to the purchase of the good. Luxuries are goods that are not typically
purchased by individuals with low income, but are by those with high income.
10. Inferior good – A good is considered inferior if its income elasticity of demand is
negative. This term has little to do with the quality of the good. It simply indicates that as
one’s income increases, one tends to buy less of the good. Knowing this can help
estimate changes in the market for such goods.
Instructions: Answer the questions in the space provided or attach additional sheets if necessary
Problems
Scenario:
Below is a hypothetical world market demand for coffee beans.
Qx = 12.5 – 10Px
Price
(Dollars per pound)
1.10
1.09
1.08
1.07
1.06
1.05
1.04
1.03
1.02
1.01
1.00
Coffee beans
(billions of pounds)
1.5
1.6
1.7
1.8
1.9
2.0
2.1
2.2
2.3
2.4
2.5
1. Calculate the arc price elasticity of demand as the price increases from $1.05 to $1.06.
One arc elasticity formula is: [(Q2 – Q1) / (P2 – P1)] * [(P2 + P1) / (Q2 + Q1)]. For this problem,
[(1.9 – 2.0) / (1.06 – 1.05)] * [(1.06 + 1.05) / (1.9 + 2.0)] = [(-0.1) / (0.01)] * [(2.11) / (3.9)] =
[-10] * [0.541] = -5.41
2. Calculate the point price elasticity of demand at the price $1.09.
One point elasticity formula is: [1 / slope] * [(P) / (Q)]. For this problem,
[-10 / (1.09 / 1.6)] = [-10 / (0.68125)] = -6.81
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3. Will total revenue from the sale of coffee beans be higher at a price of $1.10 per pound or
$1.00 per pound?
Total revenue is price times quantity sold. At a price of $1.10 per pound they can sell 1.5 billion
pounds. Total revenue will be $1.7 billion dollars. At a price of $1.00 per pound they can sell 2.5
billion pounds. Total revenue will be $2.5 billion dollars. Total revenue will be higher at the
lower price.
4. Assume that new beverage is introduced to consumers. Some consumers tend to drink the
new beverage instead of coffee, while others find mixing the two together creates a very
enjoyable drink. How might you determine if the new beverage and coffee are
complements or substitutes in the market? One would need to calculate the cross-price
elasticity of demand for these goods. If the cross-price elasticity is positive, then on
average consumers increase their consumption of one (coffee) as the price of the other
increases. Thus they are substitutes. If the cross-price elasticity is negative, then on
average consumers decrease their consumption of one (coffee) as the price of the other
increases. Thus they are complements.
5. Assume the consumption of “fancy” coffees tends to increase faster than the increase in
consumer income. Specifically, if consumer income increases by 10 percent the quantity
of “fancy” coffee demanded increases by 12%. Given this information, what is the
income elasticity of demand for “fancy” coffee and how would you classify “fancy”
coffee? Income elasticity of demand is the percentage change in the quantity demanded
divided by the percentage change in income. In this case 12% / 10% = 1.2. “Fancy”
coffee is a normal good, because the income elasticity is positive. It is a luxury good
since the income elasticity is larger than 1.
Scenario:
Below is a hypothetical market supply for Brazilian coffee beans.
Qx = 20 Px -19
Price
(Dollars per pound)
1.10
1.09
1.08
1.07
1.06
1.05
1.04
1.03
1.02
1.01
1.00
Coffee beans
(billions of pounds)
3.0
2.8
2.6
2.4
2.2
2.0
1.8
1.6
1.4
1.2
1.0
1. Calculate the arc price elasticity of supply as the price increases from $1.05 to $1.06.
One arc elasticity formula is: [(Q2 – Q1) / (P2 – P1)] * [(P2 + P1) / (Q2 + Q1)]. For this problem,
[(2.2 – 2.0) / (1.06 – 1.05)] * [(1.06 + 1.05) / (2.2 + 2.0)] = [(0.2) / (0.01)] * [(2.11) / (4.2)] =
[20] * [0.5024] = 10.05
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2. Calculate the point price elasticity of supply at the price $1.09.
One point elasticity formula is: [1 / slope] * [(P) / (Q)]. For this problem,
[20 / (1.09 / 2.8)] = [20 / (0.3893)] = 7.79
Another formula is: P/(P-a); a = price at Q=0. For this problem, 0=20 P – 19; P = 0.95. So
(1.09/(1.09-0.95) = 1.09/0.14 = 7.79.
Scenario:
Many public universities (including the University of Akron) have declining
budgetary support from the state. Simultaneously, the costs associated with higher education have
increased. These costs include utility, health insurance, recreation services and housing. Also, the
average income of college students has increased. In response, most have increased tuition in the
hopes that they will recoup some of the lost revenue.
Answer and explain the questions below about the market for higher education.
3. We have discussed several determinants of the elasticity of demand. Consider each
determinant’s impact on the elasticity demand for higher education separately and then
provide a summary indicating whether the demand is elastic or inelastic. Explain and
support your position.
There are relatively few good substitutes for higher education. One could be self-taught, but that
provides no credential for employers. This makes the demand relatively inelastic.
The cost of higher education is a major portion of most family’s income. This makes the demand
relatively more elastic.
Most students have little time to adjust to the price changes. This makes the demand less elastic.
Higher education is a relatively durable good, at least it should be. This makes the demand
relatively more elastic.
One might expect the demand of current students to be less elastic than the demand of new
(prospective) students.
There are conflicting forces at work; thus empirical studies are needed to determine the relative
importance of the opposing forces. However, I would expect the demand to be moderately
inelastic, because I expect the lack of good substitutes to dominate. In fact, one study estimates
the tuition elasticity of demand for higher education in the U.S. to be about -0.3 (McPherson,
1978, pp. 180-1; Leslie and Brinkman, 1987).
4. From their behavior, what do University of Akron administrators think the elasticity of
demand for a University of Akron education is? Since they must think that raising tuition
(price) will lead to increased revenue, they must think the elasticity of demand is
inelastic.
5. Given your understanding of the elasticity of demand, do you agree with the University
of Akron administrators’ evaluation of the elasticity of demand for a University of Akron
education? Please explain using the determinants of elasticity of demand.
While I expect the elasticity of demand for higher education to be moderately inelastic, the
demand for any one institution (U of A) will be more elastic than for the entire market. In this
case there are several substitutes available, especially for potential students – CSU, KSU,
Malone, Walsh, and several community colleges to name a few. Obviously, since many of these
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substitutes are also raising their tuition, thus focus on market elasticity is appropriate and revenue
should increase with tuition increases.
Scenario:
Elasticity varies along a linear demand curve. How might elasticity differ
between demand curves?
1. Which of the following three linear demand curves is most elastic at a price of $1.00?
Q = 20 – 10P, Q = 30 – 15P, and Q = 40 – 20P. Support your answer!
They are all unit elastic at a price of $1.00.
One point elasticity formula is: [1 / slope] * [(P) / (Q)]. For this problem,
Q = 20 – 10P: [-10] * [1/10] = -1.0
Q = 30 – 15P: [-15] * [1/15] = -1.0
Q = 40 – 20P: [-20] * [1/20] = -1.0
Another formula is: [P] / [P – a]. Since “a” is the vertical intercept and is the same for each of
these demands (a = $2), the Elasticities will be equal at the same price. [1] / [1 – 2] = -1.
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