E201 Spring 2009
HOMEWORK #5 ANSWERS
1.
Describe the basic notion of elasticity in plain English.
How responsive one thing is to a change in another.
2.
a.
Define price elasticity of demand in words.
The responsiveness of consumption to a change in price.
b.
Define price elasticity of demand mathematically.
(% ΔQ)
(% ΔP)
3.
a.
If a 1% increase in price leads to a 3% decrease in quantity demanded, what is the
elasticity coefficient? 3; elastic
b. If a 1% increase in price leads to a 0.5% decrease in quantity demanded, what is the
elasticity coefficient? 0.5; inelastic
c. If a 1% increase in price leads to a 1% decrease in quantity demanded, what is the
elasticity coefficient? 1.0; unit elastic
d.
Label the coefficients in you found in (a, b, c) above as elastic, inelastic, or unit
elastic.
4.
What is the "midpoints rule" for computing an elasticity coefficient?
5.
QUANTITY
DEMANDED
0.5
1.5
2.5
4
6
8
11
15
20
26
PRICE
$20
18
16
14
12
10
8
6
4
2
a.
b.
c.
6.
TOTAL REVENUE
$10
27
40
56
72
80
88
90
80
52
PRICE
ELASTICITY
-9.5
4.25
3.46
2.6
1.57
1.42
1.08
0.71
0.39
Calculate total revenue for each price-quantity combination.
Use the midpoint formula to calculate elasticity coefficients when price falls from
$20 to $18, from $18 to $16, from $16 to $14, etc.
Is elasticity constant along this demand schedule? Explain.
No. As price falls, elasticity of demand becomes less elastic (or more
inelastic).
d.
For which prices is demand elastic? Inelastic?
Elastic price range: $6-$20. Inelastic price range: $2-$4.
e.
Look at the total revenue column and note how it changes. For what price
changes is the change in total revenue positive? When is the change in total
revenue negative?
Prices $6-$20 (elastic range) show a positive revenue change; prices $2-$4
(inelastic range) show a negative revenue change.
Define total revenue. Show total revenue on a supply-and-demand diagram. How is total
revenue of sellers related to total expenditure by consumers?
Total revenue is price times quantity sold. TR = P x Q
Total expenditure (TE) is also equal to TR.
P
S
PO
D
QO
Q
7.
Suppose your demand schedule for compact discs is the following:
Quantity Demanded
(Income = $10,000)
40
32
24
16
8
Price
$8
10
12
14
16
a.
Quantity Demanded
(Income = $12,000)
50
45
30
20
12
Us the midpoint method to calculate your price elasticity of demand as the price
of CDs rises from $8 to $10 if (1) your income is $10,000, and (2) if your income
is $12,000.
If income is $10,000 and price rises from $8 to $10, price elasticity of demand
is
[(8/36) / (2/9)] = 0.22/0.22 = 1
If income is $12,000 and price rises from $8 to $10, price elasticity of demand
is
[(5/47.5) / (2/9)] = 0.11/0.22 = 0.5
b.
Calculate your income elasticity of demand as your income increases from
$10,000 to $12,000 if (1) the price is $12, and (2) the price is $16.
If income rises from $10k to $12k and price is $12 per CD, income elasticity
of demand is
[(6/27) / (2000/11,000)] = 0.22/0.18 = 1.22, using midpoints;
[(6/24) / (2000/ 10,000)] = 0.25/0.20 = 1.25, using endpoints.
If income rises from $10k to $12k and price is $16 per CD, income
elasticity of demand is
[(4/10) / (2000/11,000)] = 0.4/0.18 = 2.2 by midpoints;
[(4/8) / (2000/10,000)] = 0.5/0.2 = 2.5 by endpoints.
8.
a. Draw two demand curves, one relatively elastic and one relatively inelastic. Label each
curve.
P
D2
D1
Q
D1 is more inelastic; D2 is more elastic. Or, D1 is less elastic, and D2 is less inelastic.
b.
9.
10.
How is elasticity related to slope? (You may want to refer to p. 93 in Mankiw.)
Loosely speaking, a flatter the curve is more elastic; a steeper curve is more
inelastic.
AThere were nearly four million fewer [subway] riders in December 1995, the first full
month after the price of a token increased 25 cents to $1.50, than in the previous
December, a 4.3 percent decline.@ (New York Times, Feb. 17, 1996)
a.
Use these data to estimate the price elasticity of demand for subway rides.
Ed = (4.3% / 20%) = 0.215
Note that use of the midpoint rule is not appropriate for these data. We are
interested only in the response to the increase in price from $1.25 to $1.50.
Note also that a $.25 increase from $1.25 to $1.50 is a 20% increase, using the
original price as base.
b.
According to your estimate, what happens to the Transit Authority=s revenue
when the fare rises?
Since demand is price inelastic, TR rises when price rises. Inelastic demand
means that the percent increase in price is bigger than the percent decrease
in quantity.
c.
Why might your elasticity estimate be unreliable?
The data are for a one-month period, a short time for consumers to adjust
their behavior in response to the price increase. With more time, consumers
would find more substitutes, and demand would be more elastic.
If the price of a commodity is reduced from $105 to $95, and as a result, the quantity
demanded increases from 45 to 55 units, what is the elasticity coefficient?
Use the midpoints rule. What is the change in total revenue?
Ed = (10/50) / ($10/$100) = 2.0.
TR increases from $4725 to $5225.
11.
"Bad weather in the Midwest reduces harvests of wheat, corn, milo, and soybeans.
Farmers as a group will be worse off." True, false, or uncertain. Hint: use supply and
demand analysis to get started, then try to determine the effect on total revenue of
farmers.
Supply decreases, resulting in an increase in price and a decrease in quantity.
If demand is elastic, TR decreases (the percent decrease in quantity exceeds the
percent increase in price.)
If demand is inelastic, TR increases (the percent increase in price exceeds the
percent decrease in quantity).
12.
Define each of the following terms and explain what each tells you:
a.
Income elasticity of demand
Measures the responsiveness of consumption to a change income.
EI = (% ΔQ) / (% ΔI)
EI > 0 is a normal good.
EI < 0 is an inferior good.
b.
Cross price elasticity of demand
Measures how consumption of one good changes when the price of another
good changes.
E1,2 = % ΔQ(Good 1) / % ΔP(Good 2)
E1,2 > 0 indicates substitutes
E1,2 < 0 indicates complements
c.
Price elasticity of supply
Measures how responsive the quantity supplied is to a price change.
Es = (% ΔQs) / (% ΔP)
13.
What is the effect of time on the price elasticity of supply?
More time, more elastic, i.e., with more time suppliers are able to respond more to a
change in price.
14.
Beachfront resorts have an inelastic supply, and automobiles have an elastic supply.
Suppose that a rise in population doubles the demand for both products (that is, the
quantity demanded at each price is twice what it was).
a.
What happens to the equilibrium price and quantity in each market?
The doubling of demand “pivots” the demand curve out to the right from the
intersection with the price axis—see why? It’s the doubling of the old Qd at
each P, but don’t worry about this detail. The main idea is that the increase
in demand leads to an increase in P and Q in both markets, but relative
increases in P and Q are different.
P
S
D2
D1
Q
Beachfront Resorts
P
S
D2
D1
Q
Automobiles
b.
Which product experiences a larger change in price?
With the inelastic supply in the beachfront resort market, the increase in
demand causes a relatively large increase in P and not much of an
increase in Q.
15.
c.
Which product experiences a larger change in quantity?
With the elastic supply in the auto market, the increase in demand causes a
relatively large increase in Q and not much increase in P.
d.
What happens to total consumer spending on each product?
In both markets, total expenditure by consumers rises, since both P and Q
increase.
Economists have observed that spending on food at restaurant meals declines more
during economic downturns than does spending on food to be eaten at home. How might
the concept of elasticity help to explain this phenomenon?
Income elasticity of demand explains these facts. In economic downturns, average
income falls. Spending on restaurant meals is more sensitive to changes in income
than spending on food to be eaten at home. The income elasticity of restaurant
meals is 1.40; for food, it’s 0.51. Note that this is strictly a behavioral explanation.
There is no psychological or sociological change that drives this difference in
consumption. Consumption of both goods falls when incomes fall, so both are
normal goods. But consumption of restaurant meals is more income sensitive than
consumption of food at home.
16.
Read the articles at the link for HW5 and answer the following questions:
a.
According to the articles, which shift variable for Starbucks coffee
changed?
Cost conditions (prices of inputs) have risen.
b.
Use a supply-and-demand model for Starbucks coffee to show the effect
on equilibrium price and quantity. (Notice that we are applying the model to a
single seller, which is a deviation from the usual assumption of many buyers and
sellers when using the market model. In Chapters 14 and 15 we will develop
different models for single sellers. Even though Starbucks is the only seller of
Starbucks coffee, they certainly face competition from other coffee shops. An
alternative way to model this problem would be to use Specialty Coffee as the
definition of the market, which would then include many sellers.)
Leftward shift of supply, causing P to rise and Q to fall.
c.
What would you predict will happen to Starbucks’ total revenue as a result
of the price increase? Explain.
TR will rise if Q falls less (in percentage terms) than P increases.
d.
Now look up an estimate for the price elasticity of demand for coffee on
the web. If you type “coffee price elasticity of demand estimate” into a search
engine (Google, for example), you should be able to find something. Use this
demand elasticity to make a prediction of the change in revenues for Starbucks.
How is the actual price elasticity of Starbucks coffee likely to differ from the
estimate you found? Explain.
The elasticity coefficient for coffee should be less than one. The one I found
was 0.25. Starbucks coffee is an individual product, so demand for
Starbucks coffee would be more elastic than the product category of coffee.