Professor Scholz
Economics 101, Problem Set #5
Posted: 10/6/2009
Due: 10/13/2009
Elasticity and budget constraints.
Problem 1.
a) The graph above describes the number of hot drinks served in a certain coffee
shop depending on the air temperature in the street. Temperature is shown on the
Y-axis and number of hot drinks consumed is shown on the X-axis. Calculate the
weather elasticity of the number of drinks served when the temperature is between
40F and 60F.
Answer: E =
(100 −150) /(150 + 100)
50 /250
1/5
=−
=−
= −1
(60 − 40) /(60 + 40)
20 /100
1/5
b) The table below shows the number of beers served in a bar during a football game
depends on the number of points Badgers score. Calculate the score elasticity of
beer consumption when Badgers score between 30 and 40 points.
Badgers Score
0
10
20
30
40
50
Answer: E =
Number of beers
100
250
450
700
1000
1500
(1000 − 700) /(1000 + 700) 300 /1700 21
=
= = 1.235
17
(40 − 30) /(40 + 30)
10 /70
Problem 2.
Sarah has 40 hours of leisure every week, which she spends either on watching Friends
episodes or playing pool. She can watch at most 80 episodes or play 200 games.
a) How much time does she spend on one episode? One game?
b) Write down her leisure time constraint.
c) Suppose she took an additional course at the university, and it decreased her
leisure time by 25%. What is her new constraint?
d) Suppose Sarah became more proficient in pool, so it takes her now only 10
minutes per game. Draw the old and the new constraint on the same graph.
e) Suppose the new Friends episodes are 50% longer (and Sarah remains proficient
in pool). What impact does it have on Sarah’s constraint?
Answer:
a) Sarah spends 40/80 = ½ hour on one episode and 40/200 = 1/5 hour per game.
b) If X is episodes and Y is games, then 1/2X + 1/5Y=40.
c) The new time available for Sarah is 40*0.75= 30, hence the new leisure
constraint 1/2X+1/5Y=30.
d) Sarah now can play six games per hour, so her constraint shifts outward:
1/2X+1/6Y=30.
e) Sarah now spends ¾ hours per episode. It shifts her constraint inwards: 3/4X +
1/6Y=30.
Problem 3.
Bob Dylan spends his earnings on Fender Stratocasters and New York – London tickets.
He has a month budget of $ 20000, while a Fender costs $ 2500 and a ticket costs $1000.
How does BD’s budget constraint change if
a) Jimi Hendrix stops burning his Fenders and price for them falls 20%?
b) Madonna sells her private airplane and starts using public airlines, which would
increase the ticket price up to $ 2000 (and the price of Fender guitars remains
lower)?
c) iTunes sales of BD songs increase and his budget doubles (and parts a and b
continue to hold)?
Answer:
a) Initial constraint is 20000 = 2500 F + 1000 T, where F is Fenders, T are Tickets.
New Fender price is $ 2000. Dylan’s budget constraint shifts outwards: 20000 =
2000 F + 1000T.
b) 20000 = 2000 F + 2000 T. Price of Tickets rises, so less tickets are available to
Bob.
c) 40000 = 2000 F + 2000 T, parallel shift outwards.
Problem 4.
a) Walgreen’s is planning a weekly sale on brownies. Currently at price $5, they sell
10,000 packs of brownies a week. It considers decreasing price up to $2 per pack.
What should the minimum expected sales be for this price change to be
profitable? What must be true about the price elasticity of demand for the sale on
brownies to be profitable?
b) Champagne demand is elastic, which implies that are increase in price will reduce
total revenue. However just before the New Year, champagne prices do actually
increase. Does this mean suppliers make a New Year present to their customers
and lose revenue?
Answer:
a) If X is the amount sold at price $2, then 2X > 5*10000, X > 25000. Elasticity
must be greater than unity for a price decrease to increase revenues.
b) The New Year price increase can be explained by increase in the demand for
champagne, hence this price change would not result in smaller revenues.
Problem 5.
The demand for medium latte is described by the equation Qd = 45 – 2.5P, and the supply
is Qs = 5P. The government considers to impose a per unit tax of $3 on suppliers.
a) Calculate the before and after tax equilibrium prices and quantities.
b) Calculate the tax revenues and deadweight loss.
c) What is the consumers tax burden and the producers tax burden? Given your tax
incidence answer, which curve (demand or supply) is more elastic?
Answer:
a) Before: P=6, Q=30. After: P=8, Q=25.
b) TR = 25*3= 75. DWL = 5*3/2=7.5.
c) CT = 2*25=50, PT = 25. CT>PT, hence supply is more elastic than demand.
Problem 6.
Are the following scenarios consistent with elastic or inelastic demand? Explain with a
diagram.
i.
ii.
iii.
Answer:
i.
ii.
Orange groves in Florida get hit by destructive hurricanes but revenues for
orange growers increase
Fuel prices increase and airline revenues decrease
Milk prices increase and dairy farmers find themselves worse off
Supply shrinks because of the harvest destruction, equilibrium price
increases, hence, as revenues increase as well, demand is inelastic.
We consider market for airline tickets. Fuel is an input in airline industry,
So when fuel prices rise, ticket supply decreases. Then as revenues
decrease with an increase in price, demand is elastic.
iii.
As revenues decrease with an increase in price, demand is elastic.
Problem 7
a) Health-food advocates are calling for a tax of $.50 per can of Cheese Whiz, arguing
that a tax will reduce consumption of unhealthful Cheese Whiz while placing the burden
of the tax on the junk-food industry. What arguments are the health-food advocates
making in terms of elasticities?
b) Suppose you have access to the following data:
Price of Cheese Whiz
Cans Demanded
$2.25
9.45 million
$2.75
8.55 million
Calculate the relevant elasticity, using the midpoint method. Do the data support the
health-food advocates’ argument?
c) A cracker industry spokesman denounces the proposed tax, claiming that it will reduce
demand for crackers. What evidence, in terms of elasticities, would support or refute his
claim?
d) Suppose you have the following data:
Price of Cheese Whiz
Boxes of Crackers Sold
$2.25
15.75 million
$2.75
14.25 million
Calculate the relevant elasticity using the midpoint method. Does the elasticity support
the argument of the cracker industry?
Answer:
a) Since the burden is supposed to be placed on the suppliers, demand must be more
elastic than supply.
(8.55 − 9.45) /(8.55 + 9.45)
0.9 /18
0.05
=−
=−
= −0.5
b) E =
(2.75 − 2.25) /(2.75 + 2.25)
0.1
0.5 /5
Demand is not that elastic, so it is more probable that the data does not support
the argument.
c) If a tax imposed on Cheese Whiz reduces demand for crackers, it means that
crackers and Cheese Whiz are complements, so cross-price elasticity of demand
for Cheese Whiz must be negative.
(14.25 −15.75) /(14.25 + 15.75)
1.5 /30
0.05
=−
=−
= −0.5
d) E =
0.1
(2.75 − 2.25) /(2.75 + 2.25)
0.5 /5
Elasticity is negative, so the data supports the claim.