Akos Lada
Summer Program 2014
Harvard Kennedy School
Problem Set #2
(Due Monday, August 1st)
Please do this problem set on a separate sheet of paper.
Elasticity and Pricing Decisions (problems 1 and 2)
1. Here’s a short excerpt from an article: “As the chart at the right shows, it was only when the [toll]
company, in desperation, lowered the toll to $1 that it has come even close to attracting the expected
traffic flows. Although the Greenway still is losing money, it is clearly better off at this new point on the
demand curve than it was when it first opened. Average daily revenue today is $22,000, compared with
$14,875 when the ‘special introductory’ price was $1.75.”
a) What was the quantity of use of the toll road when the toll was set at $1.75? What about when it was
then set at $1?
b) Using your answers from part a) and the prices you already knew, use the midpoint method to calculate
the price elasticity of demand over this price range on the demand curve.
c) Based on the answer to part b), is the price elasticity of demand: inelastic, elastic, or unit elastic?
d) Without doing any calculations, how could we have determined whether the price elasticity of demand
was elastic, inelastic, or unit elastic?
2. Upon graduation from the Kennedy School you take a job with AT&T Wireless Communications (I know
– probably not the job you’re shooting for). Your title is Director of Revenue Management. You are in
charge of setting prices for their standard wireless usage plan (usage plans are based on allotted free
minutes of cell phone use). Currently the standard plan sells for $35 a month. You are trying to decide
whether you should continue with this price point, or increase the plan’s price to $40, or decrease the
plan’s price to $30. Operations have informed you that changes in variable costs (and hence marginal
costs) associated with usage increases or decreases of 10 million customers are negligible.
a) If you increase the price to $40 an independent consulting firm you have contracted with has projected
a decrease in plan holders from 26 million to 20 million (ceteris paribus – i.e., assuming AT&T’s
competitors don’t respond with price changes of their own). What is the price elasticity of demand
coefficient? Over this range of prices, is the price elasticity of demand elastic or inelastic? Would
revenue increase or decrease and by how much? (Use the mid-point formula)
b) If you decrease the price to $30 your consulting firm projected an increase in plan holders from 26
million to 36 million (ceteris paribus – i.e., assuming AT&T’s competitors don’t respond with price
Akos Lada
Summer Program 2014
Harvard Kennedy School
changes of their own). What is the price elasticity of demand coefficient? Over this range of prices, is
the price elasticity of demand elastic or inelastic? Would revenue increase or decrease and by how
much? (Use the mid-point formula)
c) Before making your decision you decide to consult with your industry analyst to see if they anticipate
responses from AT&T’s competitors to any price changes. They inform you that if you raise your
plan’s price your competitors will probably not follow with similar price changes. However, if you
decrease your plan’s price, your competitors probably will follow since AT&T is the price leader (due
to their dominant firm status) in the market. They project that if AT&T decreases its price by $5 on its
standard package, the competitors will follow by decreasing their prices by $5 (to $29) – their current
standard plan price is $34. Further, they predict a co-efficient cross-elasticity of demand of 1.1 for
AT&T’s pricing plans (meaning when your competitors change there price 1.1 is the relative
responsiveness of AT&T’s customers) in relation to your competitor’s pricing plans (if your
competitors were to decrease their prices after AT&T decreased its prices). Based on this information,
how would this impact your revenue forecasts in #2? How much would this impact the total number
of plan holders of AT&T’s standard usage plan? (For this problem, when dealing with % changes,
feel free to use the formula { (Qnew – Qold ) / Qold })
Note: The industry analyst also inform you that your competitors are not planning on making a
pricing change if AT&T does not make a pricing change.
d) However, you’re still not ready to make your pricing decision. You realize that you need to determine
the impact on AT&T’s own alternative usage plans. In other words, how much is your pricing
decision going to cannibalize AT&T’s other usage plans? You call a meeting with some of your
associates and ask them to run some numbers based on your potential pricing changes in regards to
other AT&T plans. They inform you that only one of AT&T’s other usage plans will be impacted by
your pricing decision. For this package, they estimate the coefficient cross-price elasticity of demand
on this other plan to be 0.9 (meaning we are looking at the other plan’s quantity change) whether you
increase your price by $5 or decrease your price by $5. Currently, AT&T sells 15 million packages of
this particular alternative plan at a price of $25. Based on this information, determine the impact of
increasing and decreasing the price of AT&T’s standard usage plan on AT&T’s total revenue. What
would be the total change to the number of alternative plan holders if AT&T increased their price on
their standard plan? Conversely what be the total change to the number of alternative plan holders if
AT&T decreased their price on their standard plan? (For this problem, when dealing with % changes,
feel free to use the formula { (Qnew – Qold ) / Qold })
e) Based on all of the analysis that you have performed, what is your pricing decision (assuming you
want to maximize profits – remember, cost are not varying based on the number of plan holders so if
revenue goes up, profits go up)?
f) A month later…your Chief Financial Officer informs you that they believe, based on economic
forecasts, the real disposable income of AT&T’s plan holders will go up an average of 3%. Further, it
is estimated that the coefficient of income elasticity of demand is 0.5 for all price points listed in the
problem. For the pricing decision you made in (e), determine the impact of 3% gain in average real
disposable income on both the quantity of standard usage plans sold and the revenue generated by the
standard usage plan. Is the standard usage plan a normal or inferior good/service? How much will
this change your revenue forecasts for next year? (For this problem, when dealing with % changes,
feel free to use the formula { (Qnew – Qold ) / Qold })
Akos Lada
Summer Program 2014
Harvard Kennedy School
Price Controls and Taxes
3. The market for digestive biscuits is described by the following equations:
QD = 150-P
QS = 2P.
The Digestives Minister has decided that he wants to reduce the consumption of digestive biscuits as
much as possible. The minister is considering either imposing a $40 per unit price ceiling or a per unit tax
of $15 on consumers of digestives.
a) What is the equilibrium price and quantity before any policy is imposed?
b) Which of the two policies better achieves the minister’s objective and why?
c) Suppose the minister implements the $15 per unit sales tax on consumers. What is the government’s
revenue?
d) Suppose the minister imposes a $15 per unit sales tax on producers instead of consumers. Compared
to the tax on consumers, does the market price and quantity change? Explain.
e) Suppose the government measured the supply curve incorrectly, and although the market equilibrium
is still the same as you calculated in part a, the actual supply curve is steeper than the government first
thought. Could your answer to part b change? Explain with reference to a graph (you need not use
exact numbers on the graph).