Transcript Two-parts pricing

Review
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Demand-oriented Pricing Strategies
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Consumer Surplus
Lecture 15 Two-parts Pricing
What is two parts pricing?
Why do we use two parts pricing?
How to design two parts pricing?
Motivation Questions
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Most of the jazz bars charge two parts pricing. You
pay the entry fee and every drink.
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Why is it optimal to do so?
How do you determine how much to charge for entry and
drinks ?
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Two-parts pricing (two-parts tariff) two separate
charges for consuming a single product.
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Services: Jazz bar, Disney Theme Parks, Visa, museum …
Products: Bell South, Rental Cars, Costco …
When do we use two parts pricing?
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There are two separate benefits of consuming a single product
There are two separate costs of offering the product:
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fixed cost and variable cost
Why do we use two parts pricing?
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significant difference in the incremental cost of serving
different segment
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for industries with high fixed costs
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ATT WorldNet
Golf Course
spur competitive innovation
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Bell South DSL
Graphical Illustration of Two-Parts Pricing
Price ($)
c
Individual Demand Curve
q
A Single Price is Inefficient
Price ($)
Money left on the table
20
Profit (p*-c)q*
No trade – deadweight loss
p*
c=10
0
5
q
Solving for Optimal Two-Parts Pricing
with Homogeneous Customers
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Step 0: Start with the inverse demand function p = a – b*q
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Step 1: Set the per-unit price to equal marginal cost, that is p* = c
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Step 2: From the demand equation, compute the quantity demanded
at this price q*(p*), so that q*(c) = (a-c)/b
Step 3: Compute the consumer surplus CS* at p* = c
and set the fixed fee as equal to CS*: (a-c)*(a-c)/(2*b)
Example: Two-parts pricing
A new health club needs to decide how much they should charge
for each visit of their patron. They know that individual
demand function for weekly usage is P=10-2T, where T is the
number of hours spent in the club. The marginal cost for
providing an hour usage is $2, and there is no capacity limit.
1). Assuming they are facing a homogeneous population, the
management is planning to charge homogeneous price (linear
pricing). Design the optimal linear price which only charges a usage
fee.
2). Since the club is brand new, the management is eager to cover all the
fixed cost involved in building the facilities in addition to the variable
cost related to each visit. A two parts pricing will help management
solve the problem by better extracting consumer surplus. Design the
optimal two-part price with an entry fee plus a usage fee. Will two-part
price improve profitability?
3). However, consumers are heterogeneous and it is impossible for you
to distinguish them. You need to make a decision on whether you
want to lower your price to serve both types of consumers or keep
the price high and focus on only Type A consumers who can bring in
more profit.
Assume there are two types of customers, A and B, 60% of the
customers are of type A and 40% of the customers are of type B.
They have following individual demand function:
Type A: P=10-2T
Type B: P= 8-2T
Price strategy I: two-part price under which both types use the club
Price strategy II: two-part price which excludes type B
Design the optimal two-part tariffs for both strategies
Take-aways from this example
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Two parts pricing is a price discrimination technique to
differentiate (unobservable) heavy users from light users.
For homogeneous consumers, optimal variable fee should
be the same as variable cost.
For heterogeneous consumers, we need to solve for
optimal variable fee and fixed fee.
Next Lecture
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Tying and Bundling