Price Discrimination

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Today's Agenda

Part 1: Capturing Surplus

Part 2: Other Strategies

First-Degree Price Discrimination

Second-Degree Price Discrimination

Third-Degree Price Discrimination

Bundling

THE SETUP

There are two groups of individuals,
which we'll simplify to imagine there's just
one individual of each type.

Type 1: Low Demand

Type 2: High Demand

B_1(x_1) = 20x_1 - \frac{1}{2}x_1^2
B_2(x_2) = 30x_2 - \frac{1}{2}x_2^2
MB_1(x_1) = 20 - x_1
MB_2(x_2) = 30 - x_2
D_1(p_1) = 20 - p_1
D_2(p_2) = 30 - p_2

First-Degree Price Discrimination

Recall: demand curve represents marginal benefit, in dollars.

Area under demand curve from 0 to q units = total benefit of q units, or B(q)

We can think of B(q) as "the most, in total, a consumer would pay in order to buy q units."

Suppose a monopolist can set a price for that many units and earn R(q) = B(q).

Then they could capture all the potential consumer surplus...(so not very fair)...

but would also produce up to the point where MB = MC...(so efficient)

Second-Degree Price Discrimination

Now suppose the monopolist cannot observe the type of consumer, and believes any individual consumer has an equal chance of being type 1 or type 2.

What quantity bundles should it choose?

It wants to maximize its revenue from the low-demand consumers without offering a deal that's so good that its high-demand consumers choose it...

Return to Price-Setting

Let's get back to the situation where a monopolist sets a price and consumers decide how much to buy.

If the monopolist has to offer the same price to both groups, what will it do?

Third-Degree Price Discrimination

Incorporating Cost

\pi(y_1,y_2) = R(y_1) + R(y_2) - c(y_1 + y_2)
\frac{\partial \pi}{\partial y_1} = R'(y_1) - c'(y_1 + y_2) = 0
\frac{\partial \pi}{\partial y_2} = R'(y_2) - c'(y_1 + y_2) = 0

"The marginal revenue in all sales markets must equal
the marginal cost of the last unit produced for any market."

Bundling

If you had to price these separately, how much revenue could you get?

If you bundled them together, how much revenue could you get?

Conclusions and Next Steps

Much of the Silicon Valley economy
is based on acquiring information for this purpose.

A lot of what we see in the world is companies trying to figure out
what people are willing to pay for their product.

Key skill: know how to take a realistic story, write down a model,
and solve it to find a core explanation of what's going on.

Far out in the uncharted backwaters
of the unfashionable end of the western spiral arm of the Galaxy lies a small unregarded yellow sun.

SCIEPRO/GETTY IMAGES

Orbiting this at a distance of roughly ninety-two million miles
is an utterly insignificant little blue green planet
whose ape-descended life forms are so amazingly primitive
that they still think digital watches are a pretty neat idea.

This planet has — or rather had —
a problem, which was this:

😢

most of the people on it were unhappy for pretty much of the time.

Many solutions were proposed
for this problem...

...but most of these were largely concerned with the movements
of small green pieces of paper,

which is odd because on the whole
it wasn't the small green pieces of paper that were unhappy.

Resources

Technology

Stuff

Happiness

🌎

🏭

⌚️

🤓

The Real Economy: Scarcity and Choice

Unit I: Consumers and Demand

Unit II: Firms and Supply

Unit III: Market Equilibrium

🤩

⚖

Little Green Pieces of Paper

🏭

The Circular Flow

Three Fundamental Tools of Analysis

Optimization (Unit I)

Given a fixed set of circumstances (prices, technology, preferences), how do economic agents (consumers, firms) make choices? 

Comparative Statics (Units II & III)

How do changes in circumstances (changing prices, shifting technology, preferences, etc.) translate into changes in behavior? 

Equilibrium (Unit IV)

How do economic systems converge toward certain outcomes?