Econ 315

In Session 1, buyers reported diferent maximum prices

for the same standardized iced cofee.

What information might be inside each WTP?

A reported willingness to pay can refect:

• how much the consumer values the good;

• resources and obligations that limit trade-ofs;

• alternatives, timing, convenience, and expectations.

Two students like iced cofee equally.

One has $20 available for lunch today; the other has $100.

Must they have the same WTP?

No. Preferences are only one part of the decision.

what I value + resources and constraints

+ alternatives I give up

Similar tastes can still produce diferent maximum payments

when constraints or opportunity costs difer

What is willingness to pay?

the maximum amount a consumer would

give up for the good in the relevant circumstances.

Does WTP equal price actually paid

No it does not. If WTP is $7 and price is $4, the consumer pays $4; valuation

does not become $4.

A student has WTP = $6 for one iced cofee.

$8: do not buy. Preference did not change

$6: buy. Preference did not change

$4: buy. Preference did not change

Each buyer can purchase at most one iced cofee.

Their WTPs are:

8, 7, 6, 5, 4, 2

How many buyers purchase at prices $5, $7, and $3?

Price P Buyers with WTP ≥ P Market Qd

$8 A 1

$7 A-B 2

$6 A-C 3

$5 A-D 4

$4 A-E 5

$2 A-F 6

many consumers + repeated purchases + varied

circumstances

a smooth approximation of market demand

Hold the boba price, consumer resources, and all other demand

conditions fxed.

Same conditional function, or a diferent one?

A and B are two evaluations of one conditional function.

Look at phone for picture

Market demand from WTPs

Look at picture on phone

An Instagram campaign is followed by higher iced-cofee sales.

Possible mechanisms: awareness, quality information, beliefs,

salience, social infuence, or preference change.

Higher observed sales do not identify the mechanism.

What is the demand function?

Qd

C

= D(PC , PB, I, Z )

What is the recurring market?

QC

= 12 − 2PC + PB + I

What is Pc?

Own price of iced coffee

What is I?

Discretionary resources

What is Z?

Other demand conditions

What is the recurring market?

QC

= 12 − 2PC + PB + I

Recurring market example

PC = 5, PB = 6, I = 4,

Qd

C = 12 − 2(5) + 6+ 4 = 12.

Thus Qd

C = 12 means 1,200 drinks per instructional day; I = 4

means $400 per month.

Suppose a $1 price increase reduces daily quantity demanded by

200 cups.

Large response or small response?

Compare a market selling 300 cups with one selling 30,000 cups.

Two hundred cups is large relative to 300 and small relative to

30,000.

What is the equation for responsiveness?

% change in Q/% change in X

Percentage changes creates?

the unit-free comparison called

elasticity.

This statement is useful shorthand. What does it leave

unstated?

Whose demand, where, when, and for which

market?

What alternatives and adjustment options are available?

A credible elasticity statement identifes the relevant:

• consumers, place, and market defnition;

• price point or interval and time horizon;

• alternatives and adjustment frictions.

Elasticity belongs to a context, not a product label.

Complete the sentence precisely:

A 1% increase in price is associated with . . .

Is demand elastic, inelastic, or unit elastic?

A 1% price rise implies about 1.8% lower quantity near this point.

Elastic price > 1 =?

Elastic and more than proportionate

Elastic price < 1 =?

Inelastic and less than appropriate

Elastic price = 1 =?

Unit elastic and proportionate

Demand tends to be more elastic when?

• close substitutes exist; the market is defined

• consumers have more time;

• expenditure share is larger;

•narrowly;

switching is easier;

• purchase can be

postponed.

What is the equation for total revenue?

P x Q

Elasticity

Elastic: TR falls when price rises, price falls then TR rises

Inelastic: TR rises when price rises, price falls then TR falls

Unit elastic: price rises then TR is unchanged locally, price falls then TR is unchanged locally

Suppose εC ,PC

= ↗0.4 and the manager raises price.

1. What is the likely direction of total revenue?

2. What is the likely direction of profit?

With inelastic demand, quantity falls less than proportionately, so

total revenue rises.

Profit is unknown.

ϑ = TR ↗ TC

Elasticity informs revenue; profit also requires cost information.

PB rises 10%; QC

d rises 4%. Find εC ,PB and interpret.

εC ,PB

= = 0.40

I rises 10%; QC

d rises 3%. Find εC ,I and classify.

εC ,PB

= = 0.30

You own a small cafe.

Nobody gives you Qd = 12 ↗ 2PC + PB + I. You have sales

C

records, limited time, and no econometrics team.

How can you learn whether customers are price

sensitive?

Start cheaply Strengthen the comparison

• ask customers for WTP; • match similar settings;

• use judgment and • test a planned price;

competitors; • repeat controlled trials.

• compare past outcomes.

A manager observes:

(P1, Q1) = (5, 12), (P2, Q2) = (6, 10).

Price rises from $5 to $6; observed sales fall from 1,200 to

1,000 cups.

Use the midpoint formula. What happens to total revenue?

(10−12)

εarc (12+10)/2 ↗2/11

= = = ↗1.

C ,PC (6−5) 1/5.5

(5+6)/2

TR1 = 5(1,200) = $6,000, TR2 = 6(1,000) = $6,000.

Unit arc elasticity matches unchanged revenue.

Week 1: price $5, sales 1,200.

Week 2: price $6, sales 1,000.

Can the manager identify the causal price e!ect

from these two weeks?

Not necessarily. Sales may also respond to:

• weather, exams, hours, or foot tra"c;

• competitor prices, promotions, or advertising;

• product quality, service, or customer mix.

Calculation is easy; causal identification is hard.

The cafe cannot run a perfect laboratory experiment.

What feasible design would make the comparison more credible?

Name what you would hold fixed, vary, record,

and repeat.

1. Match similar days, hours, locations, or customers.

2. Randomize price, or use a prewritten rotation.

3. Hold product, hours, and promotions fixed; record conditions.

4. Repeat to distinguish response from an unusual day.

The cafe raises price from $5 to $6. Observed sales fall from

1,200 to 1,000 cups, and revenue remains $6,000.

What must the manager know before deciding whether to keep,

reverse, or refine the price change?

1. Responsiveness: elasticity for this market and interval.

2. Causality: did price produce the quantity response?

3. Revenue: here, the price-quantity e!ect nets to zero.

4. Costs: required for the profit conclusion.

Elasticity informs; it does not decide.

For two goods x and y, a consumer chooses the most-preferred

a!ordable bundle:

max u(x , y ) s.t. Px x + Py y ⇒ I.

x ,y ↑0

Preferences rank bundles; the budget defines the feasible set.

Varying prices and income traces individual demand functions.

What is Pb?

Price of substitute (boba tea)