Pricing

UCSD MGT 100 Week 07

Kenneth C. Wilbur and Dan Yavorsky

Let’s reflect

• Measuring Customer Reactions to Prices

• Unchecked AB Testing Destroys Everything It Touches

• Quiz 6

• Let’s focus for now on the Unchecked AB Testing article. What did you think?
• I think it speaks to (a) principal/agent issues within the firm (rapid turnover of executives and agents), (b) poor experimental design (focusing exclusively on the metrics we care about, without considering adverse effects) and (c) the general downside of no shared theoretical framework.
• Author offers 3 remedies: Longer term testing, tracking multiple adverse metrics for every test, and warning executives of big unknown risks
• An unstated remedy: Develop and use a theoretical framework to discipline your testing. Type 2 errors are a big issue when you have numerous tests and a tendency toward lock-in. This is why we emphasize theory-driven demand models in this course.

How firms set prices

• Common approaches
• Economic Value to the Customer
• More factors
• Using Demand Model to Price

Common approaches

• Value pricing

• Competitor price benchmarking

• Cost-based pricing

• Experiments, algorithms (eg bandits, rev mgmt)

• Demand estimation

  - Requires data, price variation, causal identification, human attention/expertise 

• Customer co-determination

  - Monopsony, auctions, negotiation, pay-what-you-want

• None: Seller takes market price

• Those first three are goldilocks: too high, just right, too low

• How often is each approach used?
• Keeney, Lawless, Murphy (2010) surveyed 1k Irish businesses

Value Pricing: Price in (cost, wtp)

• But… how do you learn wtp? Esp. if you have not sold before?

  • For large time/budget: Conjoint, simulated purchase environments, test markets, …
  • For small time/budget: Economic Value to the Customer (EVC)

• EVC: estimates customer surplus for a product, relative to the next alternative

• EVC & VP are often used by new firms, highly differentiated products & when no credible market research

• Steps: Calculate EVC, then Choose a price between (Cost, EVC)

• You might need EVC for your start-up

How to calculate EVC(x\(\vert\)y)

1. Select the best available alternative y and find its price

   - If wrong alternative, EVC estimate will be too high

2. Determine non-price costs of using y and x

   - Include start-up costs and/or post-purchase costs
   - Make sure NonPriceCosts(x) exclude the price of x (why?)

3. Determine the incremental economic value of x over y

   - Usually, quantify functional benefits    

4. EVC = Price(y) + ( NonPriceCosts(y) - NonPriceCosts(x) ) + IncrementalValue(x\(\vert\)y)

   - In practice, 99% of effort is getting the assumptions right 

EVC tips

• Remember: y might not be a commercial product.

  - Choose based on customer interviews

• EVC and y can vary across customer segments

  - You can calculate EVC(x) for multiple y

• Use unquantifiable factors to influence price selection in (cost,EVC)

• If EVC(x\(\vert\)y)<0, reconsider your product or your target customer

Example: What is EVC(Batteriser\(\vert\)y)?

• The Batteriser is a durable metal sleeve that extends disposable battery life by 800%. With a thickness of just 0.1 millimetres, the sleeve can be fitted over any size battery, in any size compartment

• Assume the typical battery costs $0.50

• Reference product is no sleeve
• Batteriser allows the consumer to avoid buying 7 extra batteries, resulting in a potential cost savings of 7*0.50=3.50 for each battery whose life is extended
• Suppose one Batteriser is durable enough to extend the lives of 10 batteries
• Then IV = 10*3.50 = 35 and EVC=35
• You might reasonably assume other benefits, such as increased usefulness of battery-operated devices, or reduced nuisance costs of changing and storing batteries, but these are hard to quantify with confidence.
• Note: when selecting a price, you have to consider psychological factors such as:
• Discount factors & the time horizon over which consumers are willing to amortize a purchase
• Risk that Batteriser benefits may not work as advertised
• Consumer skepticism about marketer claims
• I would recommend a price that is far, far below EVC in this case
• (Price was 2.50 in 2019)

“Pricing Thermometer’’

• How much inducement do you give your customer?

• How will customers, competitors, suppliers react?

  - SR vs. LR? More judgment than math. "Your margin is my opportunity"

Choosing p in (cost, EVC)

• Some advise: \(Price = Cost + (EVC - Cost)*{z%}\)

   - I've heard z = 25%, 33%, 50%, and 70%
   - Do you want profits or growth? What's your exit?

• Factors to consider when making your judgment:

  - Perceived benefit - actual benefit
  - Perceived costs - actual costs
  - Consumer price sensitivity 
  - Established pricing benchmarks
  - Fairness 
  - Customer risk of adoption, skepticism; brand credibility

• These factors also pertain to other price setting approaches

More factors: Price as a signal

Signals and Perceived Quality

• Signals of high quality

  - High prices, Brand names, Warranties, Return policies, Ad spending
  - Costly signals when the firm doesn't deliver
  - Brand reputation can convey credibility

• Signals of low quality

  - Low prices, Price promotions, Price-matching guarantees
  - Signals that look too good to be true
  - "If it's so good, why is it so cheap?''

• Prescription: Price consistent with your quality position in the market

  - Otherwise, you undercut your own message and leave money on the table
  - Findings replicate in numerous contexts 

• In marketing we focus on perceived quality, because consumers typically don’t know actual quality.
• Consumers typically rely on signals to form perceptions about unobserved quality

More factors: Non-monetary costs

• Total price to customer is

  Mental energy required to figure out the terms + 
  + Effort cost to acquire the product 
  + Financial payment

• Simplicity can increase sales. Remove frictions

More factors: Price discrimination

• Amazon v. B&N

• Delivery time: Movie release windows
  

• Purchase time: Airline, Cruise tickets

• Geography: Typically accounts for 20% of variation in online prices

• Quantity: Cups of coffee, Paper towels

• Needs: Business vs. Home segments

• Best practice: To reduce resentment, price discriminate according to new/loyal customer, merit (veterans, seniors), ability to pay/sliding scale, value provided or cost of supply

• Always frame price differences as discounts

Tips: Beware a price war!

• If you explicitly mention a competitor’s price

  • You make Customer aware of Competitor
  • Competitor will notice: You invite them to match or retaliate

• Better to price-compare vs. unnamed/generic competitor

• Who wins a price war?

  • Only one winner: Customer
  • All firms suffer, some die
  • Most likely to survive: Seller with lowest cost structure
  • Smart firms avoid price wars & keep costs secret

More factors: Non-monetary costs

• Which is the better bargain?

  • Regular price $0.89, sale price $0.75
  • Regular price $0.93, sale price $0.79

• Context was margarine sales; 80+pct chose 1st pair; most likely explanation: (in)numeracy makes people think a drop in the 10s place of 2 is larger than a drop in the 10s place of 1

Left-digit bias: Demand Effects

• This graph shows grocery product demand at quasi-random price points, estimated in a careful way by Avner Strulov-Shalin at U-Chicago
• There are clear discontinuities in price elasticity when the left-most digit changes

Left-digit bias: Lyft rides

List et al. (2023): 600 million price offers & 390 million rides

           "Approximately half of the downward slope of demand occurs discontinuously as the price of a ride drops below a dollar value (e.g. $14.00 to $13.99)" 
       

• This graph shows the empirical probability of a Lyft rider declining a ride, depending on the price estimate quoted in the app
• Ran a field experiment on 21 million Lyft users, dropping some .09 prices to .99 and some .00 prices to .99. Found discontinuous effects on ride completion, consistent with observational evidence. Treated users were more likely to continue using Lyft in the future
• “Simple pricing change that we enacted is worth approximately 0.39% in profit per user… approximately $160M per year [in 2019]”

• Left-digit bias is not limited to pricing settings. It has been found in many places, such as tax effects, salary effects
• Not pricing data, but more strong evidence of consumer left-digit bias
• This graph shows the likelihood that a homeowner will appeal their property tax appraisal, as a function of the house’s appraised value
• Not only are there strong left-digit effects, crossing the hundred-thousand threshold reverses the trend in (100,110k).
• Most likely those who were over $105k have already experienced the hundred-thousand shock before, so show lower likelihood to appeal
• Source: Jones & Strulov-Shalin (2023)

More factors: Decoy effects

• Choose 1:

  • Brand A: Rated 50/100, priced at 1.80
  • Brand B: Rated 70/100, priced at 2.60

• 33% chose A

More factors: Decoy effects

• Choose 1:

  • Brand A: Rated 40/100, priced at 1.60
  • Brand B: Rated 50/100, priced at 1.80
  • Brand C: Rated 70/100, priced at 2.60

• 47% chose B (why?)

• You see this frequently in SAAS
  
• Huber and Puto (1982)

More factors: Anchoring

• “You are lying on the beach on a hot lazy afternoon. For about an hour now, you have been thinking about an ice-cold bottle of your favorite beer. One of your friends gets up to make a phone call and offers to get you your favorite beer from a small run-down grocery store on the way back. Your friend says that the beer might be expensive and asks the maximum price that you are willing to pay. If the price is higher, your friend won’t buy the beer. What is your maximum price?
  
• … fancy resort hotel …

• AKA Reference price
• Thaler (2008), Marketing Science
• This was back when we had to get up to make phone calls
• This was back when we made phone calls

More factors: Price salience

• Show the price early, late or never?

  - Drinks in a loud nightclub
  - USPS "Forever Stamps"
  - Price advertising, coupons

• Price salience emphasizes Savings or Exclusivity

Refresher: Price Elasticity of Demand

• \(elas.=\frac{d(lnQ)}{d(lnP)}=\frac{P}{Q}\frac{dQ}{dP}\le 0\)

          - "Given a 1% change in price, what is the % change in quantity demanded"
          - Elasticity is "scale-free;" comparable across markets & time

  • For \(-1<elas.<0\), we say demand is price-inelastic
  • For \(elas.<-1\), we say demand is price-elastic

• We can calculate elasticity:

  1. At a point, using a model to give us the slope

  2. Use 2 points to approximate the derivative, w/out a model

      - Approximation error increases with interval width and demand curvature
      - We can approximate at multiple points, compare implied elasticities

Refresher: Price Elasticity of Demand

• \(elas.=\frac{d(lnQ)}{d(lnP)}=\frac{P}{Q}\frac{dQ}{dP}\)

• A special class of demand functions have “constant elasticity”

  \(Q=e^b*P^{E}\) for \(E\le 0\) & \(b>0\), then \(elast.=E\)

  Implies \(ln Q=b + E * lnP\), called “log-log regression”

    Have to handle endogeneity to estimate right E 

• With constant MC=C, \(\pi=\text{max}_P (P-C)*Q(P)\) has FOC

\[Q + \frac{dQ}{dP}(P - C) = 0\]

          - multiply both terms by P/Q & substitute elas. formula

\[P+E(P-C)=0 \]

          - solve for optimal P, given your model
          

\[ P = \frac{CE}{1+E}=\frac{C}{1+E^{-1}}\]

          - This optimal price conditions on constant-elasticity demand
          - If we relax the constant-elasticity restriction, we may find a different optimal price

• C.E. imposes a particular shape on demand & enables easy price optimization, given marginal cost data

• But, constant elasticity restricts demand, thus can lead to suboptimal pricing

Use demand model to set price

• \(q_j(p_j)=N\hat{s}_j(p_j)\)

• Total contribution = \(\pi(p) = q_j(p_j)[p_j-c_j(q_j(p_j))]\)

• Grid search:

  • Choose candidate prices \(p_m = p_1, p_2, ..., p_M\)
  • \(p^*=argmax_{p_m} \pi(p_m)\)
  • Optional: Repeat using a more refined grid around \(p^*\)

• We often assume \(c_j(q_j(p_j))=c\) for convenience

          - Grid search easily accommodates non-constant cost functions

• Multiproduct line pricing requires summation over brand’s owned products

• Can you predict competitor price reaction, or how your demand responds to new competitor price? How?

• More elegant mathematical solutions assume globally concave demand & convex costs. Both may conditions may be absent (examples); grid search just works
• Tie competitor price reaction back to earlier discussion about common pricesetting approaches

• T/F: Our class discussion implies that most market prices are set optimally

Class script

• Use demand model to trace out a demand curve and optimize price

Wrapping up

Homework

• Let’s take a look

Recap

• Most common pricing methods: Value pricing, Competitor matching, Cost-based. All 3 leave much to be desired
• Pricing challenges explain why prices may be suboptimal
• Consumers strongls expect prices to reflect products’ quality positions in the market
• Optimal pricing requires attention to non-economic factors, including signaling, price perceptions, left-digit bias, cognitive costs, decoy effects, anchoring and price salience

Going further

• More than a Penny’s Worth: Left-Digit Bias and Firm Pricing

• Personalized Pricing and Consumer Welfare

• Dynamic Online Pricing with Incomplete Information Using Multiarmed Bandit Experiments

• Universal Paperclips : Good way to practice setting prices