Pricing 4, Auction Flashcards
Steps in Finding Optimal Price
- Express profit function in terms of price
- Differentiate profit function with respect to price
- Set derivative equal to 0, and solve for price
Problems with charging only one price
Leaving money on the table
- Some customers are willing to pay more
Passed-up Profit
- Some potential customers were not served even though the firm could have served them at prices above the variable cost
Customized Pricing: 2 Prices - Mathematical Steps
- Express profit function in terms of the 2 prices (High Price and Low Price)
- Differentiate profit function with respect to a) High Price and b) Low Price
- Set each derivative equal to 0, and solve for the 2 prices simultaneously (2 equations, 2 unknowns)
Why is it Important to Build “Segmentation Fences”?
We have learnt that charging multiple prices can yield higher profits.
However, the customers who pay the high price will want to pay the low price .
These valuable (=high-margin) customers will be upset if they learn about the low price.
Firms must build “segmentation fences” to prevent the high-price segment from paying the low price.
Examples: Airlines, hotels, geographical markets (e.g. textbooks)
Customization by:
Who, What, Where, When & How many
Example: Customization by Product Design (what)
Spotify’s free vs. premium access offers different features
Example: Customization by Purchase Location (where)
Textbooks sold in different geographical locations have different covers
Example: Customization by Customers (who)
Different students (international, domestic, etc.) pay different tuition fees
Customization by Time of Purchase (when)
Concert tickets are different prices depending on when they are bought (early bird sales, regular sales, etc.)
Boxing Day sales
Customization by Purchase Quantity (how many)
Consumers pay incrementally less with each additional increase in units (ex. cell phone plans, coke bottle sizes)
What are Auctions?
Prevalent in everyday life Affects country’s GDP in key industries and economic components - IPOs and stock prices - Mineral and drilling rights sales - Government procurements (10-15% GDP of the US) - Wine - Antique and art - Search engine advertising
Why use auctions?
- Seller is uncertain about the value of the good:
- Unique items (Picasso painting)
- Difficult to evaluate (gas/mineral rights)
- Demand shocks (Vancouver housing market)
- Search engine (too many goods, e.g. time x location x keyword x position) - Speed matters (fresh flowers, plants, fish)
- Efficient allocation of resources (the item goes to the highest valuation bidder)
Types of Pricing Formats
Price setting party:
- Seller
- Buyer
- Seller and buyer
Price over time/Price formation:
- Dynamic
- Static
Examples of Pricing Formats
Seller + Static: Amazon
Buyer + Static: Priceline (Name your own price option)
Buyer + Dynamic: Ebay
Seller and buyer + Dynamic: Financial markets
Design of Auctions
Buyer + Static:
- 1st price sealed-bid
- 2nd price sealed-bid
Dynamic + Buyer:
- Dutch
- English
Design of Auction: Auction Formats
- Dutch auction (D): open, descending
Ex. Flower, fish, plants - English auction (E): open, ascending
Ex. Antique/art auctions (e.g. Christie’s) - First-price sealed-bid auction (F)
Ex. Gas drilling rights (e.g. in British Columbia)
Ex. US Treasury bills
Ex. US government procurement (10-15% of GDP such as public infrastructure and military acquisitions) - Second-price sealed-bid (Vickrey) auction (S)
Ex. NZ’s communication spectrum rights
Ex. Search Engine Advertising (e.g. Bing, Google AdWords)
Auctions: Two Fundamental Questions
- (To the bidder) Which auction pairs are strategically equivalent?
- Auction A and B would be strategically equivalent if a bidder would follow the same strategy - (To the seller) Which auction pairs are revenue equivalent?
- Auction A and B would be revenue equivalent if they yield the same expected revenue
Vickery’s Assumptions
- Independent private-value (IPV) auctions:
- Each bidder’s private valuation of the item is different and independent of other bidders’ valuations.
- Ex. Soeun values a Friends Lego Set at $200 (no resale). Soeuns’ friend Sam values it at $300 (no resale). - Buyers are risk-neutral
- Bidders are rational
Vickery’s Finding 1: Strategic Equivalence Theorem
Buyers’ bidding strategies are identical in English and second-price sealed-bid auction
- Bid your true WTP
Buyers’ bidding strategies are identical in Dutch and first-price sealed-bid auction
- Bid lower than your true WTP
- Goal is to outbid the next highest bidder just a little bit. So why bid your true WTP?
Vickery’s Finding 2: Revenue Equivalence Theorem
Expected revenue is identical in all auctions (Dutch, English, first-price sealed-bid, and second-price sealed-bid)!
- If you’re a seller, you should be indifferent!
How does Google price your CPC (Cost-Per-Click; the price you pay Google for each click you get)?
The winner is the bidder with the higher Ad Rank:
Ad Rank = (Company’s CPC bid) * (quality score)
- Quality score is based on CTR, landing page experience, etc. and is predicted by Google
Definition: Common-Value Auctions
The value of the good is the same for everyone, which they don’t know before the auction.
- Different from Independent-Private Value
Ex. Oil lease (drilling rights), a jar of coins, goods traded for resale (IPO, art)
Features of Common-Value Auctions?
- Before the auction, the information of the good’s value is not fully available to bidders and bidders have different guesses about how much the item is objectively worth (e.g. different guesses about how many quarters are in a jar)
Ex. Before the auction, Soeun guesses the jar is worth $70. Before the auction, Sam guesses the jar is worth $40. - After the auction is over, all bidders have the same valuation for the good (e.g. how many quarters are actually in a jar)
Ex. After the auction, both Soeun and Sam count the coins and value the jar at $50.
Winner’s Curse in Common Value Auctions
- Winner’s curse: the winner’s bid is higher than the true value of the object.
- Win the bid but lose money!
- Imagine bidding on the jar of coins. You won but you may be paying more than its actual worth. - Most severe in English Auction
- Can only occur for common value auctions!
