MBA 201A'1a,2a Semester Review

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MBA 201A.1a,2aSemester Review

• Dylan Minor

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Semester Review

• Review Class Concepts
• Decision Trees
• Expected Value Best Moves
• Option Value and Info Value
• Costs
• Types Fixed, Variable, MC, AC, Sunk
• When are they relevant
• Pricing
• Demand Curve Pricing
• Optimal Simple Pricing Derivatives
• Price Discrimination by Customer Type
• Two-Part Tariff
• Price Elasticity of Demand

• Pricing (continued)
• Discrete Demand
• Simple Pricing
• Versioning
• Bundling
• Price Discrimination by Volume
• Strategy
• Simultaneous Games
• Sequential Games
• Repeated Games
• Auctions
• Firm Competition
• Bertrand, Cournot, Stackelberg
• Long/ Short run
• Double Marginalization

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Class Concepts Setting up Decision Trees

• Node Types
• Chance Node
• Decision Node
• Terminal Node
• Setting up a Decision Tree
• Timeline
• What has happened already? ? Sunk Costs ignore
  but record (80 vs. 20 success)? Expected value
  vs. sunk decision- but equivalence with sunk cost
• Is a given node a decision, chance, or terminal
  node?
• How many branches from the node? Are you sure?
  Continue until every branch has come to a dead
  end (i.e., a terminal node)

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Class Concepts Solving Decision Trees

• Backward Induction
• Start from each terminal node and work towards
  the beginning
• Decision Nodes
• Choose the best of the options (and mark it!)
• Chance Nodes
• Find the expected value of the outcomes
• Finally, calculate the EV of the entire tree
  each POSSIBLE terminal node X probability of each
  POSSIBLE terminal node (note all probabilities
  added together better equal 100 and generally
  NOT all terminal nodes are possible)

EV 50.4 -100.6 EV 2 6 EV -4
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Class Concepts Info and Option Value Just
Compare the trees!

• Information Value
• EValuewith information-EValuewithout
  information
• Recall if having the information does not
  (potentially) change your choices, it is
  worthless
• Option Value
• EValuewith information-EValuewithout
  information
• Recall option value and information value are
  calculated WITHOUT having paid the cost of
  information or option

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Cost Allocation- Bottom Line Always Ask
decision time horizon shut down vs. quantity
decision sunk vs. not direct vs. not fixed vs.
variable

• How do we allocate Marketing?
• Labor?
• Equipment?
• Equipment (or asset expenses) without a loan
  (maintenance, cost of capital, and depreciation
  (if any)) and with a loan (principal (if any),
  interest, maintenance, and depreciation (if any))

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The Production Decision

• When do we produce one more unit of a product?
• When do we shut down the production of a given
  product line?
• When do we shut down the firm?

Produce an additional unit as long as marginal
cost is less than marginal revenue
If all expenses that can be eliminated AND are
caused by the lines production exceed revenue
attributed to the product line, stop producing
the product line AKA average cost exceeds
average revenue gtgt SHUT DOWN LINE
When no longer have any profitable product line
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The Basics of Pricing and Elasticity

• Assuming no price discrimination, how do we
  price?
• Whats price elasticity of demand?
• How do we use elasticity?
• Whats elastic vs. unitary vs. inelastic? Why do
  we care?
• Whats the relationship between MR and elasticity?

We produce or set price until MCMR Caveat what
if MR/ MC cross more than once? What if never?
What if two goods/mkts? What if capacity
constraint?
We use it to predict the effects of small changes
of price on quantity demanded, Thus helping
determine proper pricing strategies.
Elt-1 elastic, 0gtEgt-1 inelastic, and E-1 unitary
We always want to be on the elastic part of the
demand curve
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Modes of Pricing Strategies

• What is 1st Degree Price Discrimination?
• What is 2nd Degree Price Discrimination?
• What is 3rd Degree Price Discrimination?
• Whats the two part tariff strategy?

Perfect, Per Customer Discrimination- 100
surplus sucked out How to do it? Just sell to
each customer their full WTP
Offering packages that force customers to self
reveal types How? Covered in a few slides
Weve just finished all the way through the
MIDTERM!!!
Discriminating across customer groups (assumes we
can do so and no arbitrage) How? Simply set
MR_1MR_2MC. With capacity constraints set up
profit function, Substitute in for one of the
quantities, take the derivative and set 0, then
solve.
Simple Pricing? Just set MRMC.
Discriminating via fixed (entry) and quantity
fee How? For homogeneous customers PMC and fixed
fee equals all excess consumer Surplus (e.g.,
assume Pa-bQ, then we get F.5((a-MC))x(q),
where qa/b-MC/b)F) For two types, compare
doing the above for the low type. You then have
profit of Fx(m)x(n), where m and n are the number
of low and high types, respectively. Compare
this to only using a two part tariff for the high
type. Your profit is then Fx(n) since the low
type is not served. Use whichever strategy
produces the most profit. Hot Tip we must have
each consumer types demand curve to do this! We
are also are assuming we cant use distortion.
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Class Concepts Versioning

• Versioning
• Sell two versions of the same products (usually
  high and low quality) to customers with different
  preferences for the product versions.
• How to use Versioning
• 1) Price the low type product at the low type
  customer willingness to pay
• 2) Price the high type product at the high type
  customers willingness to pay less the consumer
  surplus he/she receives from buying the low type
  product
• 3) Compare the profit of selling to the high and
  low type customer with selling to just the high
  type customer. Choose the strategy that produces
  the highest profits.
• Requirements for using Versioning
• This pricing method works best when there are two
  distinct customer groups and everyone agrees
  which product version is better than the other.
• Arbitrage? No, you are charging one price for
  each product version.
• Better than simple pricing? Depends on how
  expensive it is to create two versions

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Class Concepts Versioning Example

• Demand PhD student 3 Red Pens, 6 Black Pens
  MBA student 4 RP, 8 BP
• Cost 1 RP, 2 BP. How do we price?
• Look at each scenario, with (1,1) (1,3) PhD/
  MBA

(1,1) Price to both Sell RP for 3, BP for 7,
profit257 (1,1) Price to both Sell only BP
for 6,profit428 (1,1) Price only to MBA
Sell only BP for 8 to MBA, profit6 (1,3) Price
to both Sell RP for 3, BP for 7,
profit23517 (1,3) Price to both Sell only BP
for 6, profit4416 (1,3) Price only to MBA
Sell only BP for 8 to MBA, profit6318
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Class Concepts Price Customization by Quantity

• Price Customization by Quantity
• Sell your (same) product in a small package and a
  large package to customers with different
  quantity preferences (say high and low type)
• How to use Price Customization by Quantity
• 1) Price the low quantity product at the low type
  customer willingness to pay
• 2) Price the high quantity product at the high
  type customers willingness to pay less the
  consumer surplus he/she receives from buying the
  low quantity product
• 3) Compare the profit of above, selling to the
  high and low type customer a high a low quantity
  package, to selling the high quantity to only the
  high type customer for their full willingness to
  pay. Choose the strategy that produces the
  highest profits.
• Other Considerations
• Arbitrage? There are definite arbitrage
  opportunities. Be sure to consider whether they
  are a problem.
• Better than a single price? Not necessarily.
  Check to be sure (remember single price is a
  subset of all these other strategies)!

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Class Concepts Quantity Discrimination Example

• Selling wine to PhD vs. MBA students, MC1 per
  glass
• Whats the pricing solution with (1,1) and
  (99,1)?
• Note we are assuming you can meter customers
  (i.e., the high type cant buy 2 single glasses
  separately over a single 2 glass pair). Imagine
  youre an MBA student that instead of buying your
  2 glasses today, you plan on being a schemer too
  by only buying one glass today and then coming
  back next week for another. However, next week
  you have the same choice of 1 glass for 1 of
  surplus or 2 glasses for 1 of surplus. Hence,
  as economists we break the indifference and the
  scheme still works. The only think we must
  prohibit is buying 2 singles over the pair of
  glasses on a particular visit since we assume
  your WTP is on a per visit basis.

(1,1) Sell 2 to both (4-2)24 (1,1) Sell 2
only to MBA (7-2)5 (1,1) Sell 1 to PhD, 2 to
MBA (2-1)(6-2)5 gtgtindifferent- which
one? (99,1) Sell 2 to both (4-2)100200 (99,1)
Sell 2 only to MBA (7-2)5 (99,1) Sell 1 to
PhD, 2 to MBA(2-1)99(6-2)103
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Class Concepts Bundling

• Bundling
• Two or more products that can be consumed
  separately, packaged together and sold at one
  price
• How to use Bundling
• Try Simple Pricing
• Price each product at the profit maximizing point
• Try Pure Bundling
• Price the bundle so that it appeals to all
  consumers and determine profits
• Try Mixed Bundling
• Create smaller bundles and offer (some)
  individual products, and calculate profits
• Compare profits of each strategy
• Requirements for using Bundling
• This pricing method works best when there are two
  or more customer groups with strong willingness
  to pay for one product and weaker willingness to
  pay for the other.
• Arbitrage? Yes, think about how to prevent
  consumers from unbundling reselling.
• Better than simple pricing? Depends on how
  correlated demand is among customers

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Class Concepts Bundling Example

• Extract rents from Eran, Jeep, and Toby Opera
  and Punk Rock
• What is the best simple, pure bundled, and mixed
  bundled package?

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Games Dominated vs. Dominating Strategies

• Dominated Strategy there exists some strategy
  that is ALWAYS better than the dominated,
  REGARDLESS of what the other player/s does/do
• Dominating Strategy such strategy is ALWAYS
  better than ANY OTHER strategy, REGARLDESS of
  what the other player/s does/ do
• C is dominated for player 2 if d2gtg2 AND e2gth2
  AND f2gti2 (or similarly if a,b,c are all strictly
  greater than g,h,i, respectively OR both)- thus C
  could be ruled out by player 1 as being played by
  2
• A is dominating for player 2 if a2gtd2 AND a2gtg2,
  b2gte2 AND b2gth2, and c3gtf2 AND c3gti3- then player
  one can just consider column A
• Note we are using a basic definition of
  dominated since we only allow such strategies to
  be eliminated by pure strategies (i.e., non-mixed
  strategies). However, the full definition of
  dominated strategies also allows for the
  elimination of a strategy (that is thus dominated
  ) via mixed strategies. However, since we
  havent covered mixed strategies, I present here
  the pure (i.e., non-mixed) strategy analog.

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Games Dominated vs. Dominating Strategies Example

• Find a dominated strategy, dominating strategy,
  and the equilibria/um

C is dominating for 2, F is dominated (and maybe
more) (F,C) is our unique Nash Equilibrium
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Class Concepts Repeated Games

• Repeated Game Strategy Evaluation
• Let High Profits H, Low Profits L, Cheat
  Profits C
• Discount d
• Grim Strategy ? If both choose this strategy, is
  it an equilibrium? Will parties want to cheat?
• Profits from Both Pricing High H/(1-d)
• Profits for a Cheater Cd/(1-d)L
• If H/(1-d) gt Cd/(1-d)L, then both parties
  pricing high using the Grim Strategy is an
  equilibrium. Otherwise, parties have incentive
  to cheat, and pricing high will not be
  sustainable (i.e., only L,L is our repeat game
  equilibrium, which is always an equilibrium even
  under possible tacit collusion)

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Class Concepts Repeated Games Example

• Repeated Game Strategy Evaluation
• What discount rate is required for a tacit
  collusion equilibrium?

We need 10/(1-d)gt20d/1-d5 gtgt
10gt20(1-d)5d-15d20 gtgt dgt2/3
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Class Concepts Auctions

• Summary of optimal strategies
• Recall there are alternate ways to have an
  auction that are strategically equivalent to 1st
  price or 2nd Price (e.g., drop hand at price no
  longer want it while ascending prices are
  given2nd price)
• Uncertain values with affiliated signals (i.e.,
  another bidders valuation provides information
  on your valuation of the object) is known as
  common values and is subject to the winners
  curse- hence, the shaving of your bid under all
  auction formats
• Dont worry about risk aversion!

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Class Concepts Sequential Games and Cournot/
Bertrand/ Stackelberg competition

• See lasts section notes for a long problem on
  all this
• Similarly, see my past section that has an
  extended example/ instruction on long/ short run
  homogeneous firm markets

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Class Concepts Double Marginalization

• You make banana splits, but have to purchase your
  bananas (and everything else is free). The
  banana producer has MC1. You face demand of
  P11-Q. What are the quantities, prices, and
  profits? What if you VI?

You set MRMCgtgt 11-2QP_b, P_b is your cost of
bananas gtgt Q(11-P_b)/2 Now the banana producer
solves MRMC gtgt 11-4Q1 gtgtQ2.5, P_b6 You
produce (11-6)/22.5 banana splits for
profit(8.5-6)2.56.25 BP makes
(6-1)2.512.50 of profit. If you vertically
integrated (VI), you would have 111-2Qgtgt Q5,
P6 gtgt Profit(6-1)525 vs. 18.75 in total
before
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SO

• Thats it for now
• Thank you for a great semester
• AND GOOD LUCK!
• And just in case office hours tomorrow
  930-1130, 4-6, good time for reviewing problems
  and anything else