Basic Oligopoly with Markets for Undifferentiated Products

BASIC OLIGOPOLY WITH MARKETS FOR UNDIFFERENTIATED PRODUCTS (commodities/near-commodities):

BERTRAND undifferentiated products, firms set price to set what quantity to produce, race to the bottom ensures lack of differentiation. Equilibrium ends up at p = c+.01 because firms set price at MC. Zero profit for market participants, but assumes no capacity constraints. Simple Model: Information: 2 firms, identical goods, compete only on price, simultaneous move

- Outcome: If firm charges more, sell 0 units. If charges less, capture enter market demand at that p. If same price, split market.

- Payoffs: Constant # of consumers buy from one firm, decision only on price. firm face a constant marginal cost 𝑐, & max profits

COURNOT - Players choose capacity constraints. Firms make decisions about what quantity to produce. Firm will picture a hypothetical quantity from their rival and choose best quantity to maximize profits. Think buying inventory ahead of time & setting price to clear the market. [pic 1]

- Information: 2 firms, identical goods, simultaneous move, firms choose quantities (i.e. capacity),

- Outcome: all units sell at price (𝑞1+𝑞2).

- Payoffs: Firms face a cost of C(𝑞), although, we will usually simplify to a constant marginal cost 𝑐.  Firms maximize profits. 

Competing in a Cournot Industry - Watch capacity creep, take market share with cost reductions, merge when appropriate (i.e. when there are significant cost synergies), beware of collusion (jointly decide on capacity, but cheat by best response function)

FIRST MOVER ADVANTAGE (Leader/Follower)

- Info: 2 firms, called Leader/Follower. Identical goods, sequential move. Leader choose 𝒒L then Follower chose 𝒒F - Outcome: All units sell at price (𝑞𝐿+𝑞F ).  - Payoffs: firms face a cost of (𝑞) and maximize profits[pic 2][pic 3]

Conditions for 1st Mover: Be forward looking, commit to quantity (makes game sequential)

LIMIT-PRICING : first-mover advantage to keep follower out by producing more so it may not be profitable for others to come in. Must find q that drops p low enough to keep others out, but not so low that you lose money.

Step 1: Find limit pricing q. Find qLLimit such that ΠF(qF*(qLlimit)) = 0  Step 2: Make sure it’s credible. Check that ΠL(qLlimit)>0

Step 3: Compare profits to first mover and choose. Check that ΠL(qLlimit)> ΠL(qL*) w/ price from qL* + qF*

BASIC OLIGOPOLY, DIFFERENTIATED PRODUCTS (CPG, apparel) IN REPEATED INTERACTION: DON’T DO MR=MC

Own-Price Elasticity – Always (-) Cross-Price Elasticity – How your demand changes when another product changes price. Can be (+) for substitutes or (-). Competitor’s goods are considered imperfect substitutes – close but not quite. [pic 4]

Monopolistic  Competition

- Information: 2 firms, differentiated goods, compete only on price and product, simultaneous move

- Actions: Firms set prices - Payoffs: firms face a constant marginal cost 𝑐, no capacity constraint, maximize profits[pic 5][pic 6]

INDIVIDIUAL PRICE DISCRIMINATION 1) Perfect 2) Demographic 3) Self-selecting

1) Perfect PD: ability to charge consumers their exact WTP, profit equals total surplus.

Conditions: market power, consumers valuations differ, resale is not possible. [pic 7]

[pic 8][pic 9]

[pic 10]

2) Demographic PD: Firm target’s consumers type, correlated with valuation and offers unique prices to identifiable groups.[pic 11]

 3) Self-Selecting PD: You can’t split into enforceable demographic groups or worried you will anger customers with discriminatory pricing. SO: make deals to offer the low-valuation types unattractive to the high-valuation or sweeten the pot to make high-val types want to pay more.

Willing to Buy Constraint: Each type must get non-negative surplus so they will purchase.

Buy the Right One Constraint: higher vals value good more, so will get positive surplus from buying low-priced good. Need to “leave some money on the table” so they are happier choosing higher value good.

Other Strategies: “Damaged Goods”: damage the good to create a low-quality version. Price it lower to capture add’l consumer while still attracting high-value consumers to high-quality products. [pic 12]

“Versioning”: changing quality to match price points.

QUANTITY PRICE DISCRIMINATION 1) Qty Discount 2) Membership

1.QTY Discount – charge differently for different quantities

individual demand: how much one consumer will purchase at a given per-unit price.

Firm knows: each consumers’ exact valuation for each unit

To Capture Surplus: Set individual prices for each unit demanded

Firm captures all surplus if they know each consumers price for each unit. If NOT: firm leaves some money on the table and it is a stepped graph.

2. Membership: Price is an area under the curve in these graphs. Also applied whenever solving for a price for specific qty of good[pic 13]

QTY SELF SELECTING PRICE DESCRIMINATION:

1) Menu Pricing: offer qty bundles targeted at different consumer types, which consumers may self-select into

2) Two-Part Tariff: Charge a membership fee and a usage fee to target different segments and let them self-select their qty.[pic 14]

Case 1: Identical Consumers: Set usage fee to be marginal cost; set membership fee to be the consumer surplus given usage fee.

Case 2: Multiple Consumer Types:

Step 1: Determine low type’s consumer surplus for a given per-hour usage price P. This is max membership fee we could charge and still get low types to join.

Step 2: Figure out profits from both membership fees and usage fees using areas. Πusage = (#low)(low profit)+ (#freq)(freq. profit)

Πmembership= (#low + #freq)(membership fee)[pic 15][pic 16]

Step 3: Find usage fee that maximizes profits by taking the derivative of the total profit from step 2 in terms of p. Set it to 0.

Step 4: Make sure that this profit is greater than what we could earn from just serving frequent types.

BUNDLING For Market Power, Strategic Gain or Price Discrimination

Pure Bundling: Sale which requires customer who buys on product to also buy another product at same time.

Set Prices equal to valuations of one customer and compare profit. Doesn’t work when one party is willing to pay more for BOTH. With more than two types of consumers, at least two consumer types must be negatively correlated!

Mixed Bundling: Brute force is only way. General Rules: do not want anyone consuming a good if they value less than MC, bundle should get as close to one type of consumer’s valuation of both goods as possible. Buy the right one constraint holds.

DEALING WITH UNCERTAINTY, INSURANCE AND RISK:  * Expected value: * Exp utility:  * Willingness to pay for full insurance: payoff (gross of premium) when insured – certainty equivalent of being uninsured[pic 17][pic 18]