Econ Cheat Sheet

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- “Cooperate” (high price forever) payoff: 450+450/r

- “Undercut” payoff: 650 + 300/r

Cooperation is a Nash Equilibrium if:

450 + 450/r > 650 +300/r (i.e., if r )

Product differentiation: with product differentiation, some customers will buy at P>MC → firms can profit.

1) identify firm’s demand curve - Describes how Coke’s demand depends on Coke’s price given a price of Pepsi. 2) For each price choice by Pepsi, we can find Coke’s profit-maximizing choice -- its best response (as a monopoly):

3) graph BR curve for both firms (upward sloping), and identify Nash equilibrium (each firm is choosing its BR to what the other firm is doing):

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If Coke’s MC falls, or if product diff. falls (more elastic demand), both firms’ prices fall:

[pic 14][pic 15]

Cournot Model.

Two firms with homogeneous products choose simultaneously [pic 16]

A firm’s “residual” demand curve given rival’s capacity:

[pic 17]

And then treat it as a monopoly.

Always, to check prices and quantities:

Quantity: Monopoly

Price: Monopoly > Cournot > Competitive

- QN-firm Cournot = N/(N+1) * QCompetition

ANTITRUST:

To measure concentration: Herfindahl-Hirschman Index (HHI) = sum of squared market shares, it has to be >2,500 post merger, and change >200.

BACKWARD INDUCTION

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Think what will happen in the future given different current choices.

[pic 19]

Sequential choice of capacity:

[pic 20]

If firms choose simultaneously, they are going to choose 20,20 (Nash equilibrium), but if firm 1 chooses first, it’s going to choose 22.5.

Capacity expansion to deter rival’s entry: Capacity expansion can lead to lower prices, which is bad, but in some circumstances, it can be used to gain a strategic advantage (affects rival’s choices).

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STRATEGIC PRICING: based on recognition that consumers with (unobservable) different willingnesses to pay will make different choices → “self selection”[pic 23]

Two-part tariffs: F+p*Q

If buyer’s WTP is observable, a firm can perfectly price discriminate: creating maximal value and capturing it all: p=MC + t=CS *number of clients

If buyer WTP is unobservable:

Suppose there are two types of buyers: 100 with high WTP, 200 with low WTP. You can offer a single two-part tariff (F, p). Example: MC=$0.1, = F for both, ≠ P for each

[pic 24]

Low types use 30 min and pay $4.5+$6 → profit=$7.5

High types use 80 min and pay $4.5+$16 → profit=$12.5

Multiply * number of buyers in each type

(tariff counts towards both types of customers)

If p=MC and F=CS low type maximize value (both types buy and choose efficient number of minutes)

Move p=MC if gain from high types>loss low types

Cap the low-end plan: allows the firm to charge two different tariffs for the 2 types of customers.

CS of high demand needs to be the same for the “basic” plan and “gold” plan. After the cap, extract all of CS

The firm now offers 2 plans:

Low WTP: FL=8, PL=0.1;

High WTP: FH=20.5 (new area A + 8), PH=0.1

Total profit = (200*8) + (100*20.5) = 3,650

[pic 25]

The cap trades off lost profits from low wtp buyers vs. profits from high wtp buyers. Making this trade-off makes sense as long as the area lost*#low customers

With 200 low types and 100 high types, profit is maximized when black hatched area is ½ the height of the red hatched area (setting the marginal benefit of a tighter cap = its marginal cost):

[pic 26]

Product portfolios and pricing: allow the firm to capture more high WTP buyer value by charging + for “upgrades”

Price Discrimination: No Two-part Tariff:

[pic 27]

Price Discrimination: Two-Part-Tariff:

[pic 28]

If two firms merged, they would act like a monopoly.

Product Portfolio:

[pic 29]

Bundling: selling several products together as a package, to increase a firm’s ability to extract consumer surplus, particularly when the WTP of the bundled products are negatively correlated:

[pic 30]

Sequential Move Problem:

[pic 31]

Adverse selection: arises when the consumers who are most inclined to buy are also the costliest to serve. In extreme cases, adverse selection can make it impossible for a firm to sell a product profitably (always AC≥WTP). Examples: health insurance markets, used car market.

NEGOTIATIONS:

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