-> Cost Function:

📌Fixed cost = 0

• Marginal cost = Average cost = c

-> Both the firms choose their price in order to maximise profits. Being simoultaneously they care about what the other firm choose:

Nash Equilibrium:

-> DEF: strategies where none of the players find it convenient to change strategy given the other’s strategy.

• No one can unilaterally change its position & improve its situation.

=> Each firm chooses a price equal to c:

-> None of the two companies has an incentive to change its choice, given the other’s choice:

-> Given the market conditions the game is symmetric.

-> Prices has to be equal because:

Case I		-> Is not a nash equilibrium
Case II		-> Both firms can unilateraly deviate the prices winning the game
Case III		-> Is not a Nash equilibrium

❓π = 0 better than D = 0 ? -> Bcse it’s compensate my cost of capital. D=0 => π=0 for sure, but if π=0 we are compensating our cost of capital.

-> Reppresent location of the optimal responses. FLOOR: over than that it doesen’t matter: that floor is the marginal cost, if I go lower => I’m going bankruptcy & I don’t care other firms. CEALING:  there is a limit of the price that I set bcse we’ve to take in account consumers’ price elasticity. -> All the points in between floor & cealing are the perspective. -> The two lines never get in touc till MC = c.

Cournot Model:

-> HP: 2 companies No potential entrants (closed markets) Homogeneous good in terms of quantity: the quantity produced by the two firms is the whole quantity produced in the market. Perfect Rationality & Information (4 firms & consumers) -> Consumers will know that: There are 2 firms The prices of each of them The goods are homogeneous Price setted by the market at a level where the demand equals the joint production fo the two firms.

-> DEF: Quantity: Strategic variable (setted the quantity simultaneously => the price follow)

-> Firms choose how much they want to produce, and the price is given by the aggregated market demand (under the hypothesis of standard goods, the DD has a negative slope):

=> The two firms straetgically interact by influencing the market price through the quantity they set.

Model:

-> Given the competitor’s choice, firms choose the best strategy to maximize their profits

-> HP:

• Firms can choose the quantity tey prefer in the interval [0, +oo).
• Both profit functions can be differentiated in quantity.

-> OBJ: drive the equilbrium (two steps):

1. Determine the set of optimal choices of each firm given the rival’s behavior à determine reaction functions
2. Intersect the two reaction functions in order to find the combination of mutually compatible decisions (i.e., the Nash-Cournot equilibrium of the game)

REACTION FUNCTION: optimal response in the context of the other firm, given by the profit maximization. Taking the maximization of the firm one we compute the maximization of the firm two.

Green line is the same quantiti producted. Other point of intersection is the black line: reaction of firm 2. -> EQUILIBRIUM: lies in the middle of the two (important for social welfare!)

Equilibrium:

-> Given the inverse demand function:

• Q is total industry output:

=> We assumed the cost functions:

=> Firms 1’s profit:

-> π = revenues – costs

📌We control just our own quantity

-> First order condition:

=> By simmetry, Firms 2’s reaction function can be found immediately:

=> The equilbrium is given by a couple of values

-> We don’t know the final quantity, then to initiate the model we use expected values and in the end we find out equilibrium values:

Stackelberg Model:

-> One firm decide first and the second one after. Quantity leadership Like a Cournot oligopoly Gives the impression af an information advantage, but is not: both firms know everything. The leader has an advantage   2-Step Competition: -> SEQUANTIAL COMPETITION: competition is not simultaneous anymore and articulates in two steps. Follower maximizes profits given by leader’s choice Leader optiizes the first step by maximising profits given the follower’s reaction in the second step (known a priori). -> HP: Perfect Information: both leader and follower know everything Perfectly Rational (leader and follower)

Other Strategic Variables:

-> In real world firms’ strategic behaviours depend on serveral variables:

• Price (Bertrand model)
• Quantity (Cournot & Stackelberg models)
• R&D investments, product features, commercialization modes…

=> All these decisions imply strategic interaction and interdependence.

Entry Barriers, Entry Deterrence & Limit Pricing:

-> DEF: entry of a new firm producing a good that is a perfect substitute for the goods already produced in that industry.

• Degree of susbstainability depends on consumer preferences (they ultimately decide if a product is a substitute)
• Not necessarily imply the creation of a new firm.

Decision:

-> Depends on expected profits (π=R-C), that are in function of:

• Product Costs (C-osts)
• Demand Conditions (post entry: entry has impact on market quantity & price => new entrances forecast reaction of incumbents) (R-evenues)

Graphical reppresentation:

Green: market demand (at industry level). Blue: demand for the entrant if incumbents are producing q1. Red: demand for the entrant if incumbents are producing q2.   -> With the new entrant to absorb the market demand p, q of incumbent decrease.

-> New Entrant will face a potential demand:

: quantity that incumbents choose to produce after the new entrant.

Entry Barriers:

-> DEF: Obstacles preventing new firms from entering a market and compete against the incumbents.

• Allow the incumbents to keep price higher than the average cost

“A barrier to entry is an advantage of established sellers in an industry over potential entrant sellers, which is reflected in the extent to which established sellers can persistently raise their prices above competitive levels without attracting new firms to enter the industry.”

📌Bain’s Definition (1956)

-> Entry barriers are referred to costs!

“A barrier to entry is a cost of producing (at some or every rate of output) that must be borne by firms seeking to enter an industry but is not borne by firms already in the industry.”

📌Stigler’s definition (1968)

-> Informative, but there are some barriers that elude this definition (predatory pricing, that is usually distruptive and damage both new entrants and incumbents, the difference is in which the incumbents can substain that damage.)

-> In a market with no entry (and exit) barriers:

• Every firm can enter the market and compete with the incumbents.
• In the long run P=AC.

-> However threat of new entry affects price set by incumbents:

• After new entries, incumbents risk incurring losses
• Incumbents may tend to set lower prices in order to prevent new entries.

Cases:

1. P > AC:  firms make extra-profit => without entry barriers, π_new firms:

-> Price 🔽

-> New firms will continue to enter till P=AC

1. P < AC: firms make losses => without exit barriers, most inefficient firms leave the market.

-> Prices 🔼

-> Firms will continue to exit till p=AC

Definitions:

INSTITUTIONAL/LEGAL BARRIERS:

• Administrateive authorizations needed to conduct business
• Patents: right to exclude other people from utilizing smth that have been discovered and could create a value

-> Reduce the capability to innovate: innovation mostly is combination of techologies.

STRUCTURAL BARRIRS:

• Economies of scale (real or pecuniary), scope and learning

-> Allow to have more power with suppliers

• Customer loyalty (structural switching costs: costs that consumers icours when they change supplyers, brand loyalty: some customers stay loyal to your brand, depends on the industries)
• Access to key resources (distribution channels)

STRATEGIC BARRIERS:

• Ex ante: capacity investment (produce higher volumes), artificially induced switching costs (costs consumers incour to change product but stand for a very pourpused and targeted choiche), long-term binding contracts, product proliferation, vaporware

-> Make the new entrants stay out before to enter

• Ex post: predatory pricing: incumbents decide to sharp down prices; vaporware: power of fake annuncement.

-> Kick new entrants out defenetly

Sylow Labini Postulate:

-> DEF: New potential entrants behave assuming that incumbents will keep their production at the same level as before the new entry.

-> New entrant will assess whether entering or not considering:

• The residual demand diagram
• Its own cost function

-> INCUMBENTS REACTION:

• Potential Entrants: hypothesize that incumbents will not vary their production after the new entry
• Incumbents do not vary their production after the new entry

-> Potential demand for the new entrants is given by the difference between the market demand & the quantity already offered by incumbents.

Bain, Sylos Labini & Modigliani (B-SL-M) Model:

-> HP B-SL-M Model:

• Perfect information
• Sylos Labini postulate (no production changes after the entry)
• 2-steps competition.

-> In t=1 the incumbent is the monopolist and it decides both price and quantity.
-> In t=2 a new potential entrant decides whether to enter the market.

• Constant MC and AC
• Incumbent’s absolute cost advantage: the incumbent’s (constant) AC is strictly lower than the new entrant’s AC

ABSOLUTE COST ADVANTAGES: incumbents’ costs are always lower than new potential entrants’ costs.

-> Many factors may underlie new entrants’ cost disadvantage:

• Product differentiation (higher differentiation may be needed to compensate for switching costs)
• Institutional barriers (e.g. payment of the royalties related with a certain patent)
• Less advantageous contracts due to lack of prior relationships with suppliers

-> Entry decision taken considering potential demand & cost function (including implicit costs).

-> Potential entrant will enter the market if it can obtain positive profit:

p	: price obefore the new entry
	: average ocst for incumbent
	: average cost for the potential new entrant

-> If entrant’s residual demand diagram has part that is above the average ost curve => positive profits can be made & new firm may enter the market.    -> If allowing to the new entrant positive profits => The new entrant enters the market and the price decreases

-> There is no entry if the new entrant cannot make positive profits

-> The higher the difference between  and , the greater the possible difference between and  without incurring any new entry.   -> With a high difference between  and , the incumbent can. Charge higher prices without attracting new potential entrants. ->  is a proxy for the height of entry barriers

Limit Pricing:

-> DEF: price at which we achieve this condition:

-> Highest price that can be charged without incurring new entries:

• Higher prices the entrant may enter the market
• Lower prices the entrant cannot enter the market, but the incument is making suboptimal profits.

-> Price Limit is equal to

Economies of Scale:

-> DEF: decreasing average cost before the Minimum Efficient Scale.

• In the B-SL-M model with ES, the higher the economies of scale, the higher is the price limit (i.e. the optimal price enabling new entry deterrence).

-> HP:

• Perfect information
• Sylos Labini postulate (no production changes after the entry)
• 2-steps competition.

-> In t=1 the incumbent is the monopolist and it decides both price and quantity.
-> In t=2 a new potential entrant decides whether to enter the market.

• The two firms face the same u-shaped AC curve: no absolute cost advantages

Dynamics:

-> Essentialy, the line of reasoning is the same:

1. (SL postulate) the new entrant knows that the incumbent will keep production unchanged.
2. The potential new entrant’s decision depends on residual demand (i.e. the difference between the market demand and the incumbent’s production).

1. Considering the average cost curve of the new entrant, the incumbent sets the quantity so that residual demand will not allow any profits for the new entrant.
2. As a result, the potential new entrant refrains from entering.

->  AC is higher than the resiual demand (De) -> the price is lowewr than the AC => entrant would incur losses. -> is the minimum quantity allowing new entry deterrence ->  is the Price Limit allowing new entry deterrence PL is the highest the incumbent can set in order to prevent new firms’ entry in the market. P > PL => entry becomes feasible P < PL => extra profits reduction for the incumbent

Main Critique:

-> The Sylos-Labini postulate implies irrational conjectures of the potential entrant regarding the leader’s behavior:

• Credibility of the threat: one of the two players may want to distort the perception of the competitor by threating him.  But according to game theory the threat could be not credible. After entry incumbent might not find it convenient anymore to produce the quantity  at the price limit PL.
• Ex post, an accomodating straetgy by the incumbent may be the most rational oucome as price war would harm both players.

Dixit Model:

-> Removal of the SL postulate

Dynamics

-> Steps:

• FIRST STEP: new enterant decides whther enter the new market or not;

-> NO ENTER: If potential N.E. doesn’t enter => incumbent make monopolistic profits.

• SECOND STEP: incumbent decides whether to engage to a price war or adopt an accommodating strategy.

-> ENTER: we have two possibilities

• Price War, low profits bot player
• Acquiescence -> Cournot duopoly profits

-> We start from the end (Step Two) to understand our (entering) strategy.

• If the incumbent is perfectly rational => would choose to be accomodating (if ): price war is lower than Cournot equilibrium.
• For the new entrant would be better to enter if the incumbent is accomodating (generally πc > 0 but theoretically could be negative too).

-> CHAR:

• Therat to engage in a price war is not credible (not rationality)
• Monopolist does not have a rational interest to implement the threat
• Incumbent will produce the quantity maximizing the monopoly profits  rather than the one corresponding to the price limit.
• Entry is prevented if and only if , which is unlikely

❓How can be a threat credible? I need to find a way to commit myself to the price war…

• Anticipating some costs of the price war (like investment in additional capacity)…

⚠️It worth only when .

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