Oligopoly Flashcards
What are the conditions of a Cournot Oligopoly?
- Few firms serving many consumers
- Either differentiated or homogeneous products
- Firms choose quantity as the strategic variable, simultaneously
- Barriers to entry exist
What is a best response?
- The best response gives the profit-max level of output for a firm given the output levels of the rival’s
What is the form of a best response function?
- π1 = P{q1 + q2}q1 - C(q1)
How is a residual demand determined?
Given Firm1’s decided level of output, Firm2’s residual demand is same slope with Y-int at P where Firm1’s output quantity = market demand curve
What is a firm’s output decision as a best response to another firm, and what does this imply?
Firm acts as a monopolist on its residual D
Best response to a raise in quantity is a decrease in quantity
What does the slope of a best response function imply?
q1* decreases as q2 increases: Strategic substitutes
What is the best response to 0 output?
- If q2 = 0, firm 1 produces the industry monopoly output level
- R1 (0) = qm
In Cournot, when would a firm choose to produce 0 output?
- If q2 is so large that firm 1 expects p = MC (PERF COMP LEVEL) with q1 = 0, firm 1 would find it profit max to produce zero output
What is the profit/quantity relationship in Cournot?
- π1↑ as q1↑ (as q2↓)
What will determine the shape of the Cournot best response intersection?
- Given the same MC, the best response will be perfectly symmetric: on 45 degree line
What is the Nash Eqm of a Cournot game?
- The intersection of the two best-response functions is the Nash eqm to the Cournot game
What options are there to deriving a best response function?
- Competitive/Monopoly
2. F.O.C. π max
What are the steps to solving a Cournot game via qc and qm?
- Determine competitive market
- Determine Monopoly market
- Qa = qm - (qm/qc)Qb
- Qa = Qb = Q* (plug one into the other)
What is the relation between Cournot, monopoly and competitive Q and P?
- Industry output in Cournot is greater than the monopoly output and less than the competiviet output
- This prices if less than the monopoly price and greater than the completive
What is the relation between n and P in cournot?
As the number of firms increases, market prices decreases
What is essential in determining eqm P in Cournot?
Price is a function of total market Q, not individual firms’
What is an isoprofit and what do they look like?
- A function that defines the combinations of outputs produces by all firms that yield a given firm the same level of profits
- CURVES towards PC output
- INCREASES towards MONOPOLY output
If X axis = Qa, on whose BR function will X-Axis Qm and Qc belong to?
Qm = Firm A (x-axis) Qc = Firm B (y-axis)
If X axis = Qa, on whose BR function will Y-Axis Qm and Qc belong to?
Qm = Firm B (y-axis) Qc = Firm A (x-axis)
What does a decline in Firm Y’s MC have on it’s BR function?
BR(Y) shifts upwards
i.e. for any given level of firm 1, firm 2’s best response is going to increase
Has no effect on firm1’s best response
How do Cournot firms collude?
By reducing output (produce qm jointly/evenly)
What is true of Cournot collusion?
- Each firm cannot improve its payoff by deviating from a Nash eqn unilaterally
- Collusive agreement is not a Nash eqm and is not sustainable
- Firm’s are not playing their best responses
- Collusive agreement is not a Nash eqm and is not sustainable
What does the sustainability of Cournot collusion imply?
- In infinitely repeated game framework firms may be able to sustain collusion
- Totally not possible to be nash eqn in one shot game though
How is collusion shown in Cournot?
- Line running from Qm1 to Qm2
- Point M: both firms produce 1/2 of monopoly level
- Given that firm 1 is producing at M, firm 2 has an incentive to deviate from this level and produce to its best response curve
What are the conditions of a Stackelberg Oligopoly?
- Few firms serving many consumers
- Homogenous products
- A single firm (leader) chooses an output before all other firms choose their outputs
- All other firms (the followers) take as a given the output of the leader and choose outputs that maximise profits given the leader’s output
- Barriers to entry exist: long run profits
How can we find the Subgame Perfect Nash Eqm in a Stackelberg Oligopoly?
- use Backward indication
- Work out firms’ 2 best response given all different output levels of firm 1
What is the Follower’s best response in Stackelberg?
- Max π2 for every given possible value of q1
- Derived from the residual D for firm 2 after subtracting q1, and set MR=MC for firm 2
- Exactly the same problem as when solving the Cournot best response, q2* = R2(q1) (follower faces exactly the same Cournot best response)
What is conventional and implied form of the Leader’s profit/output decision in Stackelberg?
- In the first stage, firm 1 chooses q1 to max π1, however firm 1 does not take q2 as given
- π1 (q1, R2(q1)) = P{q1 + R2(q1)}q1 - C(q1)
What does the MR of the Leader in Stackelberg imply?
As Q1 increases: price effect, partially offset by decrease in output of firm 2 from it’s best response changing
Graphically what is the Stackelberg eqm?
- We know firm 2 produces according to it’s best response: eqn point must be on BR2
- Given this, to maximise profit, firm 1 needs to reach the highest possible isoprofit curve
- Tangence point between BR2 and π1
What is the difference in profits and output between Cournot and Stackeblerg?
- Compared to Cournot, followers profit decreased, leaders profit increased
- Total Industry Output decreased from Cournout to Stackelberg, as the slope of r2 is less than 1 (like elastic lowering price)
What is convention in Oligopoly graphing?
Firm 1 (Leader) - X-Axis
What are the steps to solving a Stackelberg Eqm?
- Determine Followers BR Function (Cournot)
- Plug This into Leader’s BR Function
- Max/f.o.c. this (FORMULA)
- Solve for Followers optimal output
- Solve for price
What are the conditions of a Bertrand Oligopoly?
- Few firms serving many consumers
- Identical (or differentiated) products
- Firms compete by choosing prices simultaneously
- Consumers have perfect information and there are not transaction costs
- Barriers to entry exist
What demand, dependent on the relationship between P1 and P2, does Firm1 face in Bertrand?
- Demand facing firm 1 is D1(p1) = D(p1) if p1 p2
- D1(p1) = 1/2D(p1) if P1 = P2
What do the firm’s demand conditions in Bertrand imply?
- Undercutting the market slightly is better than sharing the market
- For any price strictly greater than MC, firms always have incentive to undercut marginally
What is the equilibrium of Bertrand?
- The conditions for a Bertrand olitogoply imply that firms in this market will undercut one another to capture the entire market leaving the rivals with no profit. All consumer will purchase at the low price firm
- For symmetric firms with equal MC, this price war would come to an end when the price each firm charged equaled marginal cost
- In eqn, P1 = P1 = MC
- Socially efficient level of output
What does the equilibrium of Bertrand imply?
- Pair of prices such that both firms are playing their best response:
- π1(p1b,p2b) ≥π1(p1,p2b) for any p1
- π1(p1b,p2b) ≥π2(p1b,p2) for any p1
- Given the Nash eqm price of its rival, neither firm has the incentive to unilaterally deviate
- P = MC at The intersection of two best responses
- Only 1 nash eqm: P1=MC the only point where both firms play their BR against the other’s BR
How can the collusive outcome be determined?
- Derive market MR from market D
- MR = MC
- Each firm will produce half of this output
What are contestable markets?
- Contestable markets involve strategic interaction among existing firms and potential entrants into a market
When are markets contestable?
- All producers have access to the same technology
- Consumers respond quickly to price changes
- Existing firms cannot respond quickly to entry by lowering price
- There are no sunk costs
What does a contestable market result in?
- If these conditions hold, incumbent firms have no market power over consumers: 0 profits
What is essential about market price in oligolopoy?
Derived from MARKET quantity
How can a change in CS be calculated?
CS = ((y-int - P) * Output)/2
What is important about the increase in PS from a merger?
∆PS = Gain from merger - Loss of existing firms π
