Imperfect Competition Flashcards
What are the conditions of Cournot?
- Firms compete by setting output (quantity)
- No production costs
- Firms simultaneously choose qa and qb
- Q = qa + qb
How is the Nash Eqm of a Cournot model found?
- Given that qa affects πb, when choosing q, they will take into account their beliefs about how their actions will affect the others π
What is Firm A’s reaction function in Cournot and how is it derived?
- qa that maximises A’s πs for every possible choice that B makes for qb
- MRa = MCa
- MC = MR
- TRa = p.qa = (x - qa - qb)qa = xqa - qa2 - qaqb
- MRa = x - 2qa - qb = 0
- BRa: qa = (x - qb)/2
Theoretically what is the Cournot eqm?
- If we are anywhere other than equilibrium, the firms will have an incentive to change it’s production decision in response, ultimately culminating at x=y where there is no incentive to change
Mathematically how is the Cournot eqm obtained?
- Need to sub BRb into BRa
- qa = (x - qb)/2
- 2qa = x - qb
- 2qa = x - (x - qa)/2)
- 4qa = 2x - x + qa
- 3qa = x
- qa* = 1/3x
- qb* = (x - 1/3x)/2 = 1/3x
What is true of monopoly compared to cournot?
- If two firms combined and create a monopoly, quantity (market) output would have been 60 i.e. less efficient
- Determine monopoly TR, MR and set to 0 (MC)
What are the assumptions of Bertrand?
- Two firms
- Homogenous goods
- Same Constant MC (Identical Firms)
- Both choose prices simultaneously (One Period)
What is the result of Bertrand?
- Because the product is identical, the firm with the lowest price will capture the entire market
- Prices will always be identical
- They split the market evenly between them
- The only Nash Equilibrium is for both firms to set Pa = Pb = MC
- π= 0
What is the Bertrand paradox?
- No matter how many firms, when they compete on price, it will be 0DWL, maximising total surplus at the perfectly competitive market equilibrium
- Holds for any cost or demand curve
What do capacity constraints result in?
- If we have capacity constraints, then undercutting firm can’t satisfy entire market D, leaving residual D for competitor
- Reduces the incentive to undercut
What are the two periods in Bertrand with capacity constraints?
- 1st: Firm builds capacity
* 2nd: Choose prices
What are q̅ and p̅?
- q̅: maximum quantity that each can produce
- p̅: if production is at capacity for both firms
What arises in Bertrand with capacity constraints?
- Two instances arise because of the fact we’re setting price not quantity
- If pa = pb ≤ p̅ then not in Nash Eqm
- If pa = pb > p̅ then not in Nash Eqm
What occurs when pa = pb ≤ p̅?
- Firms choose q̅a and q̅b so market supply is fixed s̅
- Total quantity(D) > Total capacity
- Increase price and sell less
- We’re not setting quantity at all in this model, so increase price and take the hit in lost quantity (DEMANDED NOT SOLD) because there is untapped demand
What occurs when pa = pb > p̅?
- Firms choose q̅a and q̅b so market supply is fixed s̅
- Total quantity(D) ≤ Total capacity
- So A could cut price, increase quantity demand and sales up to q̅a (full capacity because will take entire market) and increase π
What happens in the 2nd period of Bertrand with capacity constraints?
- Only equilibrium with capacity constraints is pa = pb = p̅
- Comes down to capacity, first stage game just like Cournot
What happens in Bertrand with product differentiation?
- Law of one price will not hold
- Firms don’t face the same demand curve but they all include the competitors price
- qa = x - Pa + Pb
- Q is - related to P, and + related to competitors
- qa = x - Pa + Pb
How do we obtain a reaction function for Bertrand with product differentiation?
- Determine TR, TC and therefore π
- ∂π/∂P = 0
- Solve for Pa and Pb
What is the working for the best response function in Bertrand with product differentiation?
- TRa = Pa.qa = Pa(x - Pa + Pb)
- TC given: determine π
- ∂πa/∂Pa = x-2Pa + Pb
- Pa = (Pb + x)/2
What is true of the reaction functions in Bertrand with product differentiation?
Positive relationship between Pa and Pb therefore both upward sloping
How is eqm in Bertrand with product differentiation achieved?
- Substituting B’s reaction function in A’s
What are the two stages (and condition thereof) in competing on product characteristics?
- Select product characteristics
- Need to be similar/near consumers but have some differentiated features
- Select product characteristics
- Select price
What occurs in a Stackelberg model?
- Firm A moves first and makes a decision which B observes before making their own
What are the steps to determining a Stackelberg eqm?
- Plug b best reaction function into A’s INVERSE DEMAND CURVE FROM MARKET DEMAND, rearrange for price
- TRa
- MRa = MCa = 0
- Solve for qa*
- Plug into B’s reaction function
What will the outcome of a Stackelberg eqm be?
Not Equal
What is limit pricing?
- Can use prices to send a signal when prices are related across time
- i.e. lower than profit maximising
In what situations is limit pricing applicable?
- e.g. Large Advertising Campaigns
- Prices will be set for given period of time when advertised
- e.g. Large Advertising Campaigns
- Leaning Curve
- If expecting lower future costs due to learning, set a lower current price to deter entry - initial losses but future monopoly rent
- Leaning Curve
- Consumer Switching Costs
- Setting a lower initial price allows the firm to gain a large share of the consumer base
- Hard for captive consumers to switch
- Consumer Switching Costs
- Signalling based on Asymmetric Information
- Incumbent Firm (A) has information about it’s cost structure that B doesn’t
- Signalling based on Asymmetric Information
What is the outcome of limit pricing?
- Firm A could send a signal that it expects low costs in order to keep B out
- Problem is it’s always in A’s best entrance to keep B out of the market & therefore send signal that costs will be low
- An incumbent firm will always send a signal via low prices if the losses that they suffer from this price are less than the gain that they make through monopoly rents
What is predatory pricing?
- Illegal
- Price set artificially low i.e. P
What is the price leadership model?
- e.g. steel companies
- 1 Firm (L) is typically seems as the leader over the “Competitive Fringe” (C) in terms of setting price
- Supply Curve of Competitive Fringe vs D/MR
What is the leader’s price decision in the price leadership model?
- Leader won’t set price > P(D=S): CF can supply at all P > P(D=S))
- Any P ≤ P(D=Sc)
- At any price below P(D=S) the leader gets whatever D from the market that CF is not willing to supply
Where does the leaders demand curve occur in price leadership model?
- P(D=Sc) down to P(Sc=0)
- (Sc: supply of competitive fringe)
What are the steps in a price leadership model?
- Leader’s demand curve
- Leaders MR curve
- Leaders MC Curve
- Ql, PL
- Sc@PL = Qc
- D @ PL = Qt
What are the attributes of monopolistic competition?
- Slightly differentiated products
- Downward sloping demand curve
- Gives them some control over prices: P > MC
- Free entry and exit: πLR = 0
What are the important outmodes of monopolistic competition?
- Excess capacity: Doesn’t produce at efficient scale
- D & MR that move
What is the difference between COurnot BR and Bertrand w/ produce differentiation BR?
- qb vs + Pb
