2.4 Oligopoly Flashcards
What is a oliogopolisitc markets?
Oligopolistic markets have a relatively small number of firms, which are
strategically interdependent
When we look at monopolies firms can either choose price or quantity after choosing where mc=mr, it doesn’t make difference which way you choose, is this the same for oligopolies?
it makes a fundamental difference if firms are choosing quantities or prices, the outcomes are different.
1) For example a iphone, do you think apple chooses how much to sell, then price follows, or they choose price when Q follows?
2) Lets say you have a hotel business, and want to build hotel, are you picking quantity or price?
1) they choose price , then Q comes from demand.
2) you are choosing quantity ( you figure out how big your hotel must be, then in peak season prices might be higher and when not prices will be lower.
What 3 models will we work through to show how different oligopolies might work?
1)The Cournot duopoly model (quantity-setting); Stackelberg equilibrium;
cartels
2) The Bertrand duopoly model (price-setting); with identical goods and
imperfect substitutes
Firstly lets look at cournot duopoly, lets study this with 2 identical firms, but can extend to n firms, selling identical goods, and marginal cost of production c and no fixed costs ( you can derive the same answer with different costs), so against what is each firms strategy and what type of game is this? So lets us the example face masks, so one producer decides how much to produce and the other producer decides how much to produce. What do we want to find?
• Each firm’s strategy(what you choose) is its output – firms set quantity
• One-shot, simultaneous game
We want to find cournot nash equilibrium in outputs( where quantities are best responses to each other)
So explain the best responses scenario for the face masks trying to maxmise profits by setting q?
So basically its saying how much do i produce depending on the other guy ( so essentially q1 is a function of q2 and q2 is a function of q1
Assume total cost = mc x qi where qi is individual quantity. Now what is the profit function for firm q? As firms are identical what does it mean?Assume a > c ( so demand is high enough)
The profit function is the same for firm 2
Looking at profit function what can i deduce?
Price is not only determined by what i make but also what my rival makes, what my rivial does affects me negatively ( -bq2) because q1 and q2 affect prices so for any given quantity i make, if the rival produces more q2 that will lower my price, so i produce less
So firm 1 wants to choose q1 that maximises profit so what do we do? With your q1 function describe some parameters?
we differentiate the function with respect to q1 and check SOC ( -2b<0 so maximum) then rearrange to find q1.
if demand parameter goes up with all things being equal then q1 increases, if costs go down with all things being equal then higher q1,extra. As q2 goes up q1 goes down.
Why are quantities strategic subistutes ?
If my rivial produces more, my best response is to cartel my production a little bit ( thats the profit maximising thing to do, because im trying to dampen the effect on market price a bit)
What is the reaction function of firm 2 and what shape do they have?
as a and c are constants, they have a downward linear shape.
So we have found reaction functions of q1 and q2, what do we now want to find ?
We now need to find the q1 and q2 that satisfy these equations both simultaneously, because if both equations are satisfied, both firms are acting optimally. So sub q1 into q2.
How does this cournot quantity compare to monopoly quanitty ( individually and total quantity? and what is the total quantity?
But total quantity is bigger than monopoly quantity.
How do we find Price? ( the price follows on from quantity?
So you plug total quantity into the inverse demand function then you will find price
What does this tell me ?
This tells us if you have 2 compeitiors in the market choosing their quantities we will end up with a market price > mc ( markup). So a duopoly makes profit in equilibrium.
What is the profit made in cournot duopoly analyse this?
They will produce more than the monopoly and have a price just below monopoly but above marginal cost
How would you illustrate cournot compeition/duopoly on a diagram, where is the nash equilibrium?
Nash equilibrium is when the firms are doing their best responses at the same time, because of symmetry it falls on the 45* line.
Why does the best response for firm 1 and 2 touch y and x axis at qm( monopoly quantity?
If firm 2 chooses to produce nothing, the best thing i can do( firm 1) is behave like a monopolist, as its the profit maximising result.
If firm 1 chooses to produce nothing, the best thing i can do ( firm 2) is behave like a monopolist, as its the profit maximising thing to do. If firm 1 decides to produce something, because quantities are strategic subistutes, they scale back a little and produce less
Suppose the marginal cost of firm 1 fell ( they become more efficient what is its best response for any given q2?
q1 will increase ( as costs are less. so the best response line would shift outwards and cournot NE would be non-symmetrical( not on 45* line. Firm 1 is producing more than firm 2. Firm 2 does survive but has a smaller market share. ( ALSO NOTICE FIRM 2 CARTELS ON A BIT OF THERE PRODUCTION)
Lets think about what a cartel would look like, so suppose these 2 firms were choosing to behave like a cartel, instead of choosing quantities which were best responses to each other, so what do they have to do here? Will it be a nash equilibrium?
They want their total quantity to equal monopoly quantity, so they will want to limit production to equal total quantity of monopoly. ( most likely half the market
It will not be a nash equilibrium.
The dashed line gives any combination of q1 and q2, where the sum is qM.
Is this cartel sustainable? what would happen if both cheat?
ITS NOT AN EQUILBRIUM, if firm 2 sticks to the cartel output, then firm 1 can increase profits by increasing output, so they have incentive to cheat.
Similarly if firm 1 sticks to the cartel output, then firm 2 can increase profits by increasing output( to the point on reaction function )
If both cheated then both will increase output but make lower profits than cartel. (
So eventually what will happen when there is perpetual cheating ?
we will gravitate back to the original equilibrium
Who is the bully in the stackelberg equilibrium?
Remember we said quantities are strategic substitutes, so everytime i produce a lot, the other firm scales back, so firm 1 ( leader) has the incentive to choose a big q1, forcing firm 2 ( follower ) to pick a smaller q2 because if they also produce a lot the price will be low for both of us
So now we are going to solve using backward induction so if you are firm 2 and you know firm 1’s output so you react in the best way ( to maxmise your profits given. firm 1), so what is your reaction function which firm 2 responses on?
Because firm 1 can anticipate firm 2 response in stage 1, in stage 1 what can firm 1 do?
I will substitute firm 2’s optimal choice in stage 2 into my profit function in stage 1. So firm 1 behaves like a monopolist, but we will not have monopoly outcome because firm 2 still produces something ( hence price is lower)
What does firm 2 do in stage 2 knowing that firm 1 will produce monopoly quantity? Do they make profit? AND HOW WILL THIS COMPARE WILL MONOPOLY?
They will substitute firm 1s quantity choice into their reaction function, thus we can find out what firm 2 will do. The second firm acts like half a monopolist. they will still make profit if they produce, as compared to nothing if they don’t produce.
SO HERE TOTAL QUANITITY WILL BE HIGHER THAN MONOPOLY BUT PRICE LOWER SO PROFIT STILL LOWER THAN MONOPOLY
Find out the profit of firm 1 and 2 ? ( HINT USE this) What is a big lesson learnt?
In general profit is double quantity so for firm 2 its double quanitty
and do the maths to get profits.
As you can see clearly being a leader generates more profit.
How can we show stackelberg equilibrium on our diagram? is there anything surprising on diagram?
If firm 1 is the leader, the best thing he can do is set monopoly quantity, we look at best response of firm 2 ( green line) and thats how much firm 2 produces. Its not a coincidence that stackelberg and cartel line up horizontally, no because a cartel is when both of the firms act like half a monopoly whereas stackelberg is where 1 firm behaves like a monopoly.
Because we have assumed in Bertrand competition firm 1 and 2 are selling identical goods, what can we say about the firms market share and what happens if one price is higher than the other?
First of all draw a plain Bertrand competition diagram where we have prices on the axis and 45* line
So we want to think about what firm 2 will do in response to firm 1, so lets suppose mc = 5 and monopoly price = 10 and for some biazzarre reason firm 1 picks a price of 12, whats the best thing for firm 2 to do?
They will choose the monopoly price and get all the demand
Suppose firm 1 enters the market and chooses monopoly price 10 or lets say 8?
Firm 2 will choose just a little bit below 10 or 8 as you can see the green line is just below 45* line, its meant to denote small drop off in price
If firm 1 decides to set a price below marginal cost, then what is the best response for firm 2?
To set price at mc, hence no profit
We can do the same thing for when firm 2 decides the price and firm 1 reacts and how does this look on the diagram?
Lets say the 2 firms decide to collude, so set price = monopoly price and share profits, would they?
As the black dot are not on the reaction function they will both have an incentive to deviate, so the game will unravel and prices fall to c
(Based on past examination questions). Demand for gas by consumers is given by 𝑄 = 8 −
𝑝, where 𝑝 is the price. The cost to a firm of producing 𝑄 units of output is 4 + 2𝑄.
(i) Is it possible for the gas industry to be perfectly competitive?
(ii) If gas is produced by a monopolist what is the price, quantity produced and profit of
the monopolist?
(iii) Can the industry operate profitably as a cartel with more than two firms?
(iv) Define a Cournot-Nash equilibrium. Find the price, quantity produced and profits of
each firm in the Cournot-Nash equilibrium with two firms. If entry and exit were
possible, could there be an equilibrium with more than two firms in the market?
( PART 1 FIND Q1 AND Q2)
(iv) Define a Cournot-Nash equilibrium. Find the price, quantity produced and profits of
each firm in the Cournot-Nash equilibrium with two firms. If entry and exit were
possible, could there be an equilibrium with more than two firms in the market?
(PART 2)
Virgin Galactica and SpaceX are refining the technology for commercial space travel. They estimate that the daily Earthly demand for space travel is 𝑄 = 14 − 𝑝, where 𝑝 is the price (in millions) for a space flight. The cost to a firm of supplying 𝑄 space flights is 2𝑄 (also in millions). They are due to launch their commercial travel flights at the same time in which case they
will operate as a Cournot duopoly.2 Virgin Galactica engineers find that by investing an extra 5 now, they can launch before SpaceX and become the market leader. Virgin Galactica hires you, an economics consultant, to evaluate whether they should make this additional investment. What do you advise?
PART 1)
Virgin Galactica and SpaceX are refining the technology for commercial space travel. They estimate that the daily Earthly demand for space travel is 𝑄 = 14 − 𝑝, where 𝑝 is the price (in millions) for a space flight. The cost to a firm of supplying 𝑄 space flights is 2𝑄 (also in millions). They are due to launch their commercial travel flights at the same time in which case they
will operate as a Cournot duopoly.2 Virgin Galactica engineers find that by investing an extra 5 now, they can launch before SpaceX and become the market leader. Virgin Galactica hires you, an economics consultant, to evaluate whether they should make this additional investment. What do you advise?
PART 2)
Essentially for demand for firms output 2, if p2 increases to 2 and p1 = 1 = then the demand for q2 is still positive, this is not the case if it was perfect subsisutes ( as if the price of the good that goes up, the demand is 0)
ii)
iii)
iv)(iv) Find the Bertrand-Nash Equilibrium prices if marginal cost 𝑐 = 1. Do the firms make
profits? Explain intuitively why the outcome differs to the homogeneous goods case.
