Oligopoly Flashcards
Name the main features of an oligopoly.
Few firms Same product Not price takers Output and price choices affect profit of other firms barrier to entry No perfect knowledge.
What is a sweezy demand curve?
- Demand curve of the market of a particular oligopoly
- Composed of two crossing demand curves of firm a and b.
- Kinked demand curve
- Has a discontinuous marginal revenue curve.
Describe the demand curve in the sweezy model.
the first half is based on the assumption that if firm A increases his prices Firm B will not. If firm A decreases its prices so will firm B.
Where do classical theorists differ with Sweezy?
-Classical theorists believe that a typical demand schedule can be applied to oligopolists, sweezy argues against this as it implies oligopolists choose output and prices independent of other oligopolies.
Describe the elasticity of the kinked demand curve
Before the kink: highly elastic (price sensitive)
After the kink: highly inelastic
How can two firms in an oligopoly compete
Two strategies:
- Through output (cournot nash, stackelberg games)
- Through price (Bertrand model)
What is the name of a game where one firm sets its output and price decisions before all others?
Sequential game
What is the name of a game where one firm makes decisions and doesn’t know the decisions of all other firms same time?
simultaneous game
What is the name of the game where firms collude?
Cooperative game
Explain Π(y1;y2)=P(y1+y2)y1-C1(y1)
Π(y1;y2) (Profit as a function of y1 or y2)
p(y1+y2)= Market price as a function of y1 and y2
C1(y1)= cost of firm one as a function of its output.
What is firm one and two’s best reaction to each other in terms of output if p(Yt)= 60-Yt and c1(y1)=Y1^2 C2(Y2)=15Y2+Y2^2
Π(y1)=(60-Y1-Y2)Y1-Y1^2 Firm 1 best reaction will always be to maximise its profit, profit is maximised by taking the first differential of the profit function with respect to Y1: dΠ/dY1=60-2Y1-Y2- 2Y1=0 60-4Y1-Y2=0 60-Y2=4Y1 Y1=15-Y2/4 This is firm one's best reaction to firm 2. Firm two's best reaction is also to maximise profit. Π(y2)=(60-Y1-Y2)Y2-15Y2-Y2^2 dΠ/dY2=60-Y1-2Y2-15-2Y2=0 45-Y1-4Y2=0 (45-Y1)/4=Y2
What is a reaction curve?
It is the optimum output firm 1 should produce if firm 2 produces a certain output. To plot this graph set Y at 0 then set X at 0 and join the points.
When is cournot nash equilibrium reached?
This is when both firms have chosen outputs that are the best reaction to each other R1(Y2)=R2(Y1)
If R1(Y2*)=15-Y2/4 and R2(Y1*)= (45-Y1)/4 What is the cournot nash equilibrium output?
sub in R2(Y1) into R1(Y2): 15-[(45-Y1)/4]/4=Y1 60-(45-Y1)/4=4Y1 240-45+Y1=16Y1 195+Y1=16Y1 195=16Y1-Y1 195/15=Y1 Y1*=13 sub in R2(Y1*) 45-13/4=Y2* 32/4=Y2* 8=Y2*
What is the an isoprofit curve?
A curve that shows all the output choices of a firm against the choices of firm 2 that give the same profit.
The tops of the curves give the reaction curve for a firm. If firm in question is on the x axis then profit increases as the curves get closer towards the x axis and the same can be said for the y axis
What is the incentive for firms to co-operate?
-They can increase profits by decreasing their output which is reflected by lower overlapping isoprofit curves (lower than the cournot nash equilibrium)
What are firms called when they collude?
A cartel
What profits can both firms expect to receive under collusion.
-One firm receives at least its cournot nash profit level whilst the other receives maximised profits, This is reflected graphically through isoprofit curves for firm one (x axis) profit to be maximised, the isoprofit curve must be as close as possible to the x axis, if we’re to give firm 2 atleast it’s cournot nash equilibrium then we must choose the curve that has the cournot nash equilibrium point on it.
In a collusion what incentive do firms have to cheat?
If a firm increases output for a given level of Y then it will increase its profit. This is because the point of collusion is lower than the best reaction output.
What does the stability of a cartel depend on?
- Profits of firm in the collusion
2. Profits of a firm after it has been punished (i.e. outside of collusion).
What is each firm’s profit in a cartel if p(YT)=24-Yt c1(Y1)=Y1^2 c2(Y2)=Y2^2?
Firstly we construct the profit function: Π=(24-Y1-Y2)(Y1+Y2)-Y1^2-Y2^2 Then we find profit maximising output for both firms by taking partial differentials: dΠ/dY1=24-2Y1-Y2-Y2-2Y1=0 24-4Y1-2Y2=0 4Y1=24-Y2 Y1=6-(2Y2/4) and dΠ/dY2=24-Y1-2Y2-Y1-2Y2=0 24-4Y2-2Y1=0 24-Y1=4Y2 Y2=6-(2Y1/4) sub in Y1 6-[6-(2Y1/4)]/4=Y1 24-[6-(2Y1/4)]=4Y1 24-6+(2Y1/4)=4Y1 96-24+2Y1=16Y1 72=14Y1 Y1=4 sub in Y2 Y2= 4 sub this back in profit function Π=(24-4-4)(4+4)-16-16 16(4+4)-16-16 64+64-16-16 128-32=96 we divide this equally between the two firms so under collusion each firm earns $48.
Describe how you would find the profit of each firm after punishment.
It is the each firm’s best reaction to each other. You solve for output and then plug the values in each firm’s profit function.
What is von stackelberg games?
When one firm chooses its output before the others.
In Von stackelberg games who makes the most profit?
-The firm that chooses output first this, lets say firm 1.
-Firm two will set its output at Y2=R2(Y1)
-Firm one Knows this so sets their output at Y1=R1(R2(Y1)
-so profit function is
profit=P(Y1+R2Y1)Y1-C1(Y1)
-Firm one makes more profit as they choose a higher output which makes them more profit as shown by isoprofit curve of firm one and reaction curve of firm 2 who produces less output.
