Chapter 12 - Monopolistic competition and oligopoly

Question 1

What is monopolistic competition?

Answer 1

Monopolistic competition is competition between firms when each firm has some level of market power.

This is due to the fact that firms sell products that are not exactly equal.
There are still many firms, and entry and exit is not regulated. However, the products are a little different between firms.

Obviously, this means that the firm selling the best product will have the most monopoly power.

Question 2

What is oligopoly?

Answer 2

Oligopoly is a market where we have a few firms competing, but entry is impeded.

So, there is difficult to enter such a market. Therefore, the firms in it can work together to achieve very large prices.

Question 3

What is a cartel?

Answer 3

A cartel is a market in which some firms coordinate to get better control of the market. Aim is to maximize joint profits.

Question 4

Why are oligopolies difficult to manage?

Answer 4

A lot of the success is dependent on game theory. How do our choices affect the other firms, and how do these firms respond?

Question 5

Elaborate on equilibrium in monopoly vs equilibrium in perfectly competitive markets vs monopolistic competition.

On a general level, what is common between these markets

Answer 5

In perfect competition, we will find equilibrium where quantity supplied equals queneitty demanded.

In monopoly, equilibrium will occur wherever marginal revenue is equal to marginal cost.

In monopolistic competition, long run equilibrium establishes as long run profits goes towards 0.

These markets do not have to consider the impact of their choices on the other players. we can take price or quantity demanded as given, and ignore competitors. However, in oligopoly, a firm will set its prices based partly on the behavior of other players.
Is is possible to find some equilibrium point in such case?

Question 6

What are the key characteristics of a monopolistically competitive market?

Answer 6

1) Firms are selling differentiated products that are highly substitutable, but not perfectly substitutable. Toothpaste, for instance.

2) Free entry and exit. It is relatively easy to enter. An example of industry that is NOT FREE ENTRY is cars, as it requires large amount of inputs.

Question 7

Why is monopolistic competition similar to perfect competition?

Answer 7

Monopolistic competition is similar to perfect competition because the free entry and exit makes it easy for firms to enter the market if they see potential profit in it. Therefore, if profit is “available”, many firms will enter. As a result, each firm will receive less monopoly power, and the market will approach perfect competition. This drives economic profits to 0 (Zero-economic profits).

Question 8

What happens to the demand curve of a firm in a monopolistic market as firms enter the market?

Answer 8

The individual demand curve that the single firm is facing will shift down.

The long run demand curve will be just tangent to the average cost curve. This implies zero economic profits.

Question 8

What is the relation between monopoly power and demand curve?

Answer 8

As long as the demand curve is sloping down, the firm have monopoly power. This is because price is not given. The firm is not a price taker. We can set the price based on other factors than the market price.

Question 9

What do we mean be economically efficient markets?

Answer 9

It means, the total consumer+producer surplus is as large as it can be. There is little deadweight.

Question 10

What is Nash equilibrium?

Answer 10

Nash equilibrium is a market condition where each firm is doing the best it can given what its competitors are doing.

Question 11

What is a duopoly?

Answer 11

Duopoly is a market with 2 players that compete against each other. So, it is an oligopoly but restricted to 2 players.

Question 12

Elaborate on the Cournot Model

Answer 12

Goes like this:

Suppose the firms (duopoly) produce a homogeneous good and know the market demand curve. Each firm must make a decision on how much to produce, and the two firms make their decision at the same time. When making the decision, each firm takes the competitor into account.

If we consider one of the firms. This firm knows that the other firm is also making the same decision. Both firms knows that the market price will depend on the total output of both firms.

The essence of the Cournot model is that each firm treats the output level of the competitor as FIXED when deciding how much to produce.

Question 13

What are reaction curves?

Answer 13

A reaction curve is the relationship between a firm’s profit maximizing output and the amount he thinks the competitor will produce. It is a decreasing schedule.

Question 14

Elaborate on Cournot equilibrium

Answer 14

If we consider 2 firms, we first find the reaction curve of both firms. This gives 2 curves. The intersect between them curves will be the Cournot equilibrium. this point will give a certain number of production, which obviously is the same number for both firms.

In the Cournot equilibrium, each firm is maximizing profits based on what the competitor is thought to be doing.

Question 15

Does the Cournot (Nash) equilibrium tell us anything about the process of dynamics?

Answer 15

No. Firms will not adjust outputs based on Cournot model.

Question 16

IMPORTANT:

What is the idea of the Cournot model and Cournot equilibrium?

Answer 16

A firm will make a deicision on output level that is dependent on what it believes the other competitor will do. For instance, if firm X think firm Y will produce 100 units, it will find a level that maximize profits based on that information. If the firm do this for all possible output levels of the other firm, we get a nice curve that maps this relationship.

At the point of Cournot equilibrium, all firms are producing a level of output that it is happy with, since profits are maximized given the “information”. Therefore, no-one has any incentive to change anything.

In the Cournot equilibrium, each firm correctly assumes how much the other competitor will produce.

If initial guesses are wrong, there will be an adjustment process. However, since the Cournot model assumes the competitor has fixed its volume, this is where the model ends. It cannot predict the further behavior. As a result, this equilibrium is a situation that occurs if the firms somehow manage to assume correct from the beginning.

The Cournot equilibrium is not necessarily the goal, but is rather a symptom of the goal. The goal is to maximize profits given the other players. If every firm does this perfectly, then the Cournot equilibrium will arise.

Question 17

How do you find the reaction curve of a firm

Answer 17

The reaction curve of a firm is the curve of output levels based on the other firm’s fixed production.

We need to market demand curve.
We need the cost curve.
We need marginal revenue curve.

Marginal revenue curve is given as PQ1, for instance: (30 - Q)Q1

this gives us:
R_1 = 30Q1 - Q1^2 - Q2Q1

Then we differentiate with respect to Q1:

MR_1 = 30 - 2Q1 - Q2

Then we set this curve equal to the marginal cost curve. When we do this, and then repeat for all firms in the oligopoly, we get a system of equations. This system can be solved to get the individual production volumes. The market price is then given by the demand curve, P(Q) with Q = Total production, Q = Q1+Q2

The 2 equations we get are:

Q1 = 15 - 0.5Q2

Q2 = 15 - 0.5Q1

This gives us a Cournot equilibrium of Q1=Q2=10. The total quantity is then 20. This gives market price of P(20) = 30 - 20 = 10.

Then each firm would earn 10*10 = 100 bucks.

Total profit is 200.

Question 18

What is the collusion curve?

Answer 18

The collusion curve is the curve corresponding to all pairs of outputs from firm A and firm B that maximize the profits when the two firms are collaborating. In other words, when the firms are trying to maximize the total profit.

We find the collusion curve by doing the same logic as with non-collab, but we disregard the fact that there are multiple firms at first.

Demand curve: P(Q) = 30 - Q
Cost curve: C(Q) = 0 (constant 0 cost)

R = P(Q)*Q = 30Q - Q^2

MR(Q) = 30 - 2Q

MR = MC –> 2Q = 30 –> Q = 15

IF the 2 firms agree to share all profits, they would typically produce half each, so that Q1 = Q2 = 7.5

The price would then be:
P(15) = 30 - 15 = 15

Each firm would get a profit of 15*7.5 = 112.5

total profit is 225. This happens to be 25 more than if both firms act separate.

Question 19

Why is Cournot equilibrium not the same output level as the total profit maximization level?

Answer 19

Because, it would require both firms to slack their output a little. If one firm does this, the other firm could increase profits by upping production or remaining with the same output.

Question 20

Elaborate on the case where one of the firms in a duopoly “moves first” (change output/set output first)

Answer 20

If firm A moves first by setting an output level, it will have to do so while considering what the other competitor might do in response.

for this, we use the STACKELBERG MODEL.
The Stackelberg model is simply an oligopoly model where one of the firms sets output before the other firms.

If we consider the case where firm A has already decided an output level, and that firm B has observed this. Then, firm B can treat this output level as fixed. As a result, the reaction curve of firm B will point to the point where the opposition produce the given quantity. This gives the output that firm B will produce as a response. Say the reaction curve was this:
Q2 = 15 - 0.5Q1
Then, Q2 = 15 - 0.5*x

So, the decision for the second firm is easy. But what about the first?

Firm A will maximize profits, MR = MC.

R1 = PQ1 = 30Q1 - Q1^2 - Q1Q2

We can see that R1 depends on Q2. Therefore, we must guess. What we do know (as firm A), is that firm B will choose an output that is on its reaction curve. Therefore, we can substitute Q2 with this curve.

R1 = 30Q1 - Q1^2 - Q1(15-0.5Q1)
R1 = 15Q1 - 0.5Q1^2

Therefore, marginal revenue becomes

MR1 = 15 - Q1

If we consider MC = 0, we get that Q1 = 15.

From the reaction curve of firm B, we get Q2 = 7.5

This implies that going first gives an advantage. Why is that? It is because the first firm will produce high. If the second firm also did so, it would drive the price down, which would cause both firms to loose money. So, 15 vs 7.5 is a better deal FOR BOTH firms than say 15 + 15.

This is called first mover advantage.

Question 21

How does the Stackelberg model differ from the Cournot model? In one sentence

Answer 21

Stackelberg gives one firm the first move, while Cournot assumes both firms make the decision simultaneously.

Question 22

What is price competition, as opposed to quantity focus?

Answer 22

Instead of focusing on what output to produce, price competition looks at strategic levels of price. For instance, what happens if we set price a little lower than our competitors?

Question 23

What is the Bertrand model?

Answer 23

The Bertrand model is a model where each firm/competitor in an oligopoly produce homogenous good, and all firms treat the prices that the other firm(s) have sat at given. So, it contrasts with the Cournot model in the sense that it is now prices that are given, not volume.

just like with the Cournot model, the Bertrand model consider decisions at the same point in time.

There is nothing stopping us from using Bertrand on differenatiated goods.

If prices are homogenous, in the single-period case, the attempted undercut would be unavoidable, causing prices to be equal to MC. If prices are differentiated, we achieve equilbria that is somewhere between MC and monopoly pricing.

Question 24

Consider the elasticity of demand for monopolistic competition, how is it likely to be?

Answer 24

Relatively elastic. -5 is not uncommon. The high elasticity is due to the large number of substitutes that stems from free entry.

Question 25

Name the characteristics of monopolistic competition

Answer 25

There are 2 primary characteristics:

1) Free entry and exit
2) Differentiated products that are highly substituable, but not perfect substitutes.

This cause high elasticity of demand.

Question 26

What is a requirement of the demand curve if a firm/firms in a market is to have some monopoly power?

Answer 26

The demand curve must be downward sloping. As opposed to horizontal as in perfectly competitive markets.

Question 27

Are monoplistic markets likely to earn large profits?

Answer 27

Ney. They will have SOME monopoly power, but will not be far off perfect compettion as they are relatively competitive.

Question 28

Discuss short-run and long-run equilibrium for monopolistic markets

Answer 28

In the short run, there will be profits beyond zero-economic profits. However, as firms see possibility of making profits in this market, the “free entry” will drive more competitors to the mix. As a result, profits will decrease to the point where average revenue is equal to average cost for every long-run firm.

Therefore, in monopolistic competition, profits will always drive towards zero-economic profit.

Remember that zero-economic profit does not mean that the firm is not making money. It only means that we are not exceeding our risk-related opinion that is included in the user-cost of capital.

Question 29

in oligopoly, are products differentiated?

Answer 29

They may, and they may not.

Question 30

What is the characteristic of oligopoly?

Answer 30

Significant barrier to entry.

Question 31

What differs between the group of perfect comp, monopolistic comp, monopoly comp, and the other group consisting only of oligopoly in terms of equilibrium?

Answer 31

The structures in the first group assumes either price or demand as given, and dont care about competitors that much.

Oligopolies make decisions largely based on their competitors.

Question 32

What is NASH equilibrium?

Answer 32

Nash equilibrium is the case where all firms are doing the best they can given what their competitors are doing.

Question 33

Elaborate on the Cournot model

Answer 33

2 firms produce a homogeounous product. They are interested in competing in a way where they maximize profits based on what the other part is doing.

In the cournot model, both firms are making the decision at the same time.

There is a case to incude differentiated products, but you’d need individual demand curves.

Question 34

What is a reaction curve?

Answer 34

A reaction curve is a curve that gives the realtionship between how much a firm think the other firm will produce, and its own “reaction”-output level.

It is important to note that the reaction curve always give profit maximizing levels of output.

Denoted Q*_1(Q_2)
Optimal level of production for firm 1 is a function of the produced volume from firm 2.

Question 35

What is the Cournot equilibrium?

Answer 35

Graphically it is the point where the reaction curves of both firms intersect. At this point, both firms have absolutely no incentive to change anything because they are optimized according to what the other competitor is doing.
It is easy to see why Cournot equilibrium is a Nash equilibrium as well.

Question 36

Does the Cournot model tell us how firms move towards the Cournot equilibrium?

Answer 36

No. The model will not hold, because the model assumes the output of the other firm is fixed and sat simultenously. Therefore, it is beyond its depths to try to explain dynamic processes.

Question 37

CASE: Duopolists face the following market demand curve:

P = 30 - Q

Suppose both firms have 0 marginal costs.

find the output level of each firm.
Find market price.
find profits from both firms.

Answer 37

We need to find both reaction curves.

We start with firm 1.

R_1(Q_1) = PQ_1 = 30Q_1 - QQ_1

= 30Q_1 - (Q_1 + Q_2)Q_1

= 30Q_1 - Q_1^2 - Q_1Q_2

Differentiate to find MR(Q_1)

MR(Q_1) = 30 - 2Q_1 - Q_2

Set equal to MC, which is 0, and we get:

30 - 2Q_1 = Q_2

Then we do the same for firm 2, and we get:

30 - 2Q_2 = Q_1

These are eqatuions, but not yet reaction curves. To get them on reaction curve format, we need to get Q_1 seperate for reaction curve 1 and opposite for the other.

1) Q_1 = 15 - 0.5Q_2
2) Q_2 = 15 - 0.5Q_1

Then we solve the system of equations.

The result is Q_1=Q_2 = 10

This means that the total quantity produced is 20. with this information, we can use the demand function/curve to find the market price:

P = 30 - Q = 30 - 20 = 10

With this info, we can find the profits of both firms.
Since both produce 10, and price is 10, they earn revenue of 100 each. Since MC = 0, they earn a profit of 100 each.

Question 38

If cooperation is legal, and 2 firms decide to cooperate (duopoly) how would they change their practice? how does it differ from the case where they are competing against each other?

Answer 38

Choose output Q so that marginal revenue is equal to marginal cost.

The difference is that they choose based on considering themselves as a single unit (monopoly) rather than 2 firms.

Question 39

Elaborate on stackelberg

Answer 39

The point is that one firm choose level of output first. We are still in a duopoly, and therefore, firm 1 has to take firm 2 into account. So, firm 1 goes first, and picks a level of output that will optimize profits when firm 2 reacts to this level with an output of their own.

Question 40

Elaborate on the Bertrand model

Answer 40

Firms choose price instead of quantitiy. Both choose at the same time and treats the price of the competitor as fixed.

KEY POINT: Since products are homogeounous, the seller that supply with the lowest price will supply the entire market. Therefore, they must choose the same price for both to earn money.

In such a case, the nash equilibrium is the competitive outcome. Both firms set price equal to marginal cost.
The explanation is that a firm could capture the entire market by lowering price until the point of MR=MC, where lowering price leads to loss per unit.

The model has been criticized, as it is more common to compete with quantities rather than price.

Question 41

Elaborate on what happens if the products have some degree of differentiation

Answer 41

This is the common case, as products generally are a little different.

Whenever products are differentiated, it is not so common to compete with quantities, but rather with price. We are more willing to pay for performance etc.

Consider 2 firms with demand curves:
Firm 1: Q_1 = 12 - 2P_1 + P_2
Firm 2: Q_2 = 12 - 2P_2 + P_1

From these, we know the following:
1) If the competitor raise price, we are likely to see increased demand for our goods
2) The quantity of our good decrease if we set a higher price, or if competitor set lower price.

So then. How do we choose suitable prices?

We assume both sets prices at the same time, and that the “competitor” holds fixed price. Therefore, we can use the pricniple of Nash equilibrium to find the best spot.

Question 42

How do firms choose prices in oligopolies?

Answer 42

The key point here is that there is a level of differentiation with the products that cause the products to be different.

The key to understanding this is to know when firm 1 (or firm 2 for that matter) is maximizing profits. This will happen at the point where incremental profit from a small increase in its own price is just 0. Taking the price of firm 2 to be fixed, we get the following result:

dpi / dP_1 = 12 - 4P_1 + P_2 = 0

This equation above can be rewritten so that we get the reaction curve. Then we do the same for the other firm. For instance, we could get:

P_1 = 3 + 1/4 P_2

P_2 = 3 + 1/4 P_1

At the point of intersection, both firms are doing the best they can, given what the competitor is doing. Therefore, this equilibrium is a nash equilibrium

Question 43

A typical set of demand curves can be like this:

Q1 = 12 - 2P1 + P2
Q2 = 12 - 2P2 + P1

Elaborate on the meaning of this in regards to oligopoly with differentiated products

Answer 43

For firm 1, we see that as firm 1 increase its own price, the demand will decrease.
At the same time, the higher the price of firm 1’s good, the higher our own demand will be.

Likewise, firm 2’s demand increase if they lower the price, or if firm 1 up their price.

It is a price game. Therefore, the question becomes, what prices to we set? More specifically, the question becomes: If we consider our competitor’s price a fixed, and we set prices at the same time, what will we set?

We apply the nash equilibrium principle.

Question 44

How would the demand curve of a firm that is in a monopolistic market look like?

Answer 44

Monopolistic markets are more elastic than oligopolies and monopolies, but not as elastic as perfectly competitive markets. Therefore, the demand curve will not be horizontal, but it will be very flat to indicate the high elasticity.

The elasticity comes from the fact that the market form offers differentiated (to some degree) products with FREE ENTRY AND EXIT

Question 45

Define a monopolistic market

Answer 45

A monopolistic market is a market that contains firms that have 2 characteristics:

1) Products are differentiated, but they are highly substitutable

2) There is free entry and exit.

Question 46

Define a oligopoly

Answer 46

Oligopoly is defined by markets with barriers to entry. Can be difficult for new firms to enter the market.

Question 47

Why do we say that oligopolies are more difficult to manage than the other market structures?

Answer 47

Competition. It is basically game theory. We need to make decisions that depend on the other players.

Question 48

Define nash equilibrium

Answer 48

Nash equilibrium is a case where each firm is doing the best it can given what its competitors are doing.

Question 49

Elaborate on Cournot (IMP)

Answer 49

Cournot model considers homogenous products in a setting where both firms (duopoly) sets a quantity to produce at the same time.

The firms also considers the output of the other firm to be fixed.

The main point is that one competitor will make a decision based on what the other competitor is doing.

We say that firm 1’s profit maximizing output level is a decreasing schedule of how much it thinks firm 2 will produce. This schedule, or function, is called a reaction curve of firm 1. Firm 2 also has one.

Each point on the reaction curve (also called response curve) corresponds to firm 1’s profit maximzing level given a speicifc level of output for the other firm.

At the point of intersection between the firm’s reaction curves, we have the “cournot equilibrium”. At this point, BOTH FIRMS would think “I am doing the best I can given what the other competitor is doing”. Therefore, both competitors have no incentive to change anything.

So, how do a firm find this reaction curve?

We need the market demand curve.

We find firm 1’s revenue function by using the market demand function.

Ex, Q = 30 - P

R1(Q1) = P * Q1

R1(Q1) = (30 - Q)*Q1

R1(Q1) = (30 - Q1 - Q2)*Q1

R1(Q1) = 30Q1 - Q1^2 - Q1Q2

Then we find the profit function:

pi(Q1) = R(Q1) - C1(Q1)

We differentiate and equals 0.

MR = MC

Say MC = 5

30 - 2Q1 - Q2 = 5

Q1 = 25/2 -Q2/2

This is the reaction curve of firm 1. We do the same process for firm 2.

Now, the two firms could cooperate to gain a larger total profit. In such a case, you’d treat it like a monopoly.

MR = MC

PQ = (30 - Q)Q = 30Q - Q^2

MR = 30 - 2Q
MC = 5

25 = 2Q
Q = 25/2

Thus, the profit maximizing output level is 25/2. Therefore, if the firms choose 25/4 each, or any other combination that makes up 25/2, they would together maximize output.

Question 50

Elaborate on stackelberg (IMP)

Answer 50

The Stackelberg case involves a party choosing a level of output first, under the knowledge of the fact that there will be another firm that is going to enter. If the first mover treat the case like a monopoly, he’d limit himself when the opponent enter, and fuck up the demand curve. They would end up with a lower price and lower revenue than they otherwise would.

So, firm 1 choose first, then firm 2 observe the choice and react to it.

Firm 2 will use his reaction curve, like in the cournot model, to find the profit maximizing output level.

Let us say that firm 2 has reaction curve:
Q2 = 15 - 1/2 Q1

If firm 1 knows about this curve, then it becomes easy. Firm 1 will make a decision that involves using the reaction curve of firm 2.

We once again draw up the profit function for firm 1.

pi(Q1) = R(Q1) - C1(Q1)

Say 0 MC

pi(Q1) = (30 - Q1 - Q2)Q1

pi(Q1) = 30Q1 - Q1^2 - Q1Q2

Since we have the reaction curve of firm 2, we enter it into the function.

pi(Q1) = 30Q1 - Q1^2 - Q1(15 - 1/2 Q1)

pi(Q1) = 30Q1 - Q1^2 - 15Q1 + 1/2 Q1^2

pi(Q1) = 15Q1 - 1/2 Q1^2

Differentiate and equal 0

15 - Q1 = 0

Q1 = 15

Then we find firm 1 using the reaction curve.

Q2 = 15 - 1/2 Q1
Q2 = 15 - 1/2 * 15
Q2 = 15 - 7.5
Q2 = 7.5

Question 51

Elaborate on price competition with differentiated products

Answer 51

It appears the theory from classes treat Bertrand not as just homogenous products, but also with differentiated products. Makes sense, but the book was not clear on this. thus, we are to treat betrand as “given prices”.

Both firms will have an individual demand curve. This demand curve will include the relationship between prices. If the price of firm 1 increase, then the demand of firm 2 should increase. Therefore, cross-price elasticity becomes relevant.

Demand curves could look like this:

Q1 = 12 - 2P1 + P2
Q2 = 12 - 2P2 + P1

We draw up the profit function, which we want to maximize, to find out what we should price our good at (find nash equilibrium).

pi1 = P1Q1 - 20

pi1 = P1(12-2P1+P2) - 20

pi1 = 12P1 - 2P1^2 + P1P2 - 20

Differentiate and maximize

dpi1/dP1 = 12 - 4P1 + P2 = 0

P1 = 1/4 P2 + 3

this is the reaction curve of firm 1.

Following the same process but with the demand curve that face firm 2, we get:

P2 = 1/4 P2 + 3

Then we solve the system of equations to find the equilibrium.

P1 = P2 = $4, profit of 12$.

The differentiated products offer some great insight. In the case of price-battle, moving first is a disadvantage. This is because it allows the second firm to undercut slightly to capture a larger market share.
Keep in mind that this “model” considers fixed prices.

Question 51

Elaborate on the prisoners dilemma

Answer 51

Prisoners dilemma is the scenario where 2 players get sort of a split or steal choice. Long story short, both players would be better off by trying to undercut its opponent. Therefore, “passive” collaboration usually dont work.

Question 51

The prisoners dilemma would seem to indicate that oligopolies are doomed to low profit. is this the case?

Answer 51

No. Firms generally compete over longer periods of time. Some level of trust will emerge. Also, a simple undercut is not that detrimental.

In some industries, where there are oligopolies of some age and size, you’d typically see 3 or 4 large players that hold relatively fixed portions of market share. These players have had relatively small changes in their shares throughout the years. In these cases, it can be understood that all firms earn more by sticking to this strategy than to aggressively try to destroy the others. This is called IMPLICIT COLLUSION.

Question 52

What is implicit collusion?

Answer 52

Implicit collusion is the case where we have collusion (cooperation) without directly agreeing to it.

Question 53

Elaborate on why price rigidity is a common

Answer 53

Implicit collusion tends to be fragile. People fear wars.

If demand decrease, a firm might be reluctant to lower the price as it could send the wrong message to the competitors.
At the same time, if demand increase, a firm might be reluctant to increase prices as they fear the competitors will not.

Same applies with cost-structures. If costs increase, upping the price would be theoretically sound. However, if it sends the wrong message, a war could erupt.
If costs decrease, a lower price could fuck up if the message is “war”.

Therefore, prices tends to be rather stable in oligopolies.

Price rigidity leads to the “kinked demand curve”. The “kink point” is the point where the current price is. Above this point (to the left) the demand curve is very elastic. It is elastic because a firm will believe that if they increase price, others will not join them. Therefore, they will loose a lot of market share.
To the right of this kink point, it is believed that competitors will follow, and thus this part of the demand curve will behave more normally. Demand will increase accordingly with the price change.

Question 54

Elaborate on the kinked demand curve

Answer 54

Price rigidity leads to the “kinked demand curve”. The “kink point” is the point where the current price is. Above this point (to the left) the demand curve is very elastic. It is elastic because a firm will believe that if they increase price, others will not join them. Therefore, they will loose a lot of market share.
To the right of this kink point, it is believed that competitors will follow, and thus this part of the demand curve will behave more normally. Demand will increase accordingly with the price change.

Question 55

What is price leadership0+

Answer 55

Price leadership is a way to achieve collusion implicitly. One firm will announce higher prices, and hope that the other firms follow suit. The key to victory here is that the competitors interpret the price announcement as a signal that indicates a sign of collective price increase.

In an established oligopoly, you’d see one firm as the leader. If this firm announce a price change, the others follow.

Question 56

In Cournot, why are we considering a single market price?

Answer 56

Market price because the products are homogenous.

Question 57

What are “strategic substitutes”?

Answer 57

Substitutes that act in a way where if we increase the output of one, the other will decrease, and vice versa. this is the case with oligopolies/duopolies.

Question 58

is Cournot limited to homogenous products?

Answer 58

No, not really. the textbook seems to indicate this, but it is not a dealbreaker. I suppose you’d use individual demand curves instead of market demand curve.

Question 59

Can the cournot model be extended to more than 2 firms?

Answer 59

Yes, very easily. You just get multiple equations to solve.

Question 60

If two firms (two products) have a very high cross-price elasticity, what does this indicate?

Answer 60

It indicate that the results of a firm is HIGHLY dependent on what happens to the other firm. This is generally not preferable. Therefore, firms want to distinguish their products as much as possible.

Question 61

What is the Herfundahl-Hirschman index?

Answer 61

HHI measure that the market concentration. It works like this:

SUM(s^2)[i]

So, it sums the squares of all percentages. A percentage corresponds to a firm, and is a measure of market share for firm i.

A percentage is represented as a whole number, ex 50 would represent 50%. NOT DECIMAL.

The smaller the number, the more evenly spread out the firms are in regards to market share.

Question 62

EXTREMELY IMPORTANT:
Consider Cournot model. Consider N different firms. Draw our the final connection between HHI and markup.

Answer 62

Markup refers to the percentage of price relative to MC. HHI is the market concentration index.

Recall that the Cournot assumption is that the firms are producing homogenous products, which means that the PRICE will be equal for all firms in the market. Perfect substitutes.

We begin by considering firm i. We draw up the profit function for firm i.

pi(Qi) = R(Qi) - Ci(Qi)

pi(Qi) = P(Q)*Qi - Ci(Qi)

Then we find first order conditions so that we can find the profit maximizing level of output.

∂pi(Qi)/∂Qi = 0

we use the multiplication rule to differentiate first, then we use the Chain rule. We also just set the derivative of Ci(Qi) = MCi

(∂P(Q)/∂Qi)*Qi + P(Q) - MCi = 0

Chain rule:

Qi(∂P(Q)/∂Q)*(∂Q/∂Qi) + P(Q) -MCi = 0

We know that ∂Q/∂Qi is equal to 1, since Q is a sum of all individual demands, and we always differentiate with respect to Qi. Therefore, whenever j != i, it all cancels out. In the case where we have j=i, we get 1.

Thus:

Qi∂P/ ∂Q + P -MCi = 0

Now we multiply the term with derivative by PQ/(QP) so that we can extract the price elasticity of demand from the expression.

Qi * (P/Q)(Q/P)∂P/∂Q + P - MCi = 0

Qi(P/Q)E_p^(-1) + P - MCi = 0

P - MCi = -P(Qi/Q) * (1/E_p)

(P - MCi)/P = (Qi/Q) * (1/E_p)

Now we use the fact that Qi/Q is actually a measure of market share for firm i. Therefore we can substitute it with “s_i”, where s_i is the market share of firm i.

(P - MCi)/P = -s_i/E_p

Now we multiply both sides by s_i.

s_i*(P - MCi)/P = -s_i^2 /E_p

Since this is an equation, we take the SUM of both sides from i=1 to N.

SUM(s_i(P - MCi)/P) = SUM(-s_i^2/E_p)

When looking at the left side of the equation, we can simplify it by making use of the fact that SUM(s_i)[i=1, N] is equal to 1.

Inside the left side, ignoring the sum atm, we have:
(1/P) * (s_i*(P - MCi))

Considering the summation symbol, we can factor out the (1/P).

(1/P) * SUM(s_i(P - MCi)) = …

WE can split the sum into 2 sums.

(1/P) * (sum(s_i * P) - sum(s_i*MCi)) = …

We can factor out the P from the inner sum.

(1/P)(Psum(s_i) - sum(s_iMCi)) = …

Since sum(s_i) = 1, we get:

(1/P)(P - sum(s_iMC_i)) = …

We set SUM(s_iMCi) = MC to indicate the weighted average of marginal costs.
We also, on the RIGHT side, factor out the 1/E_p and set the sum equal to HHI by definition. we get:

(P - MC)/P = -HHI/E_p

This is the final result.

The result shows that the markup from price, relative to marginal costs, are equal to the ratio of HHI divided by price elasticity of demand.