Appunti di Managerial economics

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A firm maximises profit with best responses that come from MR = MC. In panel b, if

American believes q = 64, then its best response is q = 64.

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DEF: “Nash-Cournot equilibrium is a set of quantities chosen by firms such that,

holding the quantities of all other firms constant, no firm can obtain a higher profit by

choosing a different quantity.”

The quantity of equilibrium must be on the best response curve for all firms.

Let’s see what happens if we start as a monopoly and then another firm decides to

enter.

Under Monopoly:

- Firm faces the entire demand.

- We will set MR = MC.

Duopoly: r

- We have the total demand D, but we have to calculate the D (residual

demand), considering how much the other firm can produce. Now we

consider that United Firm will produce 64, so this causes a shift of the demand

curve to the left for America by exactly this amount. R

- When we know the residual demand we have to discover the MR . After

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imposing MR = MC, we can see that this single firm will produce 64 at the

price of 211.

Now, the single firm will produce less, because under monopoly America was

producing 96, and also at a lower price 211 < 243.

Also the other company will produce 64, so the total output will be 128. This is

higher than before at a lower price consumer benefit.

→

As the number of firms increases, we are increasing the level of competition and this

entails higher quantity at a lower price.

Example Airlines

→

American and United compete for customers on flights between Chicago and Los

Angeles (duopoly) Q = q + q

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Graphical Approach:

The strategies for American and United depend on their residual demand curves

and marginal costs.

Residual Demands:

● If American thinks United flies q passengers, American's r. d. is q = Q(P) - q

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Alternatively, United's r. d. is q = Q(p) - q

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Best Responses:

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To maximise profit, American sets MR = MC and finds its best response curve

for all possible q .

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In the graph, if q = 64, American's best response is q = 64, shuts down if q =

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192, and so on.

It also shows United's best response curve.

Nash-Cournot Equilibrium: There is only one pair of outputs where both firms are

on their best-response curves, q = q = 64. At this intersection both firms maximise

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profits, are on their best response curves, and don't want to change their outputs.

Algebraic Approach (Calculus is the same but to get the MR you derive the

revenues):

- Residual Demand, MR and MC

The market demand function is Q = 339 - p.

The residual demand function for American is q = (339 - P) - q or p = 339 - q - q .

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American's marginal revenue function is MR = 339 - 2q - q .

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Both airlines have MC = AC = $147 per passenger per flight.

- MR = MC and Best Responses

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MR = MC, so 339 - 2q - q = 147

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American's best-response: q = 96 - 0.5q

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Similarly, United's best response: q = 96 - 0.5q

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- Nash-Cournot Equilibrium

Solving the two best responses by substitution, q = 96 - 0.5 (96 - 0.5q )

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The Nash-Cournot equilibrium values: q = q = 64, Q = q + q = 128, p = $211

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The Number of Firms

If two Cournot firms set output independently, the price to consumers is lower than

the monopoly price. If there are more than two, the price is even lower.

If we have n firms so that Q = q + q + … + q , the best-response function is

1 2 n

q = 96 – ½(q + q + … + q )

1 2 3 n

for n firms q = q = … = q in the Cournot equilibrium.

1 2 n

Therefore, the best-response function can be written as

q = 96 - ½ (n - 1)q q = 192/(n + 1)

→

The table below illustrates how each firm's output, q, the market quantity, Q, and

the price vary with the number of firms in our airlines example.

If n is very large, Q = 192 and p = $147 = MC.

The Nash-Cournot equilibrium approaches the competitive outcome.

Non-identical Firms

Oligopoly firms can have different costs and differentiate their products.

Unequal Costs

● In the Cournot model, a firm's best-response function comes from MR = MC.

If MC rises or falls, then the firm's best-response function shifts.

Consider the airline example, products are identical, so American and United

charge the same price.

United's MC drops from $147 to $99, so in panel a, the new q = 88 rather than

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64. Its best-response function shifts to the right in panel b.

United wants to produce more than before for any given level of American's

output. There is no change for American's best-response.

In panel b, the Nash-Cournot equilibrium shifts from e to e , at which United

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sells 96 and American sells 48.

United's profit increases from $4.1 million to $9.2 million, while American's

profit falls to $2.3 million. Consumers also win because p falls from $211 to

$195.

What about the consumer? The total output, compared to the first one, is

higher, which means also a lower price the consumer gains too.

→

Differentiated Products

● By differentiating its product from those of a rival, an oligopolistic firm can

shift its demand curve to the right and make it less elastic.

The less elastic the demand curve, the more the firm can charge because

consumers are willing to pay more for a product that 'seems' superior.

Although differentiation leads to higher prices, which harm consumers,

differentiation is desirable in its own right. Consumers value having a choice,

and some may greatly prefer a new brand to existing ones.

If consumers think products differ, the Cournot quantities and prices may

differ across firms. Each firm faces a different inverse demand function and

hence charges a different price.

Mergers

Mergers could be vertical or horizontal and both want to increase profit.

- Vertical mergers may lower cost with a more efficient supply chain

organisation.

- Horizontal mergers may increase market power and reduce competition.

Merger that arises entirely from competition reduction

● Assume 3 identical firms in the airline example. Using q = 192/(n + 1), each firm

flies 48k passengers, p = $195 and earns $2.3 million.

Two firms merge. Now, each of the remaining two firms flies 64k passengers

and earns $4.1 million each.

Bad for the merged firms (they earn $2.05 million each) - reduction of

individual profit.

Merger that arises from cost advantage

● If the merger results in cost advantage, the merger may be worthwhile. In our

example, if MC of the merged firms drops from $147 to $138, profit becomes

$2.45 million each. Great for them - increase of individual profit.

In general, the reduction in the number of firms may raise prices insufficiently to

make a merger profitable unless there is cost reduction.

8.3. Bertrand Oligopoly

Bertrand oligopoly firms set prices and then consumers decide how many units to

buy.

In a duopoly setting, Firm 1's best response curve comes from answering "What is

Firm 1's best response - what price should it set - if Firm 2 sets a price of p = x?" for

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all possible values of x. Similarly, Firm 2's best response curve: "What is Firm 2's best

response (p ) Firm 1 sets a price of p = y?" for all possible values of y.

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The Nash-Bertrand equilibrium is a set of prices such that no firm can obtain a

higher profit by choosing a different price if the other firms continue to charge

these prices. The Nash-Bertrand equilibrium differs from the Nash-Cournot

equilibrium; it depends on whether firms produce identical or differentiated

products.

Identical Products

Let us focus on a price-setting oligopoly where firms have identical costs and

produce identical products, with MC = AC = $5.

In the graph, Firm 1's best-response curve starts at $5 and then lies slightly above

the 45° line. That is, Firm 1 undercuts its rival's price as long as its price remains

above $5.

Firm 2's best response curve also starts at $5 and undercuts its rival's price if p > 5.

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Nash-Bertrand Equilibrium at intersection point e, p = p = $5 = MC.

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The Nash-Bertrand equilibrium when firms produce identical products is the same

equilibrium as perfect competition equilibrium.

The Nash-Bertrand equilibrium differs substantially from the Nash Cournot

equilibrium. Zero profits (p = MC) versus positive profits (p > MC).

The Cournot model seems more realistic than the Bertrand model in two ways:

- Bertrand's "Competitive" Equilibrium is Implausible

In a market with few firms, why would the firms compete so vigorously that

they would make no profit?

Oligopolies typically charge a higher price than competitive firms. So, the

Nash-Cournot equilibrium is more plausible.

- Bertrand's Equilibrium Price is insensitive to demand conditions and the

number of firms. It depends only on costs.

The Nash-Cournot equilibrium price is sensitive to demand conditions and

the number of firms as well as on cost. So, it is better to study homogeneous

goods markets.

Differentiated Products

Two firms, identical costs MC = AC = $5 and differentiated products.

In the graph above, neither firm's best-response curve lies along a 45° line through

the origin because Coke and Pepsi are similar but some consumers prefer one to the

other independently of the price. So neither firm has to exactly match a price cut by

its rival.

Nash-Bertrand Equilibrium at intersection point e, p = p = $13 > MC.

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Each firm Sets its best response price given the price the other firm is charging.

Neither firm wants to change its price.

This equilibrium is plausible: Firms set p > MC, and prices are sensitive to demand

conditions and number of firms.

Bertrand firms may earn positive profits in equilibrium if they differentiate their

products. Product differentiation is costly, but, if the alternative is zero profit in a

Bertrand homogeneous-good equilibrium, it is worth the cost.

8.4. Monopolistic Competition

The monopolistic competition market structure has the price setting characteristics

of monopoly or oligopoly and the free entry of perfect competition.

These firms face downward sloping demand curves and have oligopoly market

power, but they earn zero profit due to free entry. Reasons for downward sloping

demand:

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1 Reason

Market demand may be limited so there is room for only a few firms. The residual

demand curve facing a single firm is downward sloping.

For example in a small town, the market may be large enough to support only a

few plumbing firms, each providing a similar service.

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2 Reason

Firms differentiate their products. So each firm can retain those customers who

particularly like that firm's