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Real-World Markets

Prof. Wolfram ElsnerFaculty of Business Studies and Economics

iino – Institute of Institutional and Innovation Economics

Elsner/Heinrich/Schwardt: Microeconomics of Complex Economies

Chapter 07: Real-World Markets10.06.2014

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Readings for this lecture

Required reading this time:

Real-World Markets: …, in: Elsner/Heinrich/Schwardt (2014): The Microeconomics of Complex Economies, Academic Press, pp. 157-190.

The lecture and the slides are complements, not substitutes

An additional reading list can be found at the companion website

Geben Sie hier eine Formel ein.

http://www.amazon.com/The-Microeconomics-Complex-Economies-Institutional/dp/0124115853/ref=sr_1_1?ie=UTF8&qid=1396453322&sr=8-1&keywords=Microeconomics+of+complex+economies

http://booksite.elsevier.com/9780124115859/


Chapter 07: Real-World Markets

Real-world markets are not simple, clear-cut, unique, or transparent.

They are networks of directly interdependent agents, facing information problems, different problem structures, and uncertainty.

Such situations are complex.

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Introduction



To protect themselves in such an environment, firms have various options to take strategic actions, e.g.:

Size growth (technological factors can support this)

Influencing customers and/or suppliers in production networks

Avoidance of competition (through signals among competitors, or market segmentation, for instance)

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Introduction



Decentralized market systems thus tend to develop into power-based systems.

Oligopolistic structures are the rule rather than the exception in real-world markets.

Due to direct interdependence, turbulence can nevertheless remain a factor in the environment, though.

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Introduction



Real-world markets exist in limited space, they are networks of (relatively few) directly interdependent agents.

Technological factors in production tend to favor size growth.

Informal collusion or formal cartelization help to avoid competition.

It pays to try and deter new entrants.

Network effects in consumption may favor structures with few suppliers.

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Factors leading to size and power



First-mover advantages favor few suppliers.

Learning curves in production leading to cost reductions reinforce these advantages.

Technological knowledge may be difficult to transfer, tacit knowledge can play an important part in production and distribution.

Factors’ effects are cumulative, they can combine their influences.

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Factors leading to size and power



One firm produces the total supply in a market for one good. Its goal is to maximize its profit.

Numerous buyers purchase the product.

A demand function has a negative slope – the higher the price, the lower the quantity that can be sold.

The monopolist has market power: It can select its preferred point on the demand schedule (Cournot point) through its choice of output produced.

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A model of a monopoly market



Maximize profit π – the difference between revenue R and cost C, all as function of quantity q:

max𝑞𝜋 𝑞 = 𝑅 𝑞 − 𝐶(𝑞)

From the first order condition we can derive the general rulefor profit maximization (marginal revenue = marginal cost):

𝑀𝑅 =𝑑𝑅

𝑑𝑞=𝑑𝐶

𝑑𝑞= 𝑀𝐶

In contrast to the perfect market, the market-price changeswhen the monopolist changes output.

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The demand function is 𝑞 = 𝑞(𝑝), the inverse demand functionhence 𝑝 = 𝑝(𝑞).

Revenue is 𝑅(𝑞) = 𝑝(𝑞)𝑞, …

… and marginal revenue (using the product rule ofdifferentiation):

𝑀𝑅 𝑞 =𝑑𝑅

𝑑𝑞=𝑑 𝑝 𝑞 𝑞

𝑑𝑞= 𝑝 +

𝑑𝑝

𝑑𝑞𝑞 = 𝑀𝐶

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We can rearrange this expression as (ε is the price elasticity ofdemand):

𝑝 +𝑑𝑝

𝑑𝑞𝑞 = 𝑝 1 +

𝑑𝑝

𝑑𝑞

𝑞

𝑝= 𝑝 1 +

1

𝑑𝑝 𝑑𝑞 𝑝 𝑞

𝑝 1 +1

𝑑𝑝 𝑑𝑞 𝑝 𝑞= 𝑝 1 +

1

𝜀= 𝑀𝐶

The monopolist will offer a quantity for which marginal costist below the price in the market (as 𝜀 < 0).

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The expression can be rearranged to give the Amoroso-Robinson relation:

𝑝 1 +1

𝜀= 𝑝 1 −

1

𝜀= 𝑀𝐶 ↔ 𝑝 =

𝑀𝐶

1 − 1 𝜀

In the perfect market-benchmark case, price is equal tomarginal cost. The higher price in the monopoly case, isinversely related to the elasticity of demand a company faces.

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We can analyze the welfare effects of monopoly markets as well, the benchmark case is the perfectly competitive market.

Consumer surplus (CS): the difference between the price consumers are willing to pay and the price they have to pay

Producer surplus (PS): the difference between unit cost and the price units are sold for (zero in a competitive market)

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Perfect market CS: ACF; Monopoly market CS: EDF; Monopoly market PS: ABDE; Welfare loss monopoly: BCD

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There are three standard oligopoly models, Cournot, Bertrand, and Stackelberg.

In all models, few companies provide the supply of a homogenous good to a market with many buyers. Theirindividual decisions have an impact on the overall quantitysupplied.

Companies take their decisions at the beginning of a period.These cannot be changed during the period.

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Oligopoly models



In the Cournot model, companies decide simultaneously, how much to produce. Their combined output determines the market price.

In the Bertrand model, companies set their prices. The one with the lowest price serves the entire demand. If more than one company (say, n) set an equally low price, each serves 1/nof total demand.

In the Stackelberg model, companies decide sequentially, how much to produce. Earlier decisions are known to those who choose later. Combined output determines the market price.

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Oligopoly models



2 companies, A and B.

Let the inverse demand function be p(q)=a-bq, with positive parameters a and b, and 𝑞 = 𝑞𝐴 + 𝑞𝐵. Constant unit costs for both are c.

The problem for A is (taking the decision of B as given):

max𝑞𝐴≥0𝑎 − 𝑏 𝑞𝐴 + 𝑞𝐵 𝑞𝐴 − 𝑐𝑞𝐴

The resulting first order condition is (for B equivalently):𝑎 − 2𝑏𝑞𝐴 − 𝑏𝑞𝐵 = 𝑐

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Oligopoly models – Cournot



A firm‘s best response function (BR) shows its optimal amountof output given the output of the rest.

Rearranging the FOC gives:

𝑞𝐴𝐵𝑅 𝑞𝐵 =

1

2

𝑎 − 𝑐

𝑏− 𝑞𝐵

𝑞𝐵𝐵𝑅 𝑞𝐴 =

1

2

𝑎 − 𝑐

𝑏− 𝑞𝐴

Substituting one into the other gives the mutual best response:

𝑞𝐴 = 𝑞𝐵 =1

3

𝑎 − 𝑐

𝑏

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We can compare this outcome to monopoly (M) and perfectlycompetitive (PC) market.

As price is equal to MC (𝑝 = 𝑐) in a PC, the inverse demandschedule gives 𝑞𝑃𝐶 = (𝑎 − 𝑐)/𝑏

Solving for the monopoly solution above, gives 𝑞𝑀 =𝑎−𝑐

2𝑏

Overall, thus: 1

2

𝑎 − 𝑐

𝑏𝑞𝑀

<2

3

𝑎 − 𝑐

𝑏𝑞𝐶

<𝑎 − 𝑐

𝑏𝑞𝑃𝐶

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In the Bertrand model, companies compete through pricesetting. For two companies, demand takes the form:

𝑞𝐴 𝑝𝐴, 𝑝𝐵 =

𝑞 𝑝𝐴 𝑖𝑓 𝑝𝐴 < 𝑝𝐵0.5𝑞 𝑝𝐴 𝑖𝑓 𝑝𝐴 = 𝑝𝐵0 𝑖𝑓 𝑝𝐴 > 𝑝𝐵

In the sole Nash equilibrium in this situation, price is equal to marginal cost and the companies split the market.

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Oligopoly models – Bertrand



If there was a chance for one company to undercut the other, it would do so and attract the entire demand in the market to itself.

If 𝑝𝐴 > 𝑐, it is advantageous to charge an amount just below that price for B. The limit to this dynamic is provided by marginal cost c, as negative profits result below.

If cost structures differ, the cheaper producer can undercut the other slightly and service the entire market at the resulting price.

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Oligopoly models – Bertrand



The sequential decisions in the Stackelberg model allow theleader to ask how the follower will react to its decision.

The reaction functions are the same as in the Cournot case (thebasic maximization problem stays the same):

𝑞𝐵𝐵𝑅 𝑞𝐴 =

1

2

𝑎 − 𝑐

𝑏− 𝑞𝐴

Instead of substituting in the BR, we substitute this in A’s profit function.

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Oligopoly models – Stackelberg



This gives:

max𝑞𝐴≥0𝑎 − 𝑏 𝑞𝐴 +

1

2

𝑎 − 𝑐

𝑏− 𝑞𝐴 𝑞𝐴 − 𝑐𝑞𝐴

max𝑞𝐴≥0

1

2𝑎 + 𝑐 − 𝑏𝑞𝐴 𝑞𝐴 − 𝑐𝑞𝐴

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Solving for the optimal quantities (from FOC for A, and BR for B) gives:

𝑞𝐴 =𝑎 − 𝑐

2𝑏

𝑞𝐵 =𝑎 − 𝑐

4𝑏

The first mover advantage for the leader allows it higher profits.

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We find monopolies in a number of areas in the economicsphere. – Why?

A particularly stable set are the natural monopolies.

Characterized by subadditive costs in production:

𝑖=1

𝑚

𝐶 𝑞𝑖 <

𝑗=1

𝑛

𝐶𝑞𝑗 ∀𝑚 < 𝑛

𝑤𝑖𝑡ℎ

𝑖=1

𝑚

𝑞𝑖 =

𝑗=1

𝑛

𝑞𝑗 = 𝑞

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Natural monopolies



Given such subadditivity, average costs fall with increasedproduction.

To avoid multiple investments, let one supplier provide theproduct in question and put regulations in place.

Examples include all the classic public utilities – products (gas, water, electricity, landline telephone, …) that rely on extensive networks for their delivery.

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Natural monopolies



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Natural monopolies



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Natural monopolies



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Natural monopolies



Prices tend to be sticky over time.

Instead of asking how an equilibrium in one period may look, we can ask how companies behave in a stable market.

Assume that competitors react differently to changes in prices, depending on whether another company raises or lowers itsprices.

The objective is to at least maintain market shares.

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Sticky prices in oligopoly markets



Then, price increases may not be met. Companies raisingprices lose market share.

Price decreases may be met. Market shares remain the same, revenue is reduced.

Price competition does not make sense.

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The demand function is kinked as a consequence. Standard demand schedules may not be useful under strategicinterdependence.

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Avoid price competition and bind customers more tightly –competition through non-price variables.

Creation of a niche -> market power therein.

Niches occupied by imperfect substitutes.

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Heterogenization and monopolistic competition



The above refers to the monopolistic aspect. For thecompetitive character, free entry as long as profits are realized.

Eventually, enough niches are occupied to drive prices down to average costs and profits down to zero.

If entry barriers exist, companies may be able to protect theirprofits, an oligopoly with heterogeneous products results.

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Heterogenization and monopolistic competition



Companies have various non price-based options for (further) increasing control over their environment and strengtheningtheir position. Some rooted in the character of productiontechnology (e.g., increasing returns to scale). Others include:

Brand strategies, niche creation

Horizontal integration

Deter entry

Vertical integration.

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Opportunities for strategic behavior



These measures tend to increase the turbulence for all othercompanies in a market. This remains a noticeable factor, attempts to the contrary notwithstanding.

Over time, though, some ways have been found for reducingdirect interdependence among companies, e.g.:

avoidance of product homogeneity.

circumvention of price competition through various ways ofinstituting informal arrangements

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Increasing action capabilities of companies has facilitatedmarket segmentation.

For consumers, this typically goes hand in hand withincreased search and information costs.

Competition shifts to competition for markets, as opposed tocompetition in markets.

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39

Readings for the next lecture

Required reading:

Chapter 8: Game theory II, in: Elsner/Heinrich/Schwardt: Microeconomics of Complex Economies, pp. 193-226.

For further readings visit the companion website

http://www.amazon.com/The-Microeconomics-Complex-Economies-Institutional/dp/0124115853/ref=sr_1_1?ie=UTF8&qid=1396453322&sr=8-1&keywords=Microeconomics+of+complex+economies

http://booksite.elsevier.com/9780124115859/

real-world markets - elsevier...real-world markets exist in limited space, they are networks of...

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