Markets, Games, and Competition

Context

• The majority of economic transactions take place through markets. Markets have a myriad of different structures. They are central in organizing production and allocating surpluses between participants. On some occasions, market participants cannot affect the outcome.

• However, on other occasions, market participants can follow complicated strategies to affect production allocation in their favor.
  • What kind of strategies do market participants employ?
  • How do the strategies of different participants interact?
  • Do their strategies affect market efficiency besides allocation?

Course Structure Overview

Lecture Structure and Learning Objectives

Structure

• Jonathan Lebed (Case Study)
• Markets, Strategies, and Game Theory
• Basic Foundations
• Current Field Developments

Learning Objectives

• Explain what a market is from an economic perspective?
• Illustrate why participants’ interactions are central in determining outcomes and allocations?
• Review the fundamental market structures (monopoly and perfect competition).
• Give a high-level overview of the alternative market structures and competition strategies.

Jonathan Lebed

• Lebed is a former stock market trader.

• He was raised in New Jersey, US.
• He was prosecuted by the US Securities and Exchange Commission (SEC) for stock manipulation.
• Lebed reached an out-of-court settlement with SEC in 2000; He was 15 years old.

The SEC Prosecution

• Lebed is the first minor ever prosecuted for stock-market fraud.

• Lebed tools were
  • an America Online (AOL) internet connection,
  • an E*trade account, and
  • four email accounts in Yahoo Finance Message Boards.
• SEC accused him of making his money through a pump and dump strategy.

Timeline

Lewis, 2001

• Shortly after his \(11\text{-th}\) birthday Jonathan opened an account with America Online.

• He started building a website about pro-wrestling.
• At the age of 12, he invested \($8000\) (via his father) in the stock market, taken from a bond his parents gave him at birth.
• He started building an amateur investor website www[dot]stock-dogs[dot]com"
• At 14, SEC charges him with civil fraud.
• His mother closes his trading account.
• His father opens another account for him!

The Settlement

• Lebed forfeited \($285000\) in profit and interest he had made on \(11\) trades.

• He has never admitted any wrongdoing.
• He kept close to \($500000\) in profit.

Everybody is Manipulating the Market

People who trade stocks, trade based on what they feel will move and they can trade for profit. Nobody makes investment decisions based on reading financial filings. Whether a company is making millions or losing millions, it has no impact on the price of the stock. Whether it is analysts, brokers, advisors, Internet traders, or the companies, everybody is manipulating the market. If it wasn’t for everybody manipulating the market, there wouldn’t be a stock market at all…

(Jonathan Lebed, statement to his lawyer, Lewis, 2001)

Perfect Competition

• A market is perfectly competitive if it has a large number of consumers and firms such that
  • the market does not suffer from any market failure (imperfect information, externalities, etc.),
  • consumers and firms are price takers,
  • consumers try to maximize their utility,
  • firms try to maximize their profits.
  • firms produce a homogeneous commodity or service, and
  • there are no entry barriers in the market,

Pareto Efficiency

Price Setting

• Is price taking behavior an appropriate assumption for monopolies?

• The justification for price taking is based on competition.
• Attempts to change prices do not work because other firms do not follow them.
• However, this is not a valid argument in a single seller market.
• A firm (or a consumer) is a price setter if it can influence the market price of the products it produces (consumes). Price setters consider market prices as (at least partially) endogenous.

Monopoly

• Perfect competition requires that a large number (formally an infinite number) of firms (sellers) exist in the market.

• What about the other extreme case of a single firm in a market?
• A market structure with exclusive possession of supply by a single seller is called a monopoly. The single firm (or seller) in a market is called a monopolist.
• Market demand and firm demand are identical in monopolistic markets.

Markup Pricing

• The monopolist sets the price of the commodity it produces using a markup.
• The monopolist pricing rule can be calculated by \[p_{m} = \frac{\text{Marginal Cost}}{\frac{1}{\text{Demand Elasticity}} + 1}\]

How do Marginal Cost Changes Affect Profit?

How do Elasticity Changes Affect Profit?

Deadweight Loss

Current Field Developments

• The transaction cost theory of the firm focusing on the firm relation to the market started developing in the 1930’s.
• Managerial and behavioral theories of the firm focusing on internal organization have started developing in the 1960’s.
• Industrial organization is an economic field that builds on the theory of the firm and examines the interactions of market participants and the welfare properties of market structures.

Comprehensive Summary

• For economics, markets are the primary coordination mechanism of production and allocation.
• When studying competition and market structure, it is convenient to abstract from organizational aspects and consider the firm a black box.
• Based on this, various firm models can be used to analyze competition in the market (monopoly, oligopoly, perfect competition, etc.)
• Monopoly and perfect competition are simple models that ignore the interactions of market participants.
• In reality, however, firms use various strategies based on prices and quantities to compete in a market.

Further Reading

• Belleflamme & Peitz, 2010, secs. 1.1-1.4, 2.1.1-2.1.4
• Varian, 2010, Chapter 1
• Chandler, 1992

Exercises

Group A

1. Consider a market with inverse demand given by \(p(q) = p_{0} + p_{1}q\) with \(p_{0}>0\) and \(p_{1}<0\).

   1. Calculate the demand function (i.e., invert \(p\)). For which values of price is demand non-negative?
   2. Calculate the demand elasticity as a function of price using the demand function. What is the sign of elasticity?
   3. Calculate the demand elasticity as a function of quantity using the inverse demand function.
   4. Substitute the quantity variable in the result of part (c) with the demand calculated in part (a) and verify that you get the result of part (b).
   5. Calculate the quantity for which demand exhibits unitary elasticity.

   1. Fix a value for \(p\) and solve for \(q\) to get \[q(p)=-\frac{p_{0}}{p_{1}} + \frac{1}{p_{1}} p.\] Since \(p_{1}<0\), demand is non-negative if and only if \(p \le p_{0}\).

   2. We calculate

      \begin{align*} E(p) &= \frac{\mathrm{d} q}{\mathrm{d} p} \frac{p}{q(p)} \\ &= q’(p) \frac{p}{q(p)} \\ &= \frac{1}{p_{1}} \frac{p}{-\frac{p_{0}}{p_{1}} + \frac{1}{p_{1}} p} \\ &= \frac{p}{-p_{0} + p} \end{align*}

      For every \(0 \le p\le p_{0}\) is non-positive.

   3. We have

      \begin{align*} E(q) &= \frac{\mathrm{d} q}{\mathrm{d} p} \frac{p(q)}{q} \\ &= \frac{1}{\frac{\mathrm{d} p}{\mathrm{d} q}} \frac{p(q)}{q} \\ &= \frac{1}{p’(q)} \frac{p(q)}{q} \\ &= \frac{1}{p_{1}} \frac{p_{0} + p_{1}q}{q} \end{align*}

   4. Substituting gives

      \begin{align*} E(q(p)) &= \frac{p_{0} + p_{1}q(p)}{p_{1} q(p)} \\ &= \frac{p_{0} - p_{0} + p}{- p_{0} + p} \\ &= \frac{p}{-p_{0} + p} \end{align*}

   5. Using part (c), we have \(E(q)=-1\) if and only if \[p_{0} + p_{1}q = -p_{1}q,\] or equivalently \[q = -\frac{p_{0}}{2p_{1}}.\]

2. Consider a monopolist in a market with inverse demand \(p(q) = p_{0} + p_{1}q\), where \(p_{0}>0\) and \(p_{1} < 0\). The monopolist’s cost function is given by \(c(q) = c_{1}q\), where \(0 < c_{1}\).

   1. Set up the maximization problem of the monopolist for which the monopolist chooses the produced quantity.
   2. Calculate the monopoly quantity, price, and profit.
   3. Instead, suppose that the monopolist is choosing prices. Calculate the demand function and setup the maximization problem.
   4. Calculate the quantity, price, and profit. Compare with the maximization problem over quantities. Are the results the same? Why, or why not?
   5. Calculate the consumer welfare and the total welfare.
   6. Compare with the welfare of the perfect competition case and calculate the deadweight loss.

   1. The monopolist solves \[\max_{q} \left\{ p(q)q - c(q) \right\}\]

   2. The first order condition is \[p’(q)q + p(q) = c’(q) \iff p_{0} + 2p_{1}q = c_{1},\] which gives

      \begin{align*} q_{m} &= -\frac{p_{0} - c_{1}}{2p_{1}}, \\ p_{m} &= \frac{c_{1} + p_{0}}{2}, \end{align*}

      and \[\pi_{m} = -\frac{(p_{0} - c_{1})^{2}}{4p_{1}}.\]

   3. The demand function is \[q(p) = -\frac{1}{p_{1}} (p_{0} - p)\] and the monopolist problem is \[\max_{p} \left\{ q(p)p - c(q(p)) \right\}.\]

   4. The first order condition is \[q’(p)p + q(p) = c’(q)q’(p) \iff \frac{1}{p_{1}}(2p - p_{0}) = \frac{c_{1}}{p_{1}},\] which leads to the same price, quantity, and profit as in part (b). The result is the same because inverse demand is affine (more generally because inverse demand is one-to-one).

   5. The consumer welfare is

      \begin{align*} C_{m} &= \int_{0}^{q_{m}} (p(q) - p_{m}) \mathrm{d} q \\ &= p_{0}q_{m} + \frac{p_{1}}{2} q_{m}^2 - p_{m} q_{m} \\ &= \frac{1}{2} q_{m} (p_{0} - p_{m})\\ &= -\frac{(p_{0} - c_{1})^{2}}{8p_{1}}, \end{align*}

      so the total welfare is \[W_{m} = C_{m} + \pi_{m} = - 3 \frac{(p_{0} - c_{1})^{2}}{8p_{1}}.\]

   6. In perfect competition, \(p_{c} = c_{1}\). Then, \[q_{c}=\frac{c_{1} - p_{0}}{p_{1}}\] and profits are zero. The competition total welfare is

      \begin{align*} W_{c} &= C_{c} \\ &= \int_{0}^{q_{c}} (p(q) - c_{1}) \mathrm{d} q \\ &= p_{0}q_{c} + \frac{p_{1}}{2} q_{c}^2 - c_{1} q_{c} \\ &= \frac{1}{2} q_{c} (p_{0} - p_{c})\\ &= -\frac{(p_{0} - c_{1})^{2}}{2p_{1}}. \end{align*}

      Finally, the deadweight loss is \[D = W_{c} - W_{m} = -\frac{(p_{0} - c_{1})^{2}}{8p_{1}}.\]

References

References

Topic's Concepts

• monopolist
• monopoly
• price setter
• perfectly competitive