Archive for the 'Profit maximization' Category

Mar 23 2012

Understanding Oligopoly Behavior – a Game Theory overview

What makes oligopolistic markets, which are characterized by a few large firms, so different from the other market structures we study in Microeconomics? Unlike in more competitive markets in which firms are of much smaller size and one firm’s behavior has little or no effect on its competitors, an oligopolist that decides to lower its prices, change its output, expand into a new market, offer new services, or adverstise, will have powerful and consequential effects on the profitability of its competitors. For this reason, firms in oligopolistic markets are always considering the behavior of their competitors when making their own economic decisions.

To understand the behavior of non-collusive oligopolists (non-collusive meaning a few firms that do NOT cooperate on output and price), economists have employed a mathematical tool called Game Theory. The assumption is that large firms in competition will behave similarly to individual players in a game such as poker. Firms, which are the “players” will make “moves” (referring to economic decisions such as whether or not to advertise, whether to offer discounts or certain services, make particular changes to their products, charge a high or low price, or any other of a number of economic actions) based on the predicted behavior of their competitors.

If a large firm competing with other large firms understands the various “payoffs” (referring to the profits or losses that will result from a particular economic decision made by itself and its competitors) then it will be better able to make a rational, profit-maximizing (or loss minimizing) decision based on the likely actions of its competitors. The outcome of such a situation, or game, can be predicted using payoff matrixes. Below is an illustration of a game between two coffee shops competing in a small town.

In the game above, both SF Coffee and Starbuck have what is called a dominant strategy. Regardless of what its competitor does, both companies would maximize their outcome by advertising. If SF coffee were to not advertise, Starbucks will earn more profits ($20 vs $10) by advertising. If SF coffee were to advertise, Starbucks will earn more profits ($12 vs $10) by advertising. The payoffs are the same given both options for SF Coffee. Since both firms will do best by advertising given the behavior of its competitor, both firms will advertise. Clearly, the total profits earned are less when both firms advertise than if they both did NOT advertise, but such an outcome is unstable because the incentive for both firms would be to advertise. We say that advertise/advertise is a “Nash Equilibrium” since neither firm has an incentive to vary its strategy at this point, since less profits will be earned by the firm that stops advertising.

As illustrated above, the tools of Game Theory, including the “payoff matrix”, can prove helpful to firms deciding how to respond to particular actions by their competitors in oligopolistic markets. Of course, in the real world there are often more than two firms in competition in a particular market, and the decisions that they must make include more than simply to advertise or not. Much more complicated, multi-player games with several possible “moves” have also been developed and used to help make tough economic decisions a little easier in the world of competition.

Game theory as a mathematical tool can be applied in realms beyond oligopoly behavior in Economics.  In each of the videos below, game theory can be applied to predict the behavior of different “players”. None of the videos portray a Microeconomic scenario like the one above, but in each case a payoff matrix can be created and behavior can be predicted based on an analysis of the incentives given the player’s possible behaviors.

Assignment: Watch each of the five videos below. For each one, create a payoff matrix showing the possible “plays” and the possible “payoffs” of the game portrayed in the video. Predict the outcome of each game based on your understanding of incentives and the assumption that humans act rationally and in their own self-interest.

“Batman – the Dark Night” – the Joker’s ferry game:

“Princess Bride” – where’s the poison?:

“Golden Balls” – split or steal:

“The Trap” – the delicate balance of terror

“Murder by Numbers” – the interrogation

Discussion Questions:

  1. Why is oligopoly behavior more like a game of poker than the behavior of firms in more competitive markets?
  2. What does it mean that firms in oligopolistic markets are “inter-dependent” of one another?
  3. Among the videos above, which games ended in the way that your payoff matrix and understanding of human behavior and rational decision making would have predicted?
  4. How often did the equilibrium outcomes according to your analysis of the payoff matrices correspond with the socially optimal outcome (i.e. the one where total payoffs for all players are maximized or the total losses minimized)?

12 responses so far

Jul 01 2011

Rational ‘bee’havior

Economists make several assumptions about humans, a fundamental assumption being that we are rational decision makers, able to weight costs and benefits of our actions and pursue the option that maximizes our benefits and minimizes our costs, thus leading to the greatest personal happiness, or utility. Only if this assumption holds true does a free market economic system, made up of individuals pursuing their own interests lead to a socially beneficial outcome. 

But are humans the only animal driven by rational, self-interested, benefit maximizing and cost minimizing behavior? Is our ability to make the right decision based on a complex set of options and variables made possible by our large brain and hundreds of thousands of years of adaptation? To some extent, our biology must drive our decision making and therefore the institutions and organizations that have allowed our species to thrive. But let us not think we are the only species to have thrived due to our rationality.

If you’re like me, you’ve often wondered to what extent animals can think. I have a dog, and after five years I still can’t figure out if he really likes me or if he has just learned that I’m the one who feeds him and scratches his belly, so he demonstrates the behaviors that offer the greatest rewards in terms of food and attention, and those behaviors are ones that I enjoy about him. It is a win win relationship, for sure, but is his behavior evidence of rationality, or just his biological need for food and attention? Is my dog’s behavior the outcome of a series of rational, self-interested calculations, or is it something more simple we usually associate with animal behavior: instinct?

Rationality may be as much a biological instict as an economic one. A recent study out of the UK has found that bumble bees are able to make rational decisions based on complex sets of options to mimimize costs and maximize benefits, much as humans must do countless times every day.

When deciding which flowers to fly to when collecting nectar, a bee must consider two variables: distance and the amount of nectar available in a particular flower. Of course, the distance the bee must fly represents the cost of collecting the nectar, and the amount of nectar in the flower is the benefit of having flown to it. The report explains: 

“Computers solve it (the problem of which flower to fly to) by comparing the length of all possible routes and choosing the shortest. However, bees solve simple versions of it without computer assistance using a brain the size of grass seed.”

The team set up a bee nest-box, marking each bumblebee with numbered tags to follow their behaviour when allowed to visit five artificial flowers which were arranged in a regular pentagon.

“When the flowers all contain the same amount of nectar bees learned to fly the shortest route to visit them all,” said Dr Lihoreau. “However, by making one flower much more rewarding than the rest we forced the bees to decide between following the shortest route or visiting the most rewarding flower first.”

In a feat of spatial judgement the bees decided that if visiting the high reward flower added only a small increase in travel distance, they switched to visiting it first. However, when visiting the high reward added a substantial increase in travel distance they did not visit it first.

The results revealed a trade-off between either prioritising visits to high reward flowers or flying the shortest possible route. Individual bees attempted to optimise both travel distance and nectar intake as they gained experience of the flowers.

“We have demonstrated that bumblebees make a clear trade-off between minimising travel distance and prioritising high rewards when considering routes with multiple locations,” concluded co-author Professor Lars Chittka. “These results provide the first evidence that animals use a combined memory of both the location and profitability of locations when making complex routing decisions, giving us a new insight into the spatial strategies of trap-lining animals.”

In economics, we refer to the behavior descibed above as cost, benefit analysis. It surprised me to read that insects, when faced with a trade off between further distance and more nectar, weigh both the cost and the benefit, and pursue the action that maximizes their profit, which is the bee’s case is a function of both distance of the flower and quantity or nectar collected.

Humans and our institutions make similar cost, benefit calculations. A business produces a quantity of output and sells it for a price that maximizes the difference between the price at which it can sell its product for and the average cost of production, thus maximizing its profits. A consumer will purchase a combination of goods and services at which the amount of utility per dollar is equalized across the various goods consumed, thus maximizing the consumer’s total utility

Bees, with their brains the size of a grass seed, weigh variables nearly as complex as those weighed by businesses and individuals in their economic decisions. Are bees rational? Or is their behavior purely biological instinct?

3 responses so far

Dec 02 2009

Review Lesson: Econ concepts in 60 seconds – Perfect Competition

YouTube – ACDCLeadership’s Channel

More econ review videos from my new favorite YouTube channel, Jacob Clifford’s Econ Concepts in 60 Seconds.

To review for the upcoming test, you will join a small group and watch one of the four videos on the Perfect Competition. After watching and discussing one video with your group, you will be re-assigned to another group with students who watched a different video. You will then lead a short discussion on your original video with your new group.

With your first group – 15 minutes: As your group watches its assigned video, have your notes open in front of you and draw the graphs Mr. Clifford draws along with him. Pause the video where necessary to have time to draw graphs. Take notes while watching the video so you can teach it to another group. With your group, prepare a short discussion of the video’s main points, including:

  • What rule or lesson about Perfect Competition does the video focus on?
  • What did you already know that this video reminded you of or reinforced your understanding of?
  • What did this video introduce that was new to you?
  • How were graphs used to teach the concepts?

With your second group – 20 minutes: For the second part of this assignment, there should be four new groups, each including one member of the four original groups.

  • Each group member should lead a 2-3 minute discussion of the video he or she watched in the first group.
  • Go over each of the discussion points from above.
  • Answer any questions your new group members have about video you watched.

Group 1 - The Profit Maximization Rule – MR=MC:

[youtube]http://www.youtube.com/watch?v=qaQRM6WIxpA[/youtube]

Group 2 - Perfect Competition in the short-run:

[youtube]http://www.youtube.com/watch?v=yY8f571AUxk[/youtube]

Group 3 - Perfect Competition in the long-run:

[youtube]http://www.youtube.com/watch?v=SjZmnOAPKUM[/youtube]

Group 4 - The Shut-Down Rule in Perfect Competition:

[youtube]http://www.youtube.com/watch?v=VFY2aJwpdNM[/youtube]h

4 responses so far

Nov 02 2009

When is acting irrational the rational thing to do?

FT.com / Comment / Opinion – Magic and the myth of the rational market.

Imagine you’re a poor farmer who has always had just enough to feed your family, with no surplus left over to sell. Then one day the government decides to grant your family and your neighbors enough land to grow your own food and plenty more to sell on the market. The government’s intention, of course, is for you to cultivate all your land, sell your surplus, generate income for your family to improve your quality of life, send your children to school and save for the future.

You’re the farmer. You’ve just been given land. What would you do?

1. Plant crops on all your land, harvest the crops, sell the surplus and enjoy the profits from your surplus?

OR

2. Plant crops on only part of your land, grow enough food to feed your family, and let the rest of the land lie uncultivated. You have no surplus, nothing to sell, and continue to live the way you always have lived: poorly.

The science of economics assumes that individuals always act rationally in their own self-interest. Self-interest is the ultimate motive of economic actors: firms are profit-maximizers, individuals are utility-maximizers. The theory of rational behavior would lead one to assume that the farmer would pursue option 1 above. But in Papua New Guinea, where the government recently relocated thousands of displaced farmers to new plots of land, it is more common for farmers to chose option 2:

“If they see me planting too much cocoa, they’ll do things to my land and my family, and they won’t bear fruit; really bad things; puripuri and other witchcraft.”

Such an avoidance of profit maximisation might have appeared economically irrational. But from the perspective of those villagers, putting in extra work just to make oneself a target for the jealousy of one’s neighbours would be highly irrational behaviour.

Economists need to re-think their assumptions on rational behavior. What appears irrational to one person may be perfectly rational to someone else, as in the case of the Papuan farmers who only plant half their land. Humans, it seems, are a bit more complicated than the cold, calculating arithmeticians economists have long assumed them to be.

In the wake of the largest economic crisis since the great depression, the assumption of rational actors interacting in rational markets has come into question. A new field of economics blending the traditional study of resource allocation in the market place and human psychology has arisen to tackle the challenge of better understaning the seemingly irrational behaviors of investors, buyers and sellers in today’s global economy:

One response to the current crisis has been a rise in the popularity of behavioural economics, which examines the psychological and emotional factors behind transactions. These models drop the assumption of the rational actor yet implicitly keep the same model of economic rationality at their heart. We may diverge from the path of rationality for all sorts of psychological reasons but only because emotion, Keynes’s famous “animal spirits”, clouds our judgment.

To break human behavior down to the basic pursuit of profits by producers and utility by consumers neglects to acknowledge the “animal spirits” within us all. Economics is entering a new era, in which psychology and markets are intertwined. Rational behavior will remain a basic assumption of the science, but a re-defining of what it means to be rational will allow economists to better understand the behaviors of individuals, investors and firms as the economy emerges from a slump Alan Greenspan might say was ushered in on a wave of irrational exuberance.

Discussion Questions:

  1. Are economists wrong to assume that individuals always act rationally? Why do the Papuan farmers only use half their land? Are they stupid or lazy?
  2. Can you think of any examples in which you or someone you know has done something that was not in his best economic self interest?
  3. Is charity irrational? What about gift giving? If you calculated that the chance of getting caught steeling something you REALLY wanted was 0%, wouldn’t it be irrational NOT to steal? What would keep you from stealing that thing if you deemed it rational to do so?

2 responses so far