Micro-Economics

This post contains notes from different sources about micro-economics. The backdrop is that a connection is needed between the economic models that are taught in schools and any new theory under development. Even if it were only to be able to translate from language to the other and to distinguish the conditions from the main issues, however the case may be.

If the bold hypotheses … , that complex systems achieve the edge of chaos internally and collectively, were to generalize to economic systems, our study of the proper marriage of self-organization and selection would enlist Charles Darwin and Adam Smith to tell us who and how we are in the nonequilibrium world we mutually create and transform.‘ [Kauffman, 1993 p. 401]

How does this theory relate to economic subjects? In economic theory technology is an important factor in the development of an economy. Kauffman suggests it is the important pillar of economic development: the existence of goods and services leads to the emergence of new goods and services. And conversely: new goods and services force existing goods and services out. In this way, the economy renews itself [Kauffman, 1993, pp. 395-402]. The question is how an economic structure does control its means of transforming the entry and exit of goods and services. A theory is required that describes how goods and services ‘match’ or ‘fit’ from a technological perspective.

With this model an economy can be simulated as a population of ‘as-if’ goods and services, sourcing from external sources (basic materials), that supply to each other when complementary goods and substitute when substituting goods and that each represent a utility. The equilibrium for this simulated economy can be the production ratio in that economy at a maximum utility for the whole of all present goods and services. That ratio can also be the basis for a measurement of the unit of price in the simulated economy. How does this simulated economy develop?

Introduce variations to existing goods and services through random mutations or permutations to generate new goods. Generate a new economy by introducing this new technology into it. Determine the new equilibrium: at this equilibrium some of the newly introduced goods and services will turn out to be profitable: they will stay. Some will not be profitable and they will disappear. This is of interest for these reasons:

  • Economic growth is modelled with new niches emerging as a consequence of the introduction of new goods and services
  • This kind of system leads to new models for economic take-off. The behavior of an economy depends on the complexity of the grammar, the diversity of the renewable sources, the discount factor as a part of the utility function of the consumer and the prediction horizon of the model. An insufficient level of complexity or of renewable resources leads to stagnation and the system remains subcritical. If too high then the economy can reach a supra critical level.

This class of models depends on past states and on dynamical laws. The process of testing of the newly introduced goods and services in a given generation is the basis on which future generations can build and so it guides the evolution and growth of the system. Because it will usually not be clear a priori how new goods and services are developed from the existing, the concepts of complete markets and rational agents can not be maintained as such: classical theory needs to be adapted.

An important behavioral factor of large complex adaptive systems is that no equilibrium is encountered. The economy (or the markets) is a complex system and so it will not reach an equilibrium. However, it is possible that limited rational agents are capable of encountering the edge of chaos where markets are near equilibrium. On that edge avalanches of change happen, which in the biological sphere leads to extinction and in the economy may lead to disruption.

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Whenever we try to explain the behavior of human beings we need to have a framework on which our analysis can be based. In much of economics we use a framework built on the following two simple principles.

The optimization principle: People try to choose the best patterns of consumption that they can afford.

The equilibrium principle: Prices adjust until the amount that people demand of something is equal to the amount that is supplied.

Let us consider these two principles. The first is almost tautological. If people are free to choose their actions, it is reasonable to assume that they try to choose things they want rather than things they don’t want. Of course there are exceptions to this general principle, but they typically lie outside the domain of economic behavior. The second notion is a bit more problematic.The second notion is a bit more problematic. It is at least conceivable that at any given time peoples’ demands and supplies are not compatible, and hence something must be changing. These changes may take a long time to work themselves out, and, even worse, they may induce other changes that might “destabilize” the whole system.

This kind of thing can happen . . . but it usually doesn’t. In the case of apartments, we typically see a fairly stable rental price from month to month. It is this equilibrium price that we are interested in, not in how the market gets to this equilibrium or how it might change over long periods of time. It is worth observing that the definition used for equilibrium may be different in different models. In the case of the simple market we will examine in this chapter, the demand and supply equilibrium idea will be adequate for our needs. But in more general models we will need more general definitions of equilibrium. Typically, equilibrium will require that the economic agents’ actions must be consistent with each other.

One useful criterion for comparing the outcomes of different economic institutions is a concept known as Pareto efficiency or economic efficiency. 1 We start with the following definition: if we can find a way to make some people better off without making anybody else worse off, we have a Pareto improvement. If an allocation allows for a Pareto improvement, it is called Pareto inefficient; if an allocation is such that no Pareto improvements are possible, it is called Pareto efficient.

A Pareto inefficient allocation has the undesirable feature that there is some way to make somebody better off without hurting anyone else. There may be other positive things about the allocation, but the fact that it is Pareto inefficient is certainly one strike against it. If there is a way to make someone better off without hurting anyone else, why not do it?

Let us try to apply this criterion of Pareto efficiency to the outcomes of the various resource allocation devices mentioned above. Let’s start with the market mechanism. It is easy to see that the market mechanism assigns the people with the S highest reservation prices to the inner ring namely, those people who are willing to pay more than the equilibrium price, p ∗ , for their apartments. Thus there are no further gains from trade to be had once the apartments have been rented in a competitive market. The outcome of the competitive market is Pareto efficient. What about the discriminating monopolist? Is that arrangement Pareto efficient? To answer this question, simply observe that the discriminating monopolist assigns apartments to exactly the same people who receive apartments in the competitive market. Under each system everyone who is willing to pay more than p ∗ for an apartment gets an apartment. Thus the discriminating monopolist generates a Pareto efficient outcome as well.

Although both the competitive market and the discriminating monopolist generate Pareto efficient outcomes in the sense that there will be no further trades desired, they can result in quite different distributions of income. Certainly the consumers are much worse off under the discriminating monopolist than under the competitive market, and the landlord(s) are much better off. In general, Pareto efficiency doesn’t have much to say about distribution of the gains from trade. It is only concerned with the efficiency of the trade: whether all of the possible trades have been made.

We will indicate the consumer’s consumption bundle by (x 1 , x 2 ). This is simply a list of two numbers that tells us how much the consumer is choosing to consume of good 1, x 1 , and how much the consumer is choosing to consume of good 2, x 2 . Sometimes it is convenient to denote the consumer’s bundle by a single symbol like X, where X is simply an abbreviation for the list of two numbers (x 1 , x 2 ).

We suppose that we can observe the prices of the two goods, (p 1 , p 2 ), and the amount of money the consumer has to spend, m. Then the budget constraint of the consumer can be written as

p 1 x 1+ p 2 x 2 ≤ m. (2.1)

Here p 1 x 1 is the amount of money the consumer is spending on good 1, and p 2 x 2 is the amount of money the consumer is spending on good 2.

p1 x1 + x2 ≤ m.

This expression simply says that the amount of money spent on good 1, p1 x1 , plus the amount of money spent on all other goods, x2 , must be no more than the total amount of money the consumer has to spend, m. equation (2.2) is just a special case of the formula given in equation (2.1), with

p 2 = 1

p 1 x 1 + p 2 x 2 = m

and

p 1 (x 1 + Δx 1 ) + p 2 (x 2 + Δx 2 ) = m.

Subtracting the first equation from the second gives

p 1 Δx 1 + p 2 Δx 2 = 0.

This says that the total value of the change in her consumption must be zero. Solving for Δx 2 /Δx 1 , the rate at which good 2 can be substituted for good 1 while still satisfying the budget constraint, gives

Δx 2 /Δx 1 = -p1/p2

This is just the slope of the budget line. The negative sign is there since Δx 1 and Δx 2 must always have opposite signs. If you consume more of good 1, you have to consume less of good 2 and vice versa if you continue to satisfy the budget constraint. Economists sometimes say that the slope of the budget line measures the opportunity cost of consuming good 1.

Consumer Preferences

We will suppose that given any two consumption bundles, (x 1 , x 2 ) and (y 1 , y 2 ), the consumer can rank them as to their desirability. That is, the consumer can determine that one of the consumption bundles is strictly better than the other, or decide that she is indifferent between the two bundles. We will use the symbol to mean that one bundle is strictly preferred to another, so that (x 1 , x 2 ) (y 1 , y 2 ) should be interpreted as saying that the consumer strictly prefers (x 1 , x 2 ) to (y 1 , y 2 ), in the sense that she definitely wants the x-bundle rather than the y-bundle. This preference relation is meant to be an operational notion. If the consumer prefers one bundle to another, it means that he or she would choose one over the other, given the opportunity. Thus the idea of preference is based on the consumer’s behavior. In order to tell whether one bundle is preferred to another, we see how the consumer behaves in choice situations involving the two bundles. If she always chooses (x 1 , x 2 ) when (y 1 , y 2 ) is available, then it is natural to say that this consumer prefers (x 1 , x 2 ) to (y 1 , y 2 ).

If the consumer is indifferent between two bundles of goods, we use the symbol ∼ and write

(x 1 , x 2 ) ∼ (y 1 , y 2 ). Indifference means that the consumer would be just as satisfied, according to her own preferences, consuming the bundle (x 1 , x 2 ) as she would be consuming the other bundle, (y 1 , y 2 ).

If the consumer prefers or is indifferent between the two bundles we say that she weakly prefers (x 1 , x 2 ) to (y 1 , y 2 ) and write (x 1 , x 2 ) (y 1 , y 2 ). These relations of strict preference, weak preference, and indifference are not independent concepts; the relations are themselves related! Indifference curves are a way to describe preferences. Nearly any “reasonable” preferences that you can think of can be depicted by indifference curves. The trick is to learn what kinds of preferences give rise to what shapes of indifference curves.

well-behaved indifference curves

First we will typically assume that more is better, that is, that we are talking about goods, not bads. More precisely, if (x 1 , x 2 ) is a bundle of goods and (y 1 , y 2 ) is a bundle of goods with at least as much of both goods (x 1 , x 2 ). This assumption is sometimes and more of one, then (y 1 , y 2 ) called monotonicity of preferences. As we suggested in our discussion of satiation, more is better would probably only hold up to a point. Thus the assumption of monotonicity is saying only that we are going to examine situations before that point is reached—before any satiation sets in—while more still is better. Economics would not be a very interesting subject in a world where everyone was satiated in their consumption of every good.

What does monotonicity imply about the shape of indifference curves? It implies that they have a egative slope. That is, if the consumer gives up Δx 1 units of good 1, he can get EΔx 1 units of good 2 in exchange. Or, conversely, if he gives up Δx 2 units of good 2, he can get Δx 2 /E units of good 1. Geometrically, we are offering the consumer an opportunity to move to any point along a line with slope −E that passes through (x 1 , x 2 ), as depicted in Figure 3.12. Moving up and to the left from (x 1 , x 2 ) involves exchanging good 1 for good 2, and moving down and to the right involves exchanging good 2 for good 1. In either movement, the exchange rate is E. Since exchange always involves giving up one good in exchange for another, the exchange rate E corresponds to a slope of −E.

If good 2 represents the consumption of “all other goods,” and it is measured in dollars that you can spend on other goods, then the marginal- willingness-to-pay interpretation is very natural. The marginal rate of substitution of good 2 for good 1 is how many dollars you would just be willing to give up spending on other goods in order to consume a little bit more of good 1. Thus the MRS measures the marginal willingness to give up dollars in order to consume a small amount more of good 1. But giving up those dollars is just like paying dollars in order to consume a little more of good 1.

Originally, preferences were defined in terms of utility: to say a bundle (x 1 , x 2 ) was preferred to a bundle (y 1 , y 2 ) meant that the x-bundle had a higher utility than the y-bundle. But now we tend to think of things the other way around. The preferences of the consumer are the fundamental description useful for analyzing choice, and utility is simply a way of describing preferences. A utility function is a way of assigning a number to every possible consumption bundle such that more-preferred bundles get assigned larger numbers than less-preferred bundles. That is, a bundle

(x 1 , x 2 ) is preferred to a bundle (y 1 , y 2 ) if and only if the utility of (x 1 , x 2 ) is larger than the utility of (y 1 , y 2 ): in symbols, (x 1 , x 2 ) (y 1 , y 2 ) if and only if u(x 1 , x 2 ) > u(y 1 , y 2 ). The only property of a utility assignment that is important is how it orders the bundles of goods. This is ordinal utility.

We summarize this discussion by stating the following principle: a monotonic transformation of a utility function is a utility function that represents the same preferences as the original utility function. Geometrically, a utility function is a way to label indifference curves. Since every bundle on an indifference curve must have the same utility, a utility function is a way of assigning numbers to the different indifference curves in a way that higher indifference curves get assigned larger numbers. Seen from this point of view a monotonic transformation is just a relabeling of indifference curves. As long as indifference curves containing more-preferred bundles get a larger label than indifference curves containing less-preferred bundles, the labeling will represent the same preferences.

Consider a consumer who is consuming some bundle of goods, (x 1 , x 2 ). How does this consumer’s utility change as we give him or her a little more of good 1? This rate of change is called the marginal utility with respect to good 1. We write it as M U 1 and think of it as being a ratio, MU1 = ΔU /Δx 1 = ( u(x 1 + Δx 1 , x 2 ) − u(x 1 , x 2 ) )/ Δx 1

that measures the rate of change in utility (ΔU ) associated with a small change in the amount of good 1 (Δx 1 ). Note that the amount of good 2 is held fixed in this calculation. This definition implies that to calculate the change in utility associated with a small change in consumption of good 1, we can just multiply the change in consumption by the marginal utility of the good:

ΔU = MU1 Δx 1

The marginal utility with respect to good 2 is defined in a similar manner:

M U 2 = ΔU /Δx 2 = u(x 1 , x 2 + Δx 2 ) − u(x 1 , x 2 ) ) / Δx 2

Note that when we compute the marginal utility with respect to good 2 we keep the amount of good 1 constant. We can calculate the change in utility associated with a change in the consumption of good 2 by the formula ΔU = MU2 Δx2 .

It is important to realize that the magnitude of marginal utility depends on the magnitude of utility. Thus it depends on the particular way that we choose to measure utility. If we multiplied utility by 2, then marginal utility would also be multiplied by 2. We would still have a perfectly valid utility function in that it would represent the same preferences, but it would just be scaled differently.

Solving for the slope of the indifference curve we have

MRS = MU1 / MU2 = – Δx2 / Δx1 (4.1)

(Note that we have 2 over 1 on the left-hand side of the equation and 1 over 2 on the right-hand side. Don’t get confused!).

The algebraic sign of the MRS is negative: if you get more of good 1 you have to get less of good 2 in order to keep the same level of utility. However, it gets very tedious to keep track of that pesky minus sign, so economists often refer to the MRS by its absolute value—that is, as a positive number. We’ll follow this convention as long as no confusion will result. Now here is the interesting thing about the MRS calculation: the MRS can be measured by observing a person’s actual behavior we find that rate of exchange E where he or she is just willing to stay put, as described in Chapter 3. The condition that the MRS must equal the slope of the budget line at an interior optimum is obvious graphically, but what does it mean economically? Recall that one of our interpretations of the MRS is that it is that rate of exchange at which the consumer is just willing to stay put. Well, the market is offering a rate of exchange to the consumer of −p 1 /p 2 —if you give up one unit of good 1, you can buy p 1 /p 2 units of good 2. If the consumer is at a consumption bundle where he or she is willing to stay put, it must be one where the MRS is equal to this rate of exchange:

MRS = − p1 / p2

Another way to think about this is to imagine what would happen if the MRS were different from the price ratio. Suppose, for example, that the MRS is Δx2 / Δx1 = −1/2 and the price ratio is 1/1. Then this means the consumer is just willing to give up 2 units of good 1 in order to get 1 unit of good 2—but the market is willing to exchange them on a one-to-one basis. Thus the consumer would certainly be willing to give up some of good 1 in order to purchase a little more of good 2. Whenever the MRS is different from the price ratio, the consumer cannot be at his or her optimal choice.

Revealed preferences

In Chapter 6 we saw how we can use information about the consumer’s preferences and budget constraint to determine his or her demand. In this chapter we reverse this process and show how we can use information about the consumer’s demand to discover information about his or her preferences. Up until now, we were thinking about what preferences could tell us about people’s behavior. But in real life, preferences are not directly observable: we have to discover people’s preferences from observing their behavior. In this chapter we’ll develop some tools to do this. When we talk of determining people’s preferences from observing their behavior, we have to assume that the preferences will remain unchanged while we observe the behavior. Over very long time spans, this is not very reasonable. But for the monthly or quarterly time spans that economists usually deal with, it seems unlikely that a particular consumer’s tastes would change radically. Thus we will adopt a maintained hypothesis that the consumer’s preferences are stable over the time period for which we observe his or her choice behavior.

 

I have had several occasions to ask founders and participants in innovative start-ups a question: “To what extent will the outcome of your effort depend on what you do in your firm?” This is evidently an easy question; the answer comes quickly and in my small sample it has never been less than 80%. Even when they are not sure they will succeed, these bold people think their fate is almost entirely in their own hands. They are surely wrong: the outcome of a start-up depends as much on the achievements of its competitors and on changes in the market as on their own efforts‘ [Kahneman, 2011, p. 261]

Competition neglect – excess entry – optimistic martyrs / micro economics modeling

WYSIATI – what you see is all there is. The inclination of people to react to what is immediately at hand, observable, while neglecting any other information available requiring slightly more effort. Inward looking. Basis for micro-economic model?

Utility theory as p/ Bernouilli (wealth > utilty) is flawed because 1) reference point for initial wealth and change in wealth. Utility theory is also the basis for most of economic theory, p. 274-76. Harry Markowitz suggests to use changes of wealth instead p. 278.