Friday, October 21, 2005

Quality, Uncertainty and Market Mechanism - Part 2

The Model with Automobiles as an Example:
Suppose (for the sake of clarity rather than reality) that there are only four types of cars – new and used cars, good cars (creampuff) and bad cars (lemons). A new car may either be a good one or a bad one and the same is true for used cars too. The individuals in this market buy new cars without knowing whether the car they will buy is a creampuff or a lemon. Let us say that the probability of buying a new car that is also good is “q” and that of landing up with a lemon is “1-q”. “q” by assumption is the proportion of good cars produced and “1-q” is the proportion of lemons. After owing a specific car for certain duration of time, the owner has a good idea of its quality and assigns new probability to the event that the car is a lemon. Note that this estimate is more accurate than the previous one. An asymmetry in available information has now developed for the sellers have more information about the quality of the car than do the buyers. It is also clear that a used car cannot have the same valuation as that of a new car – if it did, it would be clearly advantageous to trade a lemon at the price of a new car and buy another new car, at a higher probability q of being good and a lower probability of being bad. Thus the owner of a good car is locked in and not only cannot he receive the true value of his car but cannot even obtain the expected value of a new car.
Thus, the bad cars drive out the good cars as most traded cars are lemons. This is analogous to the way “bad money drives out the good” as stated by Gresham’s law. Gresham’s Law is explained in simple terms over at the Wikipedia. For those Indians who are reading without clicking through to Wikipedia, let me give you a quick analogy to illustrate Gresham’s law – remember the times when all the currency notes that exchanged hands were soiled, torn notes and everybody, in spite of possessing good clean bills preferred to trade in the soiled ones? As this practice continued, all the notes that were traded in the market were soiled torn ones that actually had a lower value (on account of being torn, when one exchanges these notes at the bank one is left a little short of the face value of the turned in bill) but were traded at the same exchange rate as good clean bills were. If the picture is still not clear, then I advise you to click through to Wikipedia and go through the explanation.

Utility Theory: A Brief Introduction
[Source: Wikipedia]
In economics, utility is a measure of the happiness or satisfaction gained from a good or service. There are mainly two kinds of measurement of utility implemented by economists: cardinal utility and ordinal utility. Utility was originally viewed as a measurable quantity, so that it would be possible to measure the utility of each individual in the society with respect to each good available in the society, and to add these together to yield the total utility of all people with respect to all goods in the society. Society could then aim to maximize the total utility of all people in society, or equivalently the average utility per person. This conception of utility as a measurable quantity that could be aggregated across individuals is called cardinal utility. Cardinal utility quantitatively measures the preference of an individual towards a certain commodity. Numbers assigned to different goods or services can be compared. I would assign a utility of 100 to a glass of chilled beer in summer and desire it twice as much as a cup of steaming coca which I would assign a utility of 50. There is already an obvious disadvantage – that of comparing cardinal utilities across people. The concept of cardinal utility suffers from the absence of an objective measure of utility when comparing the utility gained from consumption of a particular good by one individual as opposed to another individual.
Another approach is based on preferences - an individual is observed to prefer one choice to another. Preferences can be ordered from most satisfying to least satisfying. Only the ordering is important: the magnitudes of the numerical values are not important except in as much as they establish the order. It is nonetheless possible, given a set of preferences which satisfy certain criteria of reasonableness, to find a utility function that will explain these preferences. Such a utility function takes on higher values for choices that the individual prefers. With this approach to utility, known as ordinal utility it is not possible to compare utility between individuals.
Let X be the consumption set, the set of all packages the consumer could conceivably consume. The consumer's utility function u: X-> R assigns a happiness score to each package in the consumption set. If u(x) > u(y), then the consumer strictly prefers x to y. In microeconomics models, there are usually a finite set of L commodities, and a consumer may consume an arbitrary amount of each commodity. This gives a consumption set of R_L and each package x Є R_L is a vector containing the amounts of each commodity. For u to be a utility function on X, it must be defined for every package in X. A von Neumann-Morgenstern utility function u: X -> R assigns a real number to every element of the outcome space in a way that captures the individual's preferences over both simple and compound events. The individual will prefer a lottery L1 to a lottery L2 if and only if the expected utility (iterated over compound lotteries if necessary) of L1 is greater than the expected utility of L2.

I’ll give you guys a couple of days for all this to sink in – it is a little heavy on the digestive system

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