Utility Assignment

8/10/2019 Utility Assignment

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Definition of Utility

Utility is a term used by economists to describe the measurement of "usefulness" that aconsumer obtains from any good. Utility may measure how much one enjoys a movie, or thesense of security one gets from buying a deadbolt. The utility of any object or circumstance canbe considered. Some examples include the utility from eating an apple, from living in a certain

house, from voting for a specific candidate, from having a given wireless phone plan. In fact,every decision that an individual makes in their daily life can be viewed as a comparisonbetween the utility gained from pursuing one option or another. Utility can be seen as a measureof how much one values a particular good. This depends entirely on the preferences of thatindividual, rather than some external, or universal measure. So while an apple and an orange maygive utility values of 5 and 10 respectively to one individual, they may give 1,250 and -180 toanother. These values depend only on how they are valued by the decision makers in each case.

Rationality and Utility

In economics, we usually say that an individual is "rational" if that individual maximizes utility

in their decisions. That is, whenever an individual is to choose between a groups of options, theyare rational if they choose the option that, all else equal, gives the greatest utility. Recalling thatutility includes every element of a decision, this assumption is not particularly difficult to accept.If, when everything is taken into account, one decision provides the greatest utility, which isequivalent to meaning that it is the most preferred, then we would expect the individual to takethat most preferred option. This should not necessarily be taken to mean that individuals who failto quantify and measure every decision they make are behaving irrationally. Rather, this meansthat a rational individual is one who always selects that option that they prefer the most.

The rationality assumption may seem trivial, but it is basic to the study of economics. Thisassumption gives a basis for modeling human behavior and decision making. If we could not

assume rationality, it would be impossible to say what, when presented with a set of choices, anindividual would select. The notion of rationality is therefore central to any understanding ofmicroeconomics.

Measurement

There are no real methods of measuring utility outside of a purely theoretical framework. Anoption giving 100 utils has no real interpretation, except that it is preferred to an option giving50, and is less preferred than an option giving 101. The numbers used to model utility are onlydetermined in the functional form of the model from which they result. It is meaningless, for

example, to ask "how much utility does this apple give you?" It could only be meaningful to ask,"Would you prefer an apple or an orange?" in any non-theoretical framework.

One way to measure utility is to give the utility a monetary value. For example, if I would pay 0.70 for a piece of cake, then we can say the utility is 0.70 If a piece of cake cost 70p, it would make sense to consume 2 pieces. The first piece gives 100p of utility > than the price of 70p. The second piece gives a utility equal to the price.


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It was recognized that utility could not be measured or observed directly, so insteadeconomists devised a way to infer underlying relative utilities from observed choice. These'revealed preferences', as they were named by Paul Samuelson, were revealed e.g. inpeople's willingness to pay:

Utility is taken to be correlative to Desire or Want. It has been already argued thatdesires cannot be measured directly, but only indirectly, by the outward phenomenato which they give rise: and that in those cases with which economics is chieflyconcerned the measure is found in the price which a person is willing to pay for thefulfilment or satisfaction of his desire.

Total Utility

If we could measure utility, total utility would be the number of units of utility that a consumergains from consuming a given quantity of a good, service, or activity during a particular time

period. The higher a consumers total utility, the greater that consumers level of satisfaction.

Panel (a) of Figure 7.1 "Total Utility and Marginal Utility Curves" shows the total utility Henry

Higgins obtains from attending movies. In drawing his total utility curve, we are imagining that

he can measure his total utility. The total utility curve shows that when Mr. Higgins attends no

movies during a month, his total utility from attending movies is zero. As he increases the

number of movies he sees, his total utility rises. When he consumes 1 movie, he obtains 36 units

of utility. When he consumes 4 movies, his total utility is 101. He achieves the maximum levelof utility possible, 115, by seeing 6 movies per month. Seeing a seventh movie adds nothing to

his total utility.

Figure 7.1 Total Utility and Marginal Utility Curves

Panel (a) shows Henry Higginss total utility curve for attending movies. It rises as the number

of movies increases, reaching a maximum of 115 units of utility at 6 movies per month. Marginal

utility is shown in Panel (b); it is the slope of the total utility curve. Because the slope of the totalutility curve declines as the number of movies increases, the marginal utility curve is downward

sloping.

Mr. Higginss total utility rises at a decreasing rate. The rate of increase is given by the slope of

the total utility curve, which is reported in Panel (a) of Figure 7.1 "Total Utility and Marginal

Utility Curves" as well. The slope of the curve between 0 movies and 1 movie is 36 because
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utility rises by this amount when Mr. Higgins sees his first movie in the month. It is 28 between

1 and 2 movies, 22 between 2 and 3, and so on. The slope between 6 and 7 movies is zero; the

total utility curve between these two quantities is horizontal.

Marginal Utility

The amount by which total utility rises with consumption of an additional unit of a good, service,

or activity, all other things unchanged, is marginal utility. The first movie Mr. Higgins sees

increases his total utility by 36 units. Hence, the marginal utility of the first movie is 36. The

second increases his total utility by 28 units; its marginal utility is 28. The seventh movie does

not increase his total utility; its marginal utility is zero. Notice that in the table marginal utility is

listed between the columns for total utility because, similar to other marginal concepts, marginal

utility is the change in utility as we go from one quantity to the next. Mr. Higginss marginal

utility curve is plotted in Panel (b) of Figure 7.1 "Total Utility and Marginal Utility Curves" The

values for marginal utility are plotted midway between the numbers of movies attended. The

marginal utility curve is downward sloping; it shows that Mr. Higginss marginal utility for

movies declines as he consumes more of them.

Mr. Higginss marginal utility frommovies is typical of all goods and services. Suppose that you

are really thirsty and you decide to consume a soft drink. Consuming the drink increases your

utility, probably by a lot. Suppose now you have another. That second drink probably increases

your utility by less than the first. A third would increase your utility by still less. This tendency

of marginal utility to decline beyond some level of consumption during a period is called the law

of diminishing marginal utility. This law implies that all goods and services eventually will have

downward-sloping marginal utility curves. It is the law that lies behind the negatively slopedmarginal benefit curve for consumer choices that we examined in the chapter on markets,

maximizers, and efficiency.

One way to think about this effect is to remember the last time you ate at an all you can eat

cafeteria-style restaurant. Did you eat only one type of food? Did you consume food without

limit? No, because of the law of diminishing marginal utility. As you consumed more of one

kind of food, its marginal utility fell. You reached a point at which the marginal utility of another

dish was greater, and you switched to that. Eventually, there was no food whose marginal utility

was great enough to make it worth eating, and you stopped.

What if the law of diminishing marginal utility did not hold? That is, what would life be like in a

world of constant or increasing marginal utility? In your mind go back to the cafeteria and

imagine that you have rather unusual preferences: Your favorite food is creamed spinach. You

start with that because its marginal utility is highest of all the choices before you in the cafeteria.


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As you eat more, however, its marginal utility does not fall; it remains higher than the marginal

utility of any other option. Unless eating more creamed spinach somehow increases your

marginal utility for some other food, you will eat only creamed spinach. And until you have

reached the limit of your bodys capacity (or the restaurant managers patience), you will not

stop. Failure of marginal utility to diminish would thus lead to extraordinary levels of

consumption of a single good to the exclusion of all others. Since we do not observe thathappening, it seems reasonable to assume that marginal utility falls beyond some level of

consumption.

Maximizing Utility

Economists assume that consumers behave in a manner consistent with the maximization of

utility. To see how consumers do that, we will put the marginal decision rule to work. First,

however, we must reckon with the fact that the ability of consumers to purchase goods and

services is limited by their budgets.

The Budget Constraint

The total utility curve in Figure 7.1 "Total Utility and Marginal Utility Curves" shows that Mr.

Higgins achieves the maximum total utility possible from movies when he sees six of them each

month. It is likely that his total utility curves for other goods and services will have much the

same shape, reaching a maximum at some level of consumption. We assume that the goal of each

consumer is to maximize total utility. Does that mean a person will consume each good at a level

that yields the maximum utility possible?

The answer, in general, is no. Our consumption choices are constrained by the income available

to us and by the prices we must pay. Suppose, for example, that Mr. Higgins can spend just $25

per month for entertainment and that the price of going to see a movie is $5. To achieve the

maximum total utility from movies, Mr. Higgins would have to exceed his entertainment budget.

Since we assume that he cannot do that, Mr. Higgins must arrange his consumption so that his

total expenditures do not exceed his budget constraint: a restriction that total spending cannot

exceed the budget available.

Suppose that in addition to movies, Mr. Higgins enjoys concerts, and the average price of a

concert ticket is $10. He must select the number of movies he sees and concerts he attends so

that his monthly spending on the two goods does not exceed his budget.

Individuals may, of course, choose to save or to borrow. When we allow this possibility, we

consider the budget constraint not just for a single period of time but for several periods. For


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example, economists often examine budget constraints over a consumers lifetime. A consumer

may in some years save for future consumption and in other years borrow on future income for

present consumption. Whatever the time period, a consumers spending will be constrained by

his or her budget.

To simplify our analysis, we shall assume that a consumers spending in any one period is based

on the budget available in that period. In this analysis consumers neither save nor borrow. We

could extend the analysis to cover several periods and generate the same basic results that we

shall establish using a single period. We will also carry out our analysis by looking at the

consumers choices about buying only two goods. Again, the analysis could be extended to cover

more goods and the basic results would still hold.

Marginal Utility Theory

Marginal Utility theory examines the increase in satisfaction consumers gain from consuming anextra unit of a good.

Utility is an idea that people get a certain level of satisfaction / happiness / utility fromconsuming goods and service.

This utility is not constant. Often we get diminishing marginal utility. The first piece ofchocolate cake gives more utility than the 7th piece.

Quantity (Q) Total Utility Marginal Utility

1 100 100

2 170 70

3 190 20

4 180 -110

5 140 -4

In the above example, total utility (190) is maximized after just three pieces of chocolate cake.


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Ordinal utilityFrom Wikipedia, the free encyclopedia

Ordinalutilitytheorystates that while theutilityof a particulargoodor service cannot bemeasured using a numerical scale bearing economic meaning in and of itself, pairs of alternativebundles (combinations) of goods can be ordered such that one is considered by an individual tobe worse than, equal to, or better than the other. This contrasts withcardinal utilitytheory, whichgenerally treats utility as something whose numerical value is meaningful in its own right. Theconcept was first introduced byParetoin 1906.[1]

Contents

1 Indifference curve mappings

2 Revealed preference 3 Ordinal utility functions

4 See also

5 References

6 External links

Indifference curve mappings

When a large number of bundles of goods are compared, the preferences of the individual can beseen. This information is usually put together on a graph called an indifference map. One ofthese is shown below:

Eachindifference curveis a set of points, each representing a combination of quantities of twogoods or services, all of which combinations the consumer is equally satisfied with. The further acurve is from the origin, the greater is the level of utility. The slope of the curve (the negative ofthemarginal rate of substitutionof X for Y) at any point shows the rate at which the individual iswilling to trade off good X against good Y maintaining the same level of utility. The curve isconvex to the origin as shown assuming the consumer has a diminishing marginal rate of
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substitution. It can be shown that consumer analysis with indifference curves (an ordinalapproach) gives the same results as that based oncardinal utilitytheoryi.e., consumers willconsume at the point where the marginal rate of substitution between any two goods equals theratio of the prices of those goods (the equi-marginal principle).

Cardinal utilityFrom Wikipedia, the free encyclopedia

A simple example of two cardinal utility functions of y=2x+3

Ineconomics,a cardinal utilityfunction or scale is a utility index that preservespreferenceorderings uniquely up to positiveaffine transformations.[1][2]Two utility indices are related by an

affine transformation if for every value of one index u, occurring at quantity of the

goods bundle being evaluated, the corresponding value of the other index vsatisfies arelationship of the form

,

for fixed constants aand b. Thus the utility functions themselves are related by

The two indices differ only with respect to scale and origin.[1]
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The idea of Cardinal utility is considered outdated except for specific contexts such asdecisionmaking under risk,utilitarian welfare evaluations,anddiscounted utilities for intertemporalevaluationswhere it is still applied.[3]Elsewhere, such as in generalconsumer theory,ordinalutilityis preferred.

Expected utility

The expected utility theory deals with the analysis of choices among risky projects with (possibly

multidimensional) outcomes.

The expected utility model was first proposed by Nicholas Bernoulli in 1713 and solved by

Daniel Bernoulli in 1738 as the St. Petersburg paradox. Bernoulli argued that the paradox could

be resolved if decision makers displayed risk aversion and argued for a logarithmic cardinal

utility function.

The first important use of the expected utility theory was that of John von Neumann and OskarMorgenstern who used the assumption of expected utility maximization in their formulation of

game theory. Utility as probability of success

Castagnoli and LiCalzi and Bordley and LiCalzi (2000) provided another interpretation for VonNeumann and Morgenstern's theory. Specifically for any utility function, there exists ahypothetical reference lottery with the utility of a lottery being its probability of performing noworse than the reference lottery. Suppose success is defined as getting an outcome no worse thanthe outcome of the reference lottery. Then this mathematical equivalence means that maximizingexpected utility is equivalent to maximizing the probability of success. In many contexts, thismakes the concept of utility easier to justify and to apply. For example, a firm's utility might bethe probability of meeting uncertain future customer expectations

Conclusion:

A consumer's utility is hard to measure. However, we can determine it indirectly with consumer

behavior theories, which assume that consumers will strive to maximize their utility. According

to Daniel Bernoulli, for the usual person, utility increased with wealth but at a decreasing rate.Since consumer demand for utilities does not change dramatically with a change in price, it can

considered as a tool to speculate demand. Utility concept has lot many criticisms too. But as

utility is directly related to consumers taste and satisfaction, this topic demands further research

and exploration.
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Utility Assignment