Study Blue Suppose Bundles a and B Lie on the Same Indifference Curve

Module one: Preferences and Indifference Curves

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The Policy Question: Is a Tax Credit on Hybrid Car Purchases the Regime'southward Best Option to Reduce Fuel Consumption and Carbon Emissions?

The U.S. government, concerned virtually the dependence on imported foreign oil and the release of carbon into the atmosphere, has enacted policies where consumers tin can receive substantial tax credits toward the purchase of sure models of all-electric and hybrid cars.

This credit may seem like a practiced policy choice but information technology is a plush 1, information technology takes away resources that could be spent on other regime policies, and information technology is not the merely approach to decreasing carbon emissions and dependency on fossil fuels. And so how exercise we decide which policy is best?

Suppose that this tax credit is wildly successful and doubles the average fuel economy of all cars on U.S. roads (this is clearly not realistic just useful for our subsequent discussions). What do you lot think would happen to the fuel consumption of all U.S. motorists? Should the government expect fuel consumption and carbon emissions of U.S. cars to subtract by half in response?

The answers to these questions are disquisitional when choosing amidst the policy alternatives. In other words, is offering a subsidy to consumers the well-nigh effective style to run across the policy goals of decreased dependency on foreign oil and carbon emissions? Are there more efficient—that is, less expensive–ways to reach these goals? The ability to predict with some accuracy the response of consumers to this policy is vital to determining the merits of the policy before millions of federal dollars are spent.

Consumption decisions, such as how much automobile fuel to consume, come fundamentally frompreferences – our likes and dislikes. Human decision making, driven past our preferences, is at the cadre of economic theory. Since we tin't swallow everything our hearts desire, we have to make choices and those choices are based on our preferences. Choosing based on likes and dislikes does non mean that we are selfish–our preferences may include charitable giving and the happiness of others.

In this module, we will study preferences in economics.

1.one Key Assumptions about Individual Preferences

Learning Objective one.1: Listing and explicate the three fundamental assumptions about preferences.

1.2 Graphing Preferences with Indifference Curves

Learning Objective i.2: Define and draw an indifference curve.

ane.3 Properties of Indifference Curves

Learning Objective 1.three: Relate the backdrop of indifference curves to assumptions nearly preference

1.four Marginal Rate of Substitution

Learning Objective one.4: Define marginal rate of substitution.

1.5 Perfect Complements and Perfect Substitutes

Learning Objective 1.v: Use indifference curves to illustrate perfect complements and perfect substitutes.

i.6 Policy Example: The Hybrid Car Tax Credit and Consumer Preference

Learning Objective i.vi: Apply indifference curves to the policy of a hybrid motorcar taxation credit.

1.1 Fundamental Assumptions about Individual Preferences

Learning Objective i.one: List and explain the three primal assumptions nearly preferences.

To build a model that can predict choices when variables change, we need to make some assumptions nearly the preferences that drive consumer choices.

Economics makes three assumptions nearly preferences that are the near bones building blocks of our theory of consumer choice.

To introduce these it is useful to remember of collections or bundles of goods. To simplify, allow'southward place two bundles, A andB. The way we call up of preferences always boils downwards to comparing 2 bundles. Fifty-fifty if we are choosing among iii or more bundles, we can e'er proceed by comparing pairs and eliminating the bottom bundle until we are left with our choice.

When we telephone call something a good, nosotros mean exactly that – something that a consumer likes and enjoys consuming. Something that a consumer might not similar we call a bad. The fewer bads consumed, the happier a consumer is. To continue things unproblematic, nosotros will focus only on goods, merely it is easy to incorporate bads into the same framework by considering their absence – the fewer the bads the better.

The iii central assumptions nearly preferences are:

Completeness: We say preferences are complete when a consumer can always say 1 of the following about two bundles: A is preferred to B, B is preferred to A or A is equally good as B
Transitivity:We say preferences aretransitiveif they are internally consistent: if A is preferred to B and B is preferred to C, then it must be that A is preferred to C.
More is Better: If bundle A represents more of at least one adept, and no less of any other adept, than packet B, then A is preferred to B.

The most important results of our model of consumer beliefs concord when we only assume completeness and transitivity, merely life is much easier if we assume more than is better as well. If we assume free disposal (nosotros can become rid of extra goods at no cost) the supposition that more is meliorate seems reasonable. Information technology is certainly the case that more than is not worse in that situation and so to keep things simple we'll maintain the standard assumption that nosotros prefer more of a good to less.

Our model works well when these assumptions are valid, which seems to be most of the time in most situations. However, sometimes these assumptions do not use. For instance, in order to have consummate and transitive preferences, we must know something about the appurtenances in the bundle. Imagine an American who does not speak Hindi entering an Indian restaurant where the menu is entirely in Hindi. Without the help of translation, the client cannot act as economic theory would predict.

i.2 Graphing Preferences with Indifference Curves

Learning Objective 1.2: Define and draw an indifference curve.

Individual preferences, given the basic assumptions, can be represented using something called indifference curves. An indifference bendis a graph of all of the combinations of bundles that a consumer prefers as. In other words, the consumer would exist just as happy consuming whatever of them. Representing preferences graphically is a great way to empathise both preferences and how the consumer choice model works – so it is worth mastering them early on in your report of microeconomics.

Bundles can incorporate many appurtenances, but to simplify, we will consider but pairs of appurtenances. At kickoff, this may seem impossibly restrictive but it turns out that nosotros don't actually lose generality in and so doing. Nosotros can always consider one good in the pair to be, collectively, all other consumption appurtenances. What the 2-good restriction does and then well is to aid us come across the tradeoffs in consuming more of one good and less of another.

Figure 1.2.1Bundles and Indifference Curves

Figure one.2.one is a graph with ii goods on the axes: the weekly consumption of burritos and the weekly consumption of sandwiches for a college student. In the middle of the graph is signal A, which represents a package of both burritos (read from the horizontal centrality) and sandwiches (read from the vertical axis).

Now we can ask what bundles are meliorate, worse, or the same in terms of satisfaction to this college educatee. Conspicuously bundles that contain less of both appurtenances, like bundle D, are worse than A, B or C because they violate the more than is a better supposition. Equally articulate is that bundles that contain more than of both appurtenances, like parcel E, are improve than A, B, C, and D considering they satisfy the more is meliorate assumption.

To create an indifference curve we desire to identify bundles that this college educatee is indifferent about consuming. If a bundle has more than burritos the student would have to accept fewer sandwiches and vice versa. By finding all the bundles that are just as good as A, like B and C, and connecting them with a line, we create an indifference curvelike the 1 in the heart.

Notice that Effigy 1.2.i includes several indifference curves. Each curve represents a different level of overall satisfaction that the pupil tin achieve via burrito/sandwich bundles. A bend further out from the origin represents a higher level of satisfaction than a curve closer to the origin.

Notice also that these curves share a number of characteristics: they slope downward, they do not cantankerous and they are all bowed in. Nosotros explore these backdrop in more detail in the next section.

1.3 Properties of Indifference Curves

Learning Objective 1.3: Relate the properties of indifference curves to assumptions almost preference.

As introduced in Section 1.2, indifference curves accept three key properties:

they aredownward sloping
they do non cross
they are bowed in(a non-technical way of maxim they are convex to the origin).

For simplicity and clarity, from here on nosotros will draw preferences that lead to indifference curves with these three properties as standard preferences. This will be our default supposition – that consumers accept standard preferences unless otherwise noted. As we volition run across in this module, there are other types of preferences that are mutual as well and we will continue to study both the standard type and the other types as we progress through the material.

To understand the start two properties, it's useful to remember about what happen if they were not true.

Figure 1.3.1Upward Sloping Indifference Curves Violate the More-is-Better Assumption

Recollect about indifference curves that gradient upwards as in figure 1.3.1. In this instance nosotros accept two bundles on the same indifference curve, A and B only B has more of both burritos and sandwiches than does A. And then this violates the supposition of more is better. More is better implies indifference curves are downwards sloping.

Figure 1.three.2: Crossing Indifference Curves Violate the Transitivity Assumption

Similarly, consider Figure ane.3.ii. In this figure there are ii indifference curves that cross. Now consider packet A on one of the indifference curves. It represents more than of both goods than packet C that lies on the other indifference bend. Because the parcel B lies on the same indifference curve as bundle C the ii bundles should be equally preferred and therefore A should be preferred to B and C. B also represents more of both goods than bundle D and therefore B should be preferred to D. However D is on the same indifference curve every bit A, so B should exist preferred to A. Since A can't be preferred to B and B preferred to A at the same time, this is a violation of our assumptions of transitivity and more is better. Transitivity and more is ameliorate imply that indifference curves do not cross.

Now we come up to the third property: indifference curves bow in. This belongings comes from a fourth assumption almost preferences, which we can add together to the assumptions discussed in Section 1.1:

Consumers like variety.

The supposition that consumers prefer diversity is not necessary, but still applies in many situations. For example, virtually consumers would probably prefer to eat both sandwiches and burritos during a week and non just one or the other (remember this is for consumers who consider them both goods – who like them). In fact, if y'all had merely sandwiches to consume for a week, you'd probably be willing to requite upward a lot of sandwiches for a few burritos and vice versa. Whereas if you had reasonably equal amounts of both you'd exist willing to merchandise one for the other but at closer to 1 to 1 ratios. Observe that if we graph this we naturally get bowed in indifference curves, as shown in Figure 1.iii.3. Preference for variety implies indifference curves are bowed in.

Figure 1.3.3Preference for Variety Means that Indifference Curves are Bowed In.

Think these 3 primal points virtually preferences and indifference curves:

More is better implies indifference curves are downward sloping.
Transitivity and more is better imply indifference curves do not cross.
Preference for variety implies indifference curves are bowed in.

one.4 Marginal Rate of Substitution

Learning Objective 1.4: Define marginal rate of substitution.

From now on we will assume that consumers like multifariousness and that indifference curves are bowed in. However, it is worth considering examples on either extreme: perfect substitutes and perfect complements.

When nosotros move forth an indifference curve we can think of a consumer substituting 1 practiced for some other. Two bundles on the same indifference curve, which represent the same satisfaction from consumption, have i matter in common: they represent more of one good and less of the other. This makes sense given our assumption of 'more is amend'; if more of one good makes you better off, and so y'all must have less of the other practiced in order to maintain the same level of satisfaction.

In economics nosotros have a more technical way of expressing this tradeoff: the marginal rate of substitution. The marginal rate of substitution (MRS)is the corporeality of one practiced a consumer is willing to give up to get i more unit of another skillful and maintain the same level of satisfaction. This is 1 of the most important concepts in economics because it is critical to understanding consumer option.

Mathematically, nosotros express the marginal rate of substitution for two generic goods like this:

[latex]MRS=\frac{\Delta A}{\Delta B}[/latex]

where Δ indicates a alter in the quantity of the good.

In the case of our educatee consuming burritos and sandwiches, the expression would exist:

[latex]MRS=\frac{\Delta Sandwiches }{\Delta Burritos}[/latex]

For case suppose at his current consumption package, 5 burritos and iv sandwiches weekly, Luca is willing to give upward 2 burritos to become one more sandwich. Another style of saying the same matter is that Luca is indifferent between consuming five burritos and four sandwiches in a week or 3 burritos and 5 sandwiches in a week. The MRS for Luca at that point is:

[latex]MRS=\frac{\Delta Sandwiches }{\Delta Burritos}=\frac{-2}{1}=-2[/latex]

Note that the MRS is negative because it represents a tradeoff: more sandwiches for fewer burritos.

Figure 1.4.1 illustrates the marginal charge per unit of commutation for burritos and sandwiches graphically.

Figure one.4.1Marginal rate of substitution for burritos and sandwiches.

Detect that Figure 1.iv.ane illustrates a modify in the good on the vertical axis (sandwiches) over the change in the expert on the horizontal centrality (burritos). This is the aforementioned as maxim the rise over the run. From this discussion and graph, it should exist articulate that the MRS is same as the gradient of the indifference curve at any given point along it.

one.5 Perfect Complements and Perfect Substitutes

Learning Objective one.v: Utilise indifference curves to illustrate perfect complements and perfect substitutes.

We accept now studied the assumptions upon which our model of consumer behavior is built:

completeness
transitivity
more than is meliorate
honey of variety

Nosotros take likewise seen how these assumptions govern the backdrop of indifference curves.

It is worth taking a moment to recall most two other types of preference relations that are special cases merely not uncommon: perfect complements and perfect substitutes.

Perfect Complements

Perfect complementsare goods that consumers desire to consume but in fixed proportions.

Consider the example of an iPod Shuffle and earphones. An iPod Shuffle is useless without earphones and earphones are useless without an iPod Shuffle, but put them together and, voila, you lot have a portable stereo, which is worth quite a lot. An extra set of earphones doesn't increase the usefulness of the iPod and an extra iPod doesn't increment the usefulness of the earphones. Then these are things that we consume in a fixed proportion: one iPod goes with one fix of earphones. We telephone call such preference relations perfect complements.

Figure ane.v.1 illustrates the process of drawing indifference curves for perfect complements.

Figure 1.v.i: Indifference Curves for Goods that are Perfect Complements

In Figure i.5.1, when nosotros offset with a packet of 1 iPod and 1 set of earbuds (as in bundle A), what are the other bundles that are just as good to the consumer? Two sets of earbuds and one iPod is no better than 1 set of earbuds and one iPod, then bundle B lies on the aforementioned indifference bend. The same is true for two iPods and one set of earbuds, every bit in bundle C. From this case, we can see that indifference curves for perfect complements have correct angles.

Perfect Substitutes

Perfect substitutes are goods virtually which consumers are indifferent as to which to eat.

That is, 1 unit of measurement of ane expert is just as adept as one unit of measurement of another good. Both Morton and Diamond Crystal are brands of tabular array salt. For most consumers, a teaspoon of one table salt is just every bit good equally a teaspoon of the other regardless of the amount possessed by the consumer. Nosotros call goods like these perfect substitutes.

Drawing indifference curves for perfect substitutes is straightforward as shown in Effigy 1.five.ii.

Effigy 1.5.2: Indifference Curves for Goods that are Perfect Substitutes

Bundle A in Effigy one.five.two contains 5 teaspoons of each blazon of salt. This is simply equally good to the consumer equally a bundle with ten teaspoons of Morton salt and cypher teaspoons of Diamond Crystal as in bundle B. It is also just as good as the ten teaspoons of Diamond Crystal and zero teaspoons of Morton in package C.

You tin can think of perfect complements and perfect substitutes as polar extremes of preference relations. Figure 1.five.three shows how a typical indifference bend lies betwixt perfect complements and perfect substitutes. You should sympathize when graphically represented, that the indifference curve for well-behaved preferences lies between perfect complements and perfect substitutes.

Effigy 1.5.iii: The Relationship between Indifference Curves for Well Behaved Preferences and Perfect Complements and Substitutes

1.6 Policy Example: The Hybrid Car Tax Credit and Consumer Preference

Learning Objective i.half dozen: Apply indifference curves to the policy of a hybrid automobile tax credit

The issue of consumer preferences is central to the real-world policy question posed at the beginning of this module.

"Traffic jam" from Lynac on Flickr is licensed under CC BY-NC

Call up that we are assuming that the tax credit will crusade the boilerplate fuel economic system of U.S. cars to double. So, from a consumer behavior perspective, one of the things we desire to know in evaluating the policy is whether this improvement in gas mileage volition cause an equivalent decrease in the need for gasoline. In other words, the consumer decision is near the tradeoff of purchasing gasoline to travel in a car versus all of the other uses of the money spent on gas.

Nosotros can apply the principle of preferences and the assumptions nosotros make about them to this particular question by drawing indifference curves, equally shown in Figure 1.6.1

Figure i.6.1: Indifference Bend for Miles Drives versus Money Spent on All Other Goods

Nosotros can characterization one axis of the indifference curve map "miles driven" and the other "coin for other consumption." Doing so illustrates how confining ourselves to merely two dimensions is actually not that confining at all. By considering the other centrality equally coin for all other purchases nosotros are really looking at the general trade-off between one particular consumption good and everything else that a consumer could perhaps consume.

Then, what would our indifference curve look like? Equally before it would exist downward sloping – surely traveling more by car affords the consumer more freedom of movement and therefore more consumption choices, both of which are a good. The indifference curves would not cross for the same reasons discussed in section ane.iii. But what nigh the principle of more is better? The point here is to again remember near the principle of free disposal: equally long as the ability to drive more miles is not bad (and it is hard to imagine how it could be) then more than miles are never worse.

The remaining question is whether the preference for variety is a skillful assumption in this case. It is helpful to consider the extremes: for those consumers who ain cars, never driving any miles is probably non very applied. Likewise spending one'south entire income only on expenses relating to driving ane's car is unappealing. A good assumption, and then, is that near people with a motorcar would adopt some combination of miles driven and other consumption to either farthermost and we can draw our indifference curves every bit convex to the origin.

We are not yet in a position to say much about the policy itself, but nosotros have one slice of the model nosotros will employ to analyze information technology. With this indifference bend we tin movement on to the other pieces of the model that we will study in Modules 2, 3 and four.

Exploring the Policy Question

Suppose that a typical consumer is concerned virtually how his or her individual driving habits are negatively impacting the environment. How might such a alter in attitude modify the shape of the consumer'south indifference curves?

SUMMARY

Review: Topics and Related Learning Outcomes

one.1 Central Assumptions about Individual Preferences

Learning Objective 1.1: List and explain the 3 primal assumptions nearly preferences.

i.two Graphing Preferences with Indifference Curves

Learning Objective 1.2: Ascertain and draw an indifference curve.

1.iii Properties of Indifference Curves

Learning Objective one.3: Relate the properties of indifference curves to assumptions about preference.

1.4 Marginal Rate of Commutation

Learning Objective 1.iv: Define marginal charge per unit of substitution.

1.v Perfect Complements and Perfect Substitutes

Learning Objective ane.v: Employ indifference curves to illustrate perfect complements and perfect substitutes.

1.6 Policy Example: The Hybrid Machine Tax Credit and Consumer Preference

Learning Objective i.6: Apply indifference curves to the policy of a hybrid car taxation credit

Learn: Key Terms and Graphs

Terms

Completeness

Transitivity

More is better

Indifference bend

Marginal charge per unit of exchange (MRS)

Perfect complements

Perfect substitutes

Graphs

Indifference curve

Marginal charge per unit of commutation