Budget Constraints

Dictionaries and internet sites conclude that the definition of budget constraints is the combination of goods or services that are purchased given current prices and income. Michael Baye, in his book, Managerial Economics and Business Strategy, defines this term as, “something that restricts consumer behavior by forcing the consumer to select a bundle of goods that is affordable.”(Baye,2009, p.123)

Consumers make choices about the quantity of goods and services to consume, alleging that their objective is to maximize total utility. In maximizing total utility, the consumer faces a number of constraints, the most important of which are the consumer’s income and the prices of goods and services that the consumer wishes to use. The consumer’s effort to maximize total utility, along with these constraints, is referred to as the consumer’s problem. The solution to the consumer’s problem, which entails decisions about how much the consumer will consume of a number of goods and services, is referred to as consumer equilibrium.

Consumer equilibrium is the point on a diagram where a consumer’s indifference curve (we will discuss this term later) meets their budget line. According to Dr. John B. Horowitz, “The equilibrium consumption bundle is the affordable bundle that yields the highest level of satisfaction.” This states that a consumer can purchase anything on or below the budget line that fits their consumption bundle and everything else is above the budget line is unattainable at the present time. An example of this is the diagram from Cliff Notes.com shown below.


Consumer Equilibrium, Changes in Prices

The consumer's choice of how much to consume of various goods depends on the prices of those goods. If prices change, the consumer's equilibrium choice will also change. To see how, consider again the example considered above where the consumer must decide how much to consume of goods 1 and 2. Suppose that the price of good 1 increases from $2 per unit to $3 per unit, while the price of good 2 remains unchanged at $1 per unit. Everything else remains the same; the consumer's budget is still $5, and the marginal utility that the consumer receives from each additional unit of goods 1 and 2 is unchanged. However, the ratio of the marginal utility of good 1 to the price of good 1 is now changed, due to the increase in the price of good 1. The new situation is reported in Table 1 .



TABLE 1

Illustration of Consumer Equilibrium. Price of good 1 = $3, Price of good 2 = $1, Budget = $5





Units of good 1

MU of good 1


MU/price of good 1


Units of good 2


MU of good 2


MU/price of good 2


1

24


8


1


9


9


2

18


6


2


8


8


3

12


4


3


5


5


4

6


2


4


1


1



The increase in the price of good 1 to $3 lowers the marginal utility per dollar spent on good 1 relative to the case where the price of good 1 was $2. The new consumer equilibrium is found as before, by comparing the marginal utility per dollar spent on good 1 with the marginal utility per dollar spent on good 2. The consumer's new equilibrium choice is to consume 1 unit of good 1 and 2 units of good 2 because these quantities have the same marginal utility per dollar spent, and the purchase of these quantities completely exhausts the consumer's budget of $5.

Indifference Curves

What is an indifference curve? Stated above, it says that an indifference curve is a curve in a diagram that shows where a person is apathetic or indifferent about one bundle of goods to another. This means that at each point on the curve, the consumer does not have a preference on which bundle they will choose. This is where it can be said that each point on the curve has the same amount of utility as any other point on the curve. Utility is the same as saying satisfaction. Anything inside the curve is considered insufficient or inferior and anything outside the curve is considered to be preferred to any point on the curve. In the following diagram, and example of an indifference curve is shown and is explained in great detail.

Suppose Ms. Bain spends 2 days skiing and 3 days horseback riding per semester. She will derive some level of total utility from that combination of the two activities. There are other combination's of the two activities that would yield the same level of total utility. Combination's of two goods that yield equal levels of utility are shown on an indifference curve.[1] Because all points along an indifference curve generate the same level of utility, economists say that a consumer is indifferent between them.

Figure 2, “An Indifference Curve” shows an indifference curve for combination's of skiing and horseback riding that yield the same level of total utility. Point X marks Ms. Bain's initial combination of 2 days skiing and 3 days horseback riding per semester. The indifference curve shows that she could obtain the same level of utility by moving to point W, skiing for 7 days and going horseback riding for 1 day. She could also get the same level of utility at point Y, skiing just 1 day and spending 5 days horseback riding. Ms. Bain is indifferent among combination's W, X, and Y. We assume that the two goods are divisible, so she is indifferent between any two points along an indifference curve.

Figure 2. An Indifference Curve

Indifference_Curve.jpg

Now look at point T in Figure 2, “An Indifference Curve”. It has the same amount of skiing as point X, but fewer days are spent horseback riding. Ms. Bain would thus prefer point X to point T. Similarly, she prefers X to U. What about a choice between the combinations at point W and point T? Because, combination's X and W are equally satisfactory, and because Ms. Bain prefers X to T, she must prefer W to T. In general, any combination of two goods that lies below and to the left of an indifference curve for those goods yields less utility than any combination on the indifference curve. Such combination's are inferior to combination's on the indifference curve.

Point Z, with 3 days of skiing and 4 days of horseback riding, provides more of both activities than point X; Z therefore yields a higher level of utility. It is also superior to point W. In general, any combination that lies above and to the right of an indifference curve is preferred to any point on the indifference curve.
We can draw an indifference curve through any combination of two goods. Figure 3, “Indifference Curves” shows indifference curves drawn through each of the points we have discussed. Indifference curve A from Figure 2, “An Indifference Curve” is inferior to indifference curve B. Ms. Bain prefers all the combination's on indifference curve B to those on curve A, and she regards each of the combination's on indifference curve C as inferior to those on curves AB.


Figure 3. Indifference Curves

ch07_e8.jpg

Another term that needs to be defined is that of Marginal Rate of Substitution. This is the rate at which a consumer will give up one good for another but still keep the same level of satisfaction or utility. This term also refers to the absolute value of the slope of an indifference curve. The slope declines as you move down an indifference curve causing it to be convex to the origin. An example of this would be when a family goes on a picnic and has hotdogs and hamburgers. The marginal rate of substitution is 3 hotdogs for every hamburger. This means that someone is willing to give up 3 more hamburgers for 1 extra hotdog. The MRS is the opportunity cost of giving up one item for another.

Transitivity


In mathematics, the theory of transitivity states that if A is relative to B, and B is relative to C, then A has to be relative to C. In economics, transitivity has the same concept. The principle of transitivity is that if A is greater than B, and B is greater than C, then A is greater than C. According to Alyssa Kneller,” Transitivity is the hallmark of rational economic choice,” says Camillo Padoa-Schioppa, a postdoctoral researcher in the lab of Harvard Medical School(HMS) Professor of Neurobiology John Assad. According to transitivity, if you prefer A to B and B to C, then you ought to prefer A to C. Or, if you prefer lobster to steak, and steak to salmon, then you will prefer lobster to salmon.(Kneller, 2007, Harvard Science)


external image Figure8.3.gif
In this graph, a >c, c>b, so a >b. In this graph, ‘a’ has more of both Good A and B then ‘c’ has, and ‘c’ has less of Good A but more of Good B than ‘b’ has. So this being said, ‘a’ is better off than ‘c’ and ‘b’.

Completeness Property
This property states that when assuming that the preferences of consumers are complete, we should assume that the consumer is capable of expressing a preference for or indifferent among all bundles. (Baye, 2009, p. 119)
217px-Simple-indifference-curves.svg.png
The consumer will prefer B to A or C, but will be indifferent between A or C since they are on the same indifference curve.

More is Better Property
This means just as it sounds. When you have two bundles of goods C and D, the More is Better Property states that if bundle C has at least as much of every good and more of one good than D, than C is preferred to D. This property could also be thought of as “goods” vs. “bads”. If there are more goods in one bundle than another, then pick the bundle that has more goods.

Diminishing Marginal Utility
As was stated earlier, utility means satisfaction. From looking at the name, Diminishing Marginal Utility sounds like it should mean the point where the satisfaction of one good lowers as a person gains more and more of that same good. Horowitz, List, and McConnel state in their article called, “A Test of Diminishing Marginal Value,” “ The assumption that having more of a good will lead an individual to place a lower value on an additional unit of that good, which we call diminishing marginal value, is a pervasive component of economists’ beliefs about human behaviour.”(Horowitz, 2007, p.650)

Here is an example of this principle:


A Few Numbers

Roller Coaster Utility

Marginal Utility
Marginal Utility

To illustrate this highly useful law, take a gander at the table presented to the right. The story behind the table is this: Edgar Millbottom, Shady Valley's most devoted roller coaster devotee, has spent the day riding the Monster Loop Death Plunge roller coaster at the Shady Valley Amusement Park. After each ride, he is hooked up to a hypothetical "utilnometer" to measure his total utility from all rides, and most important to this discussion, his marginal utility from each additional ride.

As such, Edgar's first ride generates an extra 11 utils of satisfaction, the second ride provides an extra 9 utils, the third ride comes in with an extra 7 utils, and so forth. The declining marginal utility numbers--11, 9, 7, etc.--illustrate the law of diminishing marginal utility. Each additional ride generates less extra utility than the previous one. In fact, marginal utility continues to decline until the seventh and eighth rides generate negative marginal utilities. Edgar is less satisfied, in total, after 7 rides than after 6 rides.


This principle is an important part of economics, because it shows the demand price that a consumer is willing and able to pay, based on its utility. “Given the choice, people will satisfy their highest values first. This leads to the concept of diminishing marginal utility. Since people satisfy their highest values first, each subsequent unit of a good will be put to a lower-valued use.”(Koch, 2007,p.34)

When finished reading through this article, one should be able to decipher the difference between the terms: budget constraint, indifference curves, transitivity, more-is-better, completeness, consumer equilibrium, and diminishing marginal utility. This article should of provided the basic knowledge of what each term meant and gave an example of how each term is used. Examples have been provided from various sources to help strengthen the knowledge that one should have received from reading through the article. So, do you think you know enough about this part of Economics? I hope so! Here are a few review questions that hopefully you can answer.


1) If A>C, B>A, using the transitivity property, which of the following is correct:
a. C>B
b. B>C
c. B=C
d. Not enough information

Answer: b.) C>B is not correct because A>C and B>A, B=C is not correct because they cannot be equal because they would both be larger or smaller than A, and we have enough information to know that b.) is the right answer, so d.) is wrong also.

2) The point on a diagram where the indifference curve meets the budget line is known as?
a. Budget Constraint
b. Diminishing Marginal Utility
c. Marginal Rate of Substitution
d. Consumer Equilibrium

Answer: d.) Budget constraint restricts consumer behavior to select an affordable bundle. Diminishing marginal utility is where a consumer gets more of a good and places less of a value on the next unit of that good, and marginal rate of substitution is the rate at which a consumer is willing to substitute one good for another good without losing any satisfaction.

3) Which of the following is not an important constraint that consumers face while maximizing their total utility?
a. Consumer income
b. Price of goods consumers wants to consume
c. Prices of services consumers want to consume
d. None of the above

Answer: d.) All of them are important

4) In comparison to an indifference curve, where is the ideal place to be?
a. Inside the curve
b. On the curve
c. Outside the curve
d. Both A & B

Answer:
c.) Inside the curve is inferior to on or outside the curve, on the curve is not as good as being outside the curve, and being outside the curve is better than being on the curve, so outside the curve is the ideal spot.

5) The rate at which a consumer is willing to substitute one good for another good and still maintain the same level of satisfaction is known as?
a. Marginal Rate of Substitution
b. Consumer Equilibrium
c. Market Rate of Substitution
d. More is Better

Answer:
a.) Consumer equilibrium is the point where the indifference curve and the budget line meet. The market rate of substitution is slope of the budget line, and more is better is where one bundle has at least as much of every good as another bundle and has more than the other bundle in at least one good. So that leaves us with Marginal Rate of Substitution.

6) In Figure 3, which point would be the most beneficial to a consumer?
a. Point X
b. Point S
c. Point Z
d. Point V

Answer: c.) Point X,S, and V are insufficient because Curve B is the best and Point Z is the only point on this curve.



References

Baye, Michael. (2009). Managerial Economics and Business Strategy. (6th Edition) New York, NY: McGraw Hill.



CliffsNotes.com. Consumer Equilibrium, Changes in Prices. Retrieved 20 Mar 2009 from
<http:/www.cliffsnotes.com/WileyCDA/CliffsReviewTopic/topicArticleId-9789,articleId-9754.html|>



Horowitz, Dr. John B. (2009, January 26th). Chapter 4 Budget Constraints. Presented at a MBA 651 Class at Ball State University


Horowitz, List, McConnell. A Test of Diminishing Marginal Value. Economica. Retrieved 21 March, 2009 from
<
http://web.ebscohost.com.proxy.bsu.edu/ehost/detail?vid=4&hid=8&sid=81e6e3d7-d8ad-4090-bb67-815143e0ef65%40SRCSM1&bdata=JnNpdGU9ZWhvc3QtbGl2ZQ%3d%3d#db=buh&AN=27091927>


Kneller, Alyssa. Transitivity, the orbitofrontal cortex, and neuroeconomics. Harvard Science. Retrieved 20 March, 2009 from < http://www.harvardscience.harvard.edu/foundations/articles/transitivity-orbitofrontal-cortex-and-neuroeconomics>



Koch, Charles G.(2007) The Science of Success : How Market-Based Management Built the World’s Largest Private Company. Hoboken: John Wiley & Sons, Inc.


LAW OF DIMINISHING MARGINAL UTILITY. AmosWEB Encyclonomic WEB*pedia, Retrieved: March 21, 2009
< http://www.amosweb.com/cgi-bin/awb_nav.pl?s=wpd&c=dsp&k=law+of+diminishing+marginal+utility>


Rittenberg, and Tregarthen. Principles of Microeconomics. 1969 . Flat World Knowledge. Retrieved 20 Mar, 2009.
<http://www.flatworldknowledge.com/node/49> .