Marginal Utility

[Nolan]

Can someone explain it please?

[LeftSideDown]

Can someone explain it please?

Taken from Think Blue:

That marginal utility can actually increase brings about an important distinction between the Neoclassical and the Austrian understanding on utility.

From the Austrian perspective, utility is stated in terms of means to ends. For example, let's say a man is imprisoned in a tower. He wants to escape from the prison. To help him escape, he plans to construct a rope from blankets and climb down from the window. Because the blankets are necessary material for the rope, and ultimately his escape, the blankets have utility. No escape plan, means the rope is not needed, and no rope means the blankets have no utility, at least for that particular purpose.

Let's say the man needs five blankets to construct the rope. Less than five blankets, and he cannot construct the rope. Instead of five, the man has only four blankets available. Those four blankets are completely worthless for his escape, no usefulness whatsoever, and thus have no utility.

But is it really true the blankets have absolutely no utility? If the man has another end for the blankets, such as to stay warm, then the blankets do have utility, but to a lesser degree. In the Austrian view, utility is a matter of preference, such as he can rank ends from more preferred to less preferred such as:

1st. Escape from the prison
2nd. Keep comfortable in the prison

He would rather suffer in the cold and escape than stay warm in the prison. But since he has only four blankets available, he makes best use of them. His urgent need is warmth, so he uses the first blanket to cover himself. His next urgent need is something for his head, so he rolls the blanket as a pillow, and so on. Even though each blanket increases his level of comfort, each blanket has diminishing marginal utility because each additional blanket meets a less urgent need.

Let's say somebody from the outside smuggles in another blanket. He has now five blankets to construct his rope. He has a chance to meet his highest preference, escape from the prison.

Here is where the disagreement between the Neoclassical and the Austrian becomes apparent. For the Neoclassical, the fifth blanket is more valuable than the fourth blanket, and thus has increasing marginal utility, because without the fifth blanket, the rope would never be constructed. For the Austrian, the relative value between the fifth and fourth blanket is not very meaningful, since without the fifth blanket, the fourth blanket would be worthless for the highest possible end.

Is there really a marginal utility increase between the fifth and fourth blanket?

Marginal utility implies that removal of the last item should not affect the utility of the previous items. Else if the previous items were affected, then marginal utility analysis is not valid.

Let's suppose there is no escape plan, and the man's highest end is comfort in prison. Both Neoclassical and Austrian will agree that the fifth blanket is less valuable than the fourth blanket. Let's assume a guard barges in and takes away the last blanket. Even though the there is one less blanket, the marginal utility of the fourth blanket should neither increase nor decrease because of the presence or absense of the fifth blanket. In other words, the value of the previous items are preserved.

This proves that marginal utility exists for the blankets.

Let's suppose the escape plan is the man's only exclusive end, and that he has no need for prison comforts. Then it's either all or nothing. Either he has has all five blanket to complete the rope, or the blankets will be completely worthless. If a guard barges in and takes away the fifth blanket, then the value of the four remaining blankets is destroyed.

This proves that marginal utility is not valid for the blankets.

But a Neoclassical will counter that the existence of a less preferred alternative (for warmth, sleeping, etc.) will provide the remaining four blankets some value. Removal of the fifth blanket would not necessarily destroy value. Thus there is indeed marginal utility for the fifth and fourth blankets.

However an Austrian would respond back saying the real comparison should be for all five blankets, not just the fifth and fourth blanket. Either all five blankets are used for the less preferred end (prison comfort) or all five blankets are used for the more preferred end (prison escape).

Here is where the Neoclassical model breaks down. For marginal utility to be valid, the existence of an additional item presumes that the previous items are still available to meet the previous needs. In other words, the first blanket must be always available to meet the man's need for warmth at all times. But because the man must make an allocation decision, the moment he constructs a rope, he would deprive himself the warmth of the blanket. Either the first blanket is for the rope, or the first blanket is to keep him warm. He cannot have it both ways.

Furthermore, if the first blanket is reallocated from a less preferred end (warmth) to a more preferred end (escape), then by definition the utility of the first blanket has increased. This is also true for the remaining blankets, as the utility of each blanket increases from a less preferred to more preferred end.

The problem with the Neoclassical conception is that it assumes the previous four blankets are still servicing the less preferred end (prison comfort), while at the same time servicing the more preferred end (prison escape). From the Austrian perspective, all five blankets services the same greater end, at the exclusion of the lesser end, thus all five blankets have higher utility.

If the Neoclassical insists that the fifth blanket has an increasing marginal utility, then the Austrian can counter that the first to fourth blankets must have increasing utility as well!!

In conclusion, the Neoclassical makes two fundamental errors in the marginal utility analysis:

1. The Nth good has no affect on the utility of the (Nth - 1) good.
2. The 1 to (Nth - 1) good are still servicing the lower utility preference.

It was in response to a question concerning a teacher who didn't believe in DMU (Diminishing Marginal Utility) but it also sums up marginal utility pretty well.

[inyourhouse]

Can someone explain it please?

Marginal utility simply refers to the increase in utility brought about by an additional unit of a good, all other things the same. For example, suppose a consumer has a utility function for some good, x, that can be characterized as UX = sqrt(x). The marginal utility of the good is simply the derivative of the utility function, dUX/dx = 1/(2*sqrt[x]). I used sqrt(x) in that particular example because it illustrates the law of diminishing marginal utility: every additional unit of a good will bring about a smaller increase in utility than the last unit, all other things the same.

The concept of marginal utility is central to modern consumer theory (the broader concept of marginalism is central to modern economics as a whole). For example, a consumer's utility maximizing consumption basket with two goods is the point at which one of their indifference curves is tangent to their budget constraint. This might sound complicated, but it boils down to the fact that a consumer's optimal consumption basket with two goods is where the ratio of the marginal utilities of the two goods is equal to the ratio of the prices of those goods. In other words, for two goods, x and y, the optimum basket is where MUX/MUY = PX/PY. Theories like this allow economists to analyze the effects of, say, vouchers on consumption.

[mikelepore]

Marginal utility is a theory proposed by William Stanley Jevons in his book "The Theory of Political Economy", 1871. The book is online at

http://www.econlib.org/library/YPDBooks/Jevons/jvnPE.html

Jevons says he wants to make an economic theory that is scientific, and to be scientific it has to be mathematical, but the data he's going to work with consists of "feelings of the mind", "pleasure" and "pain", etc. Just how scientific that project is going to be, judge for yourself.

-------------

"It is clear that Economics, if it is to be a science at all, must
be a mathematical science. There exists much prejudice against
attempts to introduce the methods and language of mathematics into
any branch of the moral sciences. Many persons seem to think that
the physical sciences form the proper sphere of mathematical
method, and that the moral sciences demand some other method, -- I
know not what. My theory of Economics, however, is purely
mathematical in character."

Chapter I, Introduction, section I.4

"Many will object, no doubt, that the notions which we treat in
this science are incapable of any measurement. We cannot weigh,
nor gauge, nor test the feelings of the mind; there is no unit of
labour, or suffering, or enjoyment. It might thus seem as if a
mathematical theory of Economics would be necessarily deprived for
ever of numerical data."

Chapter I, Introduction, section I.10

"Now there can be no doubt that pleasure, pain, labour, utility,
value, wealth, money, capital, etc., are all notions admitting of
quantity; nay, the whole of our actions in industry and trade
certainly depend upon comparing quantities of advantage or
disadvantage. Even the theories of moralists have recognised the
quantitative character of the subject. Bentham's Introduction to
the Principles of Morals and Legislation is thoroughly
mathematical in the character of the method. He tells us to
estimate the tendency of an action thus: 'Sum up all the values of
all the pleasures on the one side, and those of all the pains on
the other.....'"

Chapter I, Introduction, section I.14

"'But where,' the reader will perhaps ask, 'are your numerical
data for estimating pleasures and pains in Political Economy?' I
answer, that my numerical data are more abundant and precise than
those possessed by any other science, but that we have not yet
known how to employ them. The very abundance of our data is
perplexing."

Chapter I, Introduction, section I.15

[Left-Reasoning]

Marginal utility is a theory proposed by William Stanley Jevons in his book "The Theory of Political Economy", 1871. The book is online at

http://www.econlib.org/library/YPDBooks/Jevons/jvnPE.html

Jevons says he wants to make an economic theory that is scientific, and to be scientific it has to be mathematical, but the data he's going to work with consists of "feelings of the mind", "pleasure" and "pain", etc. Just how scientific that project is going to be, judge for yourself.

That's not what marginalism is though.

[Left-Reasoning]

"In economics (http://en.wikipedia.org/wiki/Economics), the marginal utility of a good (http://en.wikipedia.org/wiki/Good_%28economics%29) or service (http://en.wikipedia.org/wiki/Service_%28economics%29) is the utility (http://en.wikipedia.org/wiki/Utility) gained (or lost) from an increase (or decrease) in the consumption (http://en.wikipedia.org/wiki/Consumption) of that good or service. In general, preferences display diminishing marginal utility (http://en.wikipedia.org/wiki/Diminishing_returns). That is, the first unit of consumption of a good or service yields more utility than the second and subsequent units. The concept of marginal utility played a crucial role in the marginal revolution (http://en.wikipedia.org/wiki/Marginal_revolution) of the late 19th century, and led to the replacement of the labor theory of value (http://en.wikipedia.org/wiki/Labor_theory_of_value) by neoclassical (http://en.wikipedia.org/wiki/Neoclassical_economics) value theory (http://en.wikipedia.org/wiki/Value_theory) in which the relative prices (http://en.wikipedia.org/wiki/Relative_prices) of goods and services are simultaneously determined by marginal rates of substitution (http://en.wikipedia.org/wiki/Marginal_rate_of_substitution) in consumption and marginal rates of transformation (http://en.wikipedia.org/wiki/Marginal_rate_of_transformation) in production, which are equal in economic equilibrium (http://en.wikipedia.org/wiki/Economic_equilibrium)." - Wikipedia[1]

[1] http://en.wikipedia.org/wiki/Marginal_utility

[mikelepore]

I understand the concept "marginal", that is, it's not about utility U, but rather dU/dx. Can someone please explain to me how this sheds any light on economic value, which is about relationships among tangible numbers? Suppose a pair of shoes exchanges for 50 loaves of bread, but a new car exchanges for 10,000 loaves of bread. These ratios are hard numbers, you can look them up in an almanac, they are not my mental patterns when I go shopping. How does any reference to utility generate actual numbers? In Marx's approach, value is linked to the manufacturing process, real numbers arising out of real numbers.

[LeftSideDown]

I understand the concept "marginal", that is, it's not about utility U, but rather dU/dx. Can someone please explain to me how this sheds any light on economic value, which is about relationships among tangible numbers? Suppose a pair of shoes exchanges for 50 loaves of bread, but a new car exchanges for 10,000 loaves of bread. These ratios are hard numbers, you can look them up in an almanac, they are not my mental patterns when I go shopping. How does any reference to utility generate actual numbers? In Marx's approach, value is linked to the manufacturing process, real numbers arising out of real numbers.

There are no actual numbers in utility. Subjective values are ordinal. I can say I prefer on apple to one orange but I cannot say that an apple has so-and-so many more units of utility than one orange. Nor can you make interpersonal comparisons of utility. Preference scales of individuals only give ordinal rankings.

[Left-Reasoning]

Can someone please explain to me how this sheds any light on economic value, which is about relationships among tangible numbers?

The economic value, or price, of a good most certainly has a relationship with the utility that the good provides.


Suppose a pair of shoes exchanges for 50 loaves of bread, but a new car exchanges for 10,000 loaves of bread. These ratios are hard numbers, you can look them up in an almanac, they are not my mental patterns when I go shopping. How does any reference to utility generate actual numbers?

Firstly, economics is not a quantitative science.

However, if an individual prefers a car to $1000 and has $1000 and another individual prefers $1000 to a car and has a car then a mutually beneficial exchange is possible.

[inyourhouse]

I understand the concept "marginal", that is, it's not about utility U, but rather dU/dx. Can someone please explain to me how this sheds any light on economic value, which is about relationships among tangible numbers? Suppose a pair of shoes exchanges for 50 loaves of bread, but a new car exchanges for 10,000 loaves of bread. These ratios are hard numbers, you can look them up in an almanac, they are not my mental patterns when I go shopping. How does any reference to utility generate actual numbers? In Marx's approach, value is linked to the manufacturing process, real numbers arising out of real numbers.

I'll try to give a quick overview, but the concepts involved tend to be quite difficult to grasp at first. Let's assume there are two goods: food (f) and clothing (c). Suppose a consumer's utility function for these goods can be expressed as Uf,c = f*c. The marginal utility of food is the partial derivative of that function with respect to f (holding c constant); ie. MUf = c. Similarly, the marginal utility of clothing is the partial derivative of that function with respect to c (holding f constant), so MUc = f. Of course, a consumer does not actually use a utility function to work out what they consume, but they are able to evaluate various bundles of goods, so we can just use a mathematical function as a representation of that.

Now, I mentioned earlier the concept of indifference curves. An indifference curve represents all the combinations of the two goods that give the same total utility. For example, the indifference curve U = 15 shows all the bundles of goods for which total utility is equal to 15. Using our utility function above, that would include {f = 1, c = 15}, {f = 3, c = 5}, etc. Again, a consumer does not actually work out the quantitative level of utility in their head, but they do have some idea of how much of one good they'd be willing to replace with the other good without being worse off. In an advanced economics course you see the concept of indifference curves derived from purely ordinal rankings, but cardinal rankings are easier for a simple exposition of the main concepts. Here is a generic illustration of indifference curves I just found online: cdc.gov/owcd/EET/CBA/images/CBA_indif.gif

Another key concept is the consumer's budget constraint, which simply means that a consumer is only able to select from combinations of those goods that they can afford. For the sake of simplicity, let's assume that the consumer wants to spend all of their income (I) on these goods. That means that their total expenditure on food (price of food times units of food) plus their total expenditure on clothing (price of clothing times units of clothing) will be equal to their income. In other words, I = Pf*f + Pc*c. For example, the budget line for a consumer with an income of $20, where the price of a unit of food is $2 and where the price of a unit of clothing is $4, includes {f = 2, c = 4}, {f = 4, c = 3}, etc. Here's a generic illustration of a budget constraint: phoenix.liu.edu/~tbarr/eco61/chapter3/budget-line.png

Now, we can combine these concepts to find a consumer's optimum consumption basket. Note that on the indifference curve diagram, the further from the origin the curve is, the higher the overall level of utility is. Ergo, to maximize their utility, consumers will want to choose a combination on their highest indifference curve. However, remember that they are constrained by their budget constraint, so they will have to pick the indifference curve that is highest whilst still touching the budget constraint. This occurs with the indifference curve that is tangent to the budget line - that is, where the slope of the indifference curve is equal to the slope of the budget line. You can see this in this generic illustration: all-science-fair-projects.com/science_fair_projects_encyclopedia/upload/c/cf/Consumer_constraint_choice_income_shift.png

Mathematically, the slope of the indifference curve is the marginal utility of food over the marginal utility of clothing (ie. MUf/MUc) and the slope of the budget line is the price of food over the price of clothing (ie. Pf/Pc). Thus the optimum basket is where MUf/MUc = Pf/Pc. For our utility function, MUf = c and MUc = f, so taking Pf as $2 and Pc as $4, we can say that c/f = 2/4. That simplifies to f = 2c, which means that the consumers optimum basket will involve twice as many units of food as clothing. So, putting this into the budget constraint above for an income of $20, we get 20 = 2*(2c) + 4*c. This simplifies to 8c = 20, so the consumer will buy 2.5 units of clothing, and from our equation f = 2c, they will buy 5 units of food. That is their optimum basket.

Now, that was very specific, but we can generalize it for our given utility function of Uf,c = f*c. The optimum basket occurs where MUf/MUc = Pf/Pc, so for any price of food or clothing, c/f = Pf/Pc. This rearranges to c = f*(Pf/Pc), so given a general budget constraint of I = Pf*f + Pc*c, we can substitute that into it. That gives I = Pf*f + Pc*f*(Pf/Pc), which simplifies to I = 2*Pf*f, or f = I/(2*Pf). That last equation is the consumers demand curve for food given our utility function. As you may know, the market demand curve is the sum of all consumer demand curves. A similar analysis can be done on the supply side to produce firm supply curves and market supply curve. Overall, in equilibrium the price of food will be where the market demand curve and market supply curve intersect.

The production side is too long to go into here, but I hope you can see how prices are (partially) determined by marginal utility. And remember that we've only assumed that utility is cardinal (ie. quantifiable) here for the sake of simplicity; economists like Paul Samuelson used much more complicated mathematics to derive these theories with purely ordinal utility (ie. the consumer can only rank baskets, without assigning any specific level of utility to them). By the way, I apologize if I've not explained this very clearly - it's been a while since I went over this stuff.