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Our next task in this lesson is to formulate and

solve the consumer's optimization problem using Utility Theory.

That sounds pretty technical and complicated but

all we are saying is that given the money they have in their pockets,

consumers are going to find the best way to spend it, that's optimizing behavior.

[SOUND] In fact, this is another key assumption that drives much of economics.

The assumption that all economic agents optimize something as

a way to explaining their behavior.

For example, firms typically assume to maximize profits.

In the consumers case we assume that consumers maximize utility,

subject to a budget or income constraint.

In plain terms this means that consumers have a certain amount of income to spend.

And given that budget constraint and a menu of prices, they will choose a market

basket of goods and we'll provide them with the greatest utility or satisfaction.

The question of course is how do consumers do this?

And the answer lies in a key concept called the Utility Maximizing Rule,

or Equimarginal Principle.

According to the Equimarginal Principle, the consumer, with a fixed income,

facing market prices, will achieve maximum satisfaction when

the marginal utility of the last dollar spent on each good is exactly

the same as the marginal utility and the last dollar spent on any other good.

To put this another way, if I obey the Equimarginal Principle and

therefore maximize my satisfaction,

I will be sure that every single good in my market basket will bring

me the same marginal utility per dollar of expenditure.

As to why I'm bothering you with what would appear to be a rather obscure and

technical idea, it's really very simple.

The Equimarginal Principle is actually the magic tool that lets us derive

a downward sloping demand curve.

And thereby gain further marketing insight into the mysteries of the consumer's mind.

Let me show you what I mean now with this example.

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To begin our example, let's introduce Luis Gonzalez.

Against the strong advice in his heart doctor,

he is trying to decide how many Big Mac hamburgers versus french fries

he should buy with his daily fixed income of $10.

[SOUND] This tape summaries the marginal utility that Luis will get from

the consumption, the first, second, third, and so on units of each of these goods.

Note carefully for both products marginal utility is declining.

Now in order to make this table really work for us,

we have to take into account the different prices of each of the two product.

We can do so by converting the marginal utilities in

a table to a per dollar spent basis.

We do this by simply dividing each marginal utility by the product price.

This allows us to compare apples and oranges, as the saying goes or

in this case, Big Macs and French Fries.

Adding these columns to the table, here's what this looks like.

Take a minute now as you pause the presentation.

Try and fill in the empty boxes in columns three and five.

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Did you get it?

You can see that since the price of French Fries is 1,

the marginal utility per dollar is the same as the marginal utility.

However for Big Macs, the marginal utility of say 18 converts

to a marginal utility per dollar of 9 because its price is $2.

Now take a look at this next table.

It illustrates the sequence of purchases that Luis will make to

maximize his utility.

With this first potential choice, he'll start by buying one Big Mac,

this will yield then a marginal utility per dollar of 12, and

leave him with a dollars income.

Thus the purchase of the first Big Mac is clearly superior to buying the first

bag of french fries which only yields a marginal utility of 10 per dollar.

Next, Luis will buy his first French Fries for $1 and a second Big Mac for $2.

This is because both yield a marginal utility per dollar of 10.

So, what will Luis do next with this remaining $5?

Try to filling in the remaining boxes as you pause the presentation.

[MUSIC]

That's right, in his third potential choice, Luis opts for a third Big Mac.

And with his fourth potential choice,

he spends his remaining income of $3 on a second French Fries and a fourth Big Mac.

What's really interesting about this, besides the fact that Louis is a heart

attack waiting to happen, is that Luis runs out of money exactly where

the marginal utility per dollar of the two goods are equal.

In this case where the marginal utility is equal to eight for both goods.

Of course this proves more generally that utility will be maximized

when the marginal utility of the last dollar spent on each good is exactly

the same as the marginal utility of the last dollar spend on any other good.

And that is, indeed, the Utility Maximizing Rule or

Equimarginal Principle we set out to prove, so QED.

[SOUND] Now, why do we care about this?

Simply because by proving the Equimarginal Principle,

we now have a perfect explanation of why the demand curves slope downward.

Let me show you why.

[SOUND] Suppose that at the equilibrium point in our last example,

we hold the marginal utility per dollar constant for the two goods.

In this case, it would be equal to 8.

Now, further suppose that the price of French Fries increases.

What happens to the marginal utility per dollar of French Fries?

And more importantly, how do you think that our consumer Luis will respond?

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Well, because price is in the denominator,

by simple math the marginal utility per dollar or French Fries will fall.

And in this case it will fall below the same ratio for Big Macs.

Therefore, in order to maximize his utility,

Luis will have to decrease his French Fries consumption and

increase that of Big Macs, this clearly implies a downward sloping demand curve.

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It's not that just that the Equimarginal Principle helps

us to derive the downward sloping demand curve.

It also helps us better understand the income and

substitution effects that we introduced in the previous lecture.

In this case the substitution effect is obvious.

As we've shown when the price of French Fries rises,

Luis increases his consumption of Big Macs.

This is because the last dollar spent on French Fries yields less utility

than the last dollar spent on Big Macs.

But what about the income effect?

To understand this we have to understand the difference

between Nominal Income and Real Income.

This is a really key definition and

here is the really important difference between Nominal and Real Income.

Nominal Income represents the actual face value of the money you're holding in your

pocket or a bank account.

In contrast, Real Income adjust nominal income for the effects of inflation,

and how such inflation reduces your actual purchasing power.

Now in Luis' case, his nominal income is $10.

Note, however, that when inflation increases,

in this case when the price of French Fries rises,

this inflation reduces Luis' actual purchasing power, why is this so?

Because after the price rise, Luis can no longer afford to buy the same combination

of French Fries and Big Macs that he once could.

That is why we say his real income has fallen,

even though his nominal income remains unchanged.

Now here's the punchline.

The portion of the increase in Luis' purchase of Big Macs due to his

reduction in real income is?

You guessed it, the Income Effect.

Now to complete these thoughts,

let's use a little algebra to generalize the utility maximizing or

Equimarginal Principle to the case in many goods.

And please note here, I won't throw a lot of math at you like this in the course,

because I think it often gets in the way of students

understanding the power of economic thinking.

But in this case this simple formula is useful.

[SOUND] So take a look at this formula and study it carefully for

a minute as you pause the presentation.

And when you're ready, let's end this module with a neat little exercise.

[MUSIC]

Okay, now take a look at this figure and try to fill in the empty boxes

correctly with either an = sign, a > sign, or a < sign.

Pause the presentation now if you wanted to do so and

make check your answers at the end

[MUSIC]

Did you get it right?

If not see if you can find your mistakes before moving on to the next module

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Consumer Optimization; The Equimarginal Principle; Nominal vs. Real Income; Income and Substitution Effects

Strategic Business Management - Microeconomics

Meet the Instructors