Educational Songs with Free Worksheets

Maximum Utility

Learn key terms such as the equation for a budget line and its slope, indifference curves and marginal rate of substitution (MRS) in this clever song.

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This rap song teaches about utility maximization in economics. "Maximum Utility" describes key terms such as the equation for a budget line and its slope, indifference curves, and marginal rate of substitution (MRS). The final verse discusses utility maximization using the constraints described in verse 1 and verse 2.

This economics song is suitable for explaining utility maximization to high school, college, and graduate school students.
Verse I
On consumer choice, the budget line sets a limit
The total you can spend on goods must fall within it
So anything on the line or down below is OK
Anything above it? Gotta say “no way.”

There’s one point on each of the axes
Representing the max; please, you can’t go past these
If you spent your whole budget, every last cent
On one good or the other, that’s what these represent

So now you have two intercepts, what do you find
Between one and the other? That’s the Budget Line
Now let’s define the slope algebraically
No time to derive it, but basically

It’s the price of the good on the horizontal x
Over the price of the good on the vertical axis
Multiply this by negative one
That’s the slope of the Budget Line, but you’re not done, because...

Maximum utility
Consumers acting rationally
They maximize their satisfaction
And we predict their actions

Maximum utility
Is the goal of consumers like you and me
We're spending time, we're spending cash
So here's how you can do the math

Verse II
Indifference curves we observe ambivalence
To the consumer, all points are equivalents
So if she can get anything above it, she’ll love it
Anything below, man, you can shove it

Now infinite curves exist, and could be made
To map consumer tastes, but they all look the same:
Start from the left at maximum height
Then become less steep as they move to the right

But even though it’s not straight like the Budget Line
There’s still a slope that we’re gonna wanna define
It’s the Marginal Rate of Substitution
We’ll call it MRS for the rest of this solution

It’s the rate you can exchange this good for that
Where the consumer’s utility will just stand pat
MRS is not constant, you’ll see it decrease
As indifference curves move from West to East, it's like...


Verse III
Now that we’ve had our two hors d’oeuvres
Talking Budget Lines and Indifference Curves
We move on to the main course of this oration:
Utility maximization

Now, there are only two constraints you gotta satisfy:
(1) You must be on or below the Budget Line
To comply with the limits of purchase ability
Or else you get infinite utility

(2) Now within the budget, find a spot
Upon the highest indifference curve you’ve got
The point on the line where the curve has landed
The slope is the same, it’s called the tangent

That’s a lot to learn, I’ll help you out with a rhyme
Just a couple of lines that you can use any time:
Where the ratio of prices equals MRS,
That’s where utility is the best


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