The equimarginal principle - YouTube

In this video we’ll learn about the equimarginal principle.

By the end of this video you’ll understand how economists expect a rational consumer

to use the equimarginal principle in determining how to maximise utility.

Before we learn more about the equimarginal principle, we must set a few assumptions.

First, consumer income is fixed and held constant.

Prices do not change and neither do tastes and preferences.

We also make a significant assumption that consumers are able to perform utility calculations

for multiple goods.

In reality, this is far from the case.

There are many reasons why consumers may not engage in rational behaviour, but we will

examine that in the video following this one.

The equimarginal principle states that consumer utility is maximised where the marginal utility

per dollar (or other unit of currency) for all goods is equal.

In this equation, MU represents the marginal utility received from the consumption of a

good.

P represents the price of the good and a, b and c represent three different goods.

We could continue this for as many choices as a consumer faces.

If you imagine yourself in the supermarket you can understand how overwhelming it can

be to maximise utility from the expenditure of your next dollar when considering amongst

thousands of goods.

For now let’s just focus on using 2 in a simplified model.

Let’s consider two goods, product A, which costs $5 per unit and product B, which costs

$10 per unit.

We’ll start with a table of quantity consumed and the associated total utility.

I will use the word utils in this lesson which means one unit of utility.

In this table we can see the total utility gained from the consumption of 1 to 5 units

of product A. Total utility is still rising, but as we learned from before marginal utility

is not.

We next need to calculate the marginal utility for each unit of product A.

The marginal utility in this case is the difference between the total utility at that quantity

of consumption minus the previous total utility.

Since we are always increasing by one unit, we don't need to divide the marginal utility

gain.

The marginal utility as we consume our first unit is 100, given that total utility at quantity

0 is 0.

Total utility increases to 170 as consume the second unit, so the second unit adds 70

utils.

After three units, total utility rises to 220 which is an additional 50 utils.

This continues with the fourth, which brings 30 additional utils and finally the fifth

unit which brings 10 additional utils.

The last step we need to do is to calculate the value of the marginal utility per dollar

for each level of consumption.

For the first utility, our marginal utility is 100.

Since the price is $5, our marginal utility per dollar is equal to 20.

Essentially one dollar is worth 20 utils.

We continue this calculation for the second unit, arriving at 14 utils per dollar.

It’s 10 utils per dollar for the third, 6 for the fourth and 2 for the fifth.

Now that we have this complete, let’s do the same thing for Product B.

Similar to product A, we have a total utility table for consuming five units of product

B.

The utility values look much higher here, but remember - we need to consider marginal

utility and the marginal utility per dollar in this case.

Marginal utility decreases as more units of product B are consumed.

The first unit brings a marginal utility of 180, the second 150, the third 90, the fourth

60 and the fifth unit just 30 utils.

As we did before, we must do again.

To calculate the marginal utility per dollar for our first unit, we divide 180 utils by

the price of $10, resulting in 18 utils per dollar.

The second gives us 15 utils per dollar, the third 9, the fourth 6 and the fifth and final

unit provides 3 utils.

Now let’s bring both product A and product B together assuming a $60 budget.

If I have a budget of $60, I should consume the product that gives me the highest value

of marginal utility per dollar.

Facing a choice, I will first purchase product A as 20 is greater than 18.

That will cost me $5.

I will then purchase a unit of good B for $10.

Third I will purchase a unit of good B for an additional $10.

Fourth, I will select product A at a price of $5.

I still have about $30 left so I will continue to spend.

Fifth I will consume a unit of product A for $5.

Sixth will be a unit of product B for $10.

Seventh I am indifferent between product A and B, but I will choose product A for $5.

I still have $10 left and that will be spent on a fourth unit of product B.

I have now spent my entire $60 and maximised my utility.

I purchased four units of each.

Next I will do a quick check of my work to ensure this is correct given the budget constraint.

If I have $60 and purchased four units of A at $5 each, that is $20 gone.

That leaves me with $40 and if I purchased four units of B at $10 each, that is the remaining

$40 gone.

This works out and I have maximised my utility.

If you have understood what I’ve explained, then congratulations you understand the equimarginal

principle.

Now we are at the end of the video and I hope you understand this quite complicated principle

clearly.

I struggled with finding the best way to explain it clearly to you and I hope it makes more

sense now.

If you have any questions or comments, leave them below or email me at [email protected].

You can also find some more resources online at www.enhancetuition.co.uk.

For now, that’s us done and I will see you in the next one!