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## Microeconomics

### Course: Microeconomics>Unit 5

Lesson 1: Introduction to consumer theory: total utility and marginal utility

# Utility maximization: equalizing marginal utility per dollar

How should you allocate money between two different products or services in order to maximize utility, or "bang for your buck?" Marginal utility refers to the utility gained from an incremental purchase, in order to make rational decisions. In many cases, the goal is to reach a point where the marginal utility per price of the two products is equal. Created by Sal Khan.

## Want to join the conversation?

• Does the point where the graphs crosses have any meaning in this case? • what is equi-marginal principle? • the equi-marginal principle is what Sal is explaining here. the fact that MUa/Pa = MUb/Pb. If one good has a better marginal utility, then you would buy more of that good, decreasing the marginal utility of one more unit of that good. However, the best situation would be where you get the same "bang for your buck" from both goods. This point where the two sides of the equation are the same. the point where the marginal utility per price is equal (equi-marginal principle).
• What is marginal utility? • Margin means edge or the next one. Marginal utility is the utility you receive from the next one or "at the margin." In economics it is often assumed that consumers maximize their utility at the margin or get the best deal for the next dollar spent.
Maximizing utility at the margin isn't necessarily simple. Do you maximize the utility of each item you buy at the store or do you get the most for a fixed amount you intend to spend so the margin is the shopping trip not each item.
• Is there a way that by purchasing one product or another, that the other product's marginal utility would be altered? I could see complimentary items being a common positive example where by purchasing a car your marginal utility for gas increases, but is there a negative example? Where by purchasing one item, another is worth less to you? Because in that case, wouldn't the rule that the two curves equalize at some point be negated? • Sal probably implicitly uses "Ceteris paribus" (all things being equal) here for simplicity. It's easy to imagine lots of goods with dependent marginal utility values. In that case, graphs would move in a more "dynamic" way. The more movies you rent online, the less demand you have for movie theater tickets. The more water filters you get, the less need there is for purchasing water bottles. On the other hand, we can also consider human psychology affecting things in perhaps unpredictable ways. For every 10 movies watched at home (e.g. renting DVD's), your desire to watch at the theater slowly increases; after all, home experience can't compare to the theater one. Things that seem interchangeable could have an unexpected effect on each other.
• i'm a bit confused. according to the graph, after about \$4 you will no longer switch between A and B and just start purchasing B right?

at that point, it seems that the marginal utility of A stops becoming equal to the marginal utility of B (by drawing a straight line through the two lines).

am i wrong? • No you keep switching all the time. Even after the crossing point. Thats the whole idea. Keep in mind the things you have to compare here:
You dont compare the utility for each product at 4 \$. You rather compare the utility with the last of the 4 dollars spent at total. so maybe you spend 2 on product A and 1 on Product B. Now you have one more dollar. you can spend that dollar at A (that would be the third "A dollar" or on B (that would be the second "B dollar". So you compare the Y values of B (at X=3) with the one of A (at X=1). You dont compare the Y values at 4...
• so our utility is maximized in the equalibrium? where the two marginal utility per dollar spent- curves cross each other?

or is it wrong, like: we should allocate our money, in other words spend our money where the mu/price for the two goods is bigger? and we should stop doing this where the equalibrium starts?

i hope you understand my question, my english is not my first language. • shouldn't the Y axis just be MU not MU/P? • Simple but interesting question. Sal is graphing `MU/P`, because he's not expressing what the MU is directly. The graph is for the amount of `MU` for any incremental spending, at any given amount that you already spent (`P`). He did mention calculus, but I think he tried to get through the video without explaining that by integrating `MU/P` for change in P, you get an area that's expressed in `MU`. However, despite all that, I think Sal used the term "marginal utility" incorrectly. At he describes the area under the curve as "total marginal utility", but it should just be "total utility". (I think he did it a bit strangely here in order to emphasize that the marginal utility of each curve was expressed per price, not per pound or per unit.)
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• I learned from a textbook that the formula derived at the end is the 'utility maximizing rule'. Could somebody please explain this?
(1 vote) • Is there a way to find how to maximize total utility without drawing a graph?
(1 vote) • Wouldn't the 5th dpollar be spent on the next unit of fruit at 50 utils per price? Why was the last dollar spent on the same unit at 60 utils?
(1 vote) 