# Utility maximizing

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##### Intros
###### Lessons
1. Utility Maximizing Overview:
• List all the possible combination of goods
• Find the total utility of each
• Find the highest total utility
• An Example
3. Choosing the Margin
• Marginal utility per dollar of good x
• Marginal utility per dollar of good y
• Setting them equal
• An Example
##### Examples
###### Lessons
1. Understanding Method 1: Using a Spreadsheet
Pencils are $2 each, and erasers are$4 each. Suppose you have an income of $12, and the utility you gain from each good is shown in this table:  Quantity (per pencil) Total Utility Quantity (per eraser) Total Utility 0 0 0 0 1 50 1 40 2 80 2 75 3 90 3 95 4 100 4 110 5 105 5 120 6 107 6 125 Use a spreadsheet to find the choice which maximizes utility. 1. Candy are$4 each, and Chocolate are $8 each. Suppose you have an income of$16, and the utility you gain from each good is shown in this table:
 Quantity (per candy) Total Utility Quantity (per chocolate) Total Utility 0 0 0 0 1 35 1 50 2 65 2 90 3 85 3 120 4 100 4 130 5 110 5 135 6 115 6 137

Using a spreadsheet to find the choice which maximizes utility.
###### Topic Notes

Knowing a personβs budget line and utility, how can we maximize the utility? There are 2 methods.

Assuming all income is used,
1. Write out the possible combinations of goods from the specified income.
2. Write out the total utility gained from each number of good.
3. Add the utilities together from both goods
4. Find out which combination of good gives the most total utility.

Choosing the Margin

Recall that we learned about finding the marginal utility last section. We can put it to use this section!

Assuming all income is used, the consumer maximizes their utility between two goods when

$\large \frac{MU_x}{P_x}=\frac{MU_y}{P_y}$

Where:

1. $MU_x$ is the marginal utility of good x.
2. $P_x$ is the marginal utility of good x.
3. $MU_y$ is the marginal utility of good y.
4. $P_y$ is the marginal utility of good y.