**Law of Equi Marginal Utility**

The law of equi marginal utility is an essential concept within the framework of Marginal Utility Analysis. It states that a rational consumer will allocate their limited resources in such a way that the marginal utility derived from the last unit of each good consumed is equal. In simpler terms, it means that a consumer will distribute their expenditure in a way that maximizes their overall satisfaction.

**Explanation:**

The law of equi marginal utility is based on the assumption that individuals are rational and seek to maximize their satisfaction or utility from the goods and services they consume. It suggests that consumers will derive the most satisfaction when they allocate their resources in a way that balances the marginal utility per unit of money spent across different goods.

To understand this concept better, let's consider an example. Suppose a person has $20 to spend on either apples or oranges. The marginal utility derived from each additional unit of apples or oranges is as follows:

**Apples:**
- 1st apple: 10 utils
- 2nd apple: 8 utils
- 3rd apple: 6 utils
- 4th apple: 4 utils
- 5th apple: 2 utils

**Oranges:**
- 1st orange: 12 utils
- 2nd orange: 10 utils
- 3rd orange: 8 utils
- 4th orange: 6 utils
- 5th orange: 4 utils

According to the law of equi marginal utility, the consumer should allocate their $20 in a way that the marginal utility per dollar spent on apples is equal to the marginal utility per dollar spent on oranges.

Let's calculate the marginal utility per dollar for both apples and oranges:

**Apples:**
- 1st apple: 10 utils / $1 = 10 utils per dollar
- 2nd apple: 8 utils / $2 = 4 utils per dollar
- 3rd apple: 6 utils / $3 = 2 utils per dollar
- 4th apple: 4 utils / $4 = 1 utils per dollar
- 5th apple: 2 utils / $5 = 0.4 utils per dollar

**Oranges:**
- 1st orange: 12 utils / $1 = 12 utils per dollar
- 2nd orange: 10 utils / $2 = 5 utils per dollar
- 3rd orange: 8 utils / $3 = 2.67 utils per dollar
- 4th orange: 6 utils / $4 = 1.5 utils per dollar
- 5th orange: 4 utils / $5 = 0.8 utils per dollar

Based on the calculations, we can observe that the marginal utility per dollar spent on apples and oranges differs for each unit. To maximize satisfaction, the consumer should allocate their $20 in a way that equalizes the marginal utility per dollar for both goods.

In this example, the consumer could purchase 1 apple and 1 orange, which would result in a marginal utility per dollar of 10 utils for both goods. Alternatively, they could buy 2 apples and 2 oranges, which would also result in the same marginal utility per dollar for both goods.

Overall, the law of equi marginal utility guides consumers in making rational decisions about resource allocation to maximize their satisfaction or