Strongly Monotonic Preferences and Constant Marginal Utility (MU=1)

When marginal utility is 1, it means that the additional satisfaction or utility gained from consuming an additional unit of a good is constant and equal to 1. In other words, the consumer values each additional unit of the good equally.

If a consumer's preferences are strongly monotonic, it means that they prefer more of a good to less of it. This can be shown as follows:

Assume a consumer has two bundles of goods A and B, where A has more of the good than B. Let U(A) and U(B) be the utility levels associated with bundles A and B, respectively.

If the consumer's marginal utility for the good is 1, then the additional utility gained from consuming the extra units in bundle A must be equal to the difference in the number of units between A and B. That is:

U(A) - U(B) = (number of additional units in A compared to B)

Since the marginal utility is constant and equal to 1, the difference in utility between A and B will always be greater than or equal to the difference in the number of units. Therefore, the consumer will always prefer bundle A to bundle B, and their preferences are strongly monotonic.

In summary, when marginal utility is 1, the consumer values each additional unit of the good equally, which ensures that their preferences are strongly monotonic.