Is it possible for marginal utility to be negative and total utility positive? Explain.

Marginal utility refers to the change in total utility derived from consuming an additional unit of a good or service. Mathematically, it can be represented as the derivative of the total utility function with respect to the quantity consumed: MU = \frac{d(TU)}{dQ} Total utility, on the other hand, represents the overall satisfaction a consumer derives from consuming a given amount of a good or service. It can be obtained by integrating the marginal utility function over the quantity consumed: TU = \int MU dQ Notice that if MU ≥ 0, an increase in the consumption of the good or service increases the total utility, while if MU < 0, an increase in the consumption leads to a decrease in total utility.

A negative marginal utility implies that consuming an additional unit of a good or service decreases the total utility. However, before throwing any conclusions, it is crucial to consider the initial base of consumption as well as the overall total utility. Let's say for example, the consumption of ice cream is enjoyable at first, giving positive utility to a consumer. As the consumption increases, there might come a point when additional ice cream starts bringing little to no satisfaction, and ultimately, discomfort or displeasure. At this point, the marginal utility would be negative.

Now, let's analyze if the negative marginal utility scenario above translates into a positive total utility. The total utility is the sum of utilities generated from the initial consumption and the additional ones that led to the negative marginal utility. In our example, a consumer starts by deriving positive utility from initial ice cream consumption. Even after the marginal utility turns negative, the total utility remains positive as it includes the satisfaction from initial consumption, which was positive. As long as the decrease in utility due to negative marginal utility is smaller than the initial positive total utility, the net total utility will remain positive despite the presence of negative marginal utility.

Yes, it is possible for marginal utility to be negative while total utility is positive. This can happen when the overall satisfaction from initial consumption outweighs the dissatisfaction from additional consumption, resulting in positive net total utility.