As consumption of good X increases, the total utility increases at an increasing rate

The correct answer is FALSE.

Let's assume U(X) is our utility function. The X between brackets means that utility is a function that depends on the consumption of good X. Just for the sake of simplicity, we assume that X is the only good that exists in our economy.

The main properties of the utility function are the following:

1) U'(X) > 0

2) U(X) < 0

These properties mean that the first derivative of U with respect to X is positive and the second derivative is negative. In consequence, we are saying that when we increase the consumption of good X, then the utility increases (U'(X) > 0). However, since U(X) < 0, that means that total utility increases at a decreasing rate.

In other words, these properties of the utility function establish quite an intuitive fact, which is the following: when the consumer consumes more of a certain good (pizza for example, but it could be any good), It increases the level of utility. However, since the consumer gets satiated, each additional unit of good X gives the consumer less utility than the previous one (the second pizza adds less utility than the first one, since now the consumer is more satiated than before).