I'm trying to figure out what the shaded rectangle represents in this supply curve. In addition. I'm trying to figure out why the S(x) is a generally increasing function of x.

Producer Surplus. A producer's supply curve is the function p = S(x), which shows the price per unit at which producers are willing to sell a units of product. The producer surplus is the extra satisfaction (or utility) that producers get from selling a product at a price that is higher than their minimum. For example, suppose that we want to purchase used textbooks from students. (In this example, students are the producers). For a particular text, we know from experience that if we offer a price of $7, no students will sell. However, for each $1 increase in what we offer, 10 additional students will decide to sell. At this particular campus, there are approximately 500 students who own the used text. The number of used textbooks the students will supply is then x = 10(p - 7). Solving for p in terms of a gives the supply curve p = S(x) = 7 + 0.1. (0