APPLICATION OF THE INTEGRAL I: CONSUMER AND PRODUCER SURPLUS

1. Supply and demand One of the most fundamental economic models is the law of supply and demand for a certain product (milk, bread, fuel etc.) or service (transportation, health care, education etc.) in a free-market environment. In this model the quantity of a certain item produced and sold is described by two curves, called the supply and demand curves of the item. Definition 1.1. The supply function or supply curve gives the quantity of an item that producers will supply at any given price. The demand function or demand curve gives the quantity that consumers will demand at any given price. We will denote the price per unit by p and the quantity supplied or demanded at that price by q. As is the convention in economics, we will always write p as a function of q. Thus the supply curve will be denoted by the formula p = S(q) and represented by a graph where the x and y axes correspond to q and p values respectively. Similarly, we will use p = D(q) to denote the demand curve. As you might expect, the supply function S is increasing – the higher the price, the more the producers will supply. The demand function D is decreasing – the higher the price, the less the consumers will buy. Definition 1.2. The point of intersection (qe , pe ) of the supply and demand curves is called the market equilibrium point. The numbers qe and pe are termed equilibrium quantity and equilibrium price respectively. The economic significance of the market equilibrium is the following: consider the case of bread. As long as p < pe , the demand for bread exceeds its supply, pushing up the price until it reaches equilibrium price pe . At this point, the quantity supplied is equal to the quantity demanded which is the equilibrium quantity. Conversely, if the price exceeds equilibrium, the supply of bread exceeds demand, bringing the