In deriving demand curve in a perfectly competitive market, we use a benefit function B(Q) for consumers’ benefit from consuming Q units of the good. We assume that its first derivative is positive, B’(Q)>0 and its second derivative is negative, B”(Q)<0. Explain the economic meaning of these two assumptions.

In a perfectly competitive market, for a given price P, the quantity demanded is determined by P=B’(Q). Give an intuitive explanation for why this equation makes sense. How does this equation relate to the law of demand?

In deriving supply curve in a perfectly competitive market, we use a cost function C(Q) for producers’ cost to produce Q units of the good. We assume that its first and second derivatives are positive, C’(Q)>0 and C”(Q)>0. Explain the economic meaning of these two assumptions.

In a perfectly competitive market, for a given price P, the quantity supplied is determined by P=C’(Q). Give an intuitive explanation for why this equation makes sense. How does this equation relate to the law of supply?