The demand curve

Suppose that starting from a condition of equilibrium, the price of X falls relative to Y.  We now have a condition where the utility from the last shilling spent on X will be greater than the utility from the last shillings spent on Y.  Mathematically this can be written as:

In order to restore the equilibrium the consumer will buy more of X (and less of Y), thus reducing the marginal utility of X.  The consumer will continue substituting X for Y until equilibrium is achieved.  Thus we have attained the normal demand relationship that, ceteris paribus, as the price of X falls, more of it is bought.  We have therefore a normal downward-sloping demand curve.  The demand curve we have derived is the individuals' demand curve for a product.  The market demand curve can be then obtained by aggregating all the individual demand curves.

The explanation we have obtained here is of the price (or substitution) effect.