Derivation of Demand Curve:

The consumer purchases various units of a commodity 'X'. He can either buy a commodity X or retain or retain his money with him. Under these conditions, the consumer is in equilibrium when the marginal utility of a commodity 'X' is equal to its market price Px.

It is written as:

MUx = Px

If the marginal utility of a commodity is measured in terms of money, the demand curve for a commodity is identical to the positive portion of the marginal utility curve. The negative portion of the marginal utility curve does not form part of the demand curve, since negative quantities do not make sense in economics.

Derivation of Demand Curve

In figure A, at Q1, the marginal utility is MU1 = 10, which is equal to P1 = 10 by definition. Hence at P1, the consumer demands Q1 quantity of the commodity in figure B.

Similarly at Q2, the marginal utility is MU2 = 8, which is equal to P2 = 8. Hence, at P2 = 8 the consumer will buy Q2 in figure B and so on.

As the consumer consumes more and more units of a commodity its marginal utility goes on diminishing. So the consumer would like to demand more products at a diminishing price as shown in figure B. It reflects that there is an inverse relation between price and the quantity demanded of a commodity having negatively slopped demand curve in figure B that is derived with the help of the marginal utility curve in figure A which is also negatively slopped.