Demand Curve

 

Derivation of Demand Curve

According to Alfred Marshall the law of demand can be derived with the assistance of utility analysis. He derived the law of demand in case of single commodity and in case of two or over two commodities. Within the words of Alfred Marshal the law of diminishing marginal utility states that if a consumer purchases more and more units of the same commodity at the same time, as a result the units of purchase increases the utility for the same commodity decreases. A rational consumer will purchase more and more units of commodity, if the utility of a commodity is greater than price or up to the value. If the consumer consumes more and more units of commodity, its utility goes on diminishing. The law of demand or demand curve may be explained with the assistance of the subsequent figures.

1: Derivation of demand curve in case of single commodity.

Explanation

In the figure the MU X is that the utility which is negatively sloped and PX is that the price of the commodity. It shows that because the consumer gain more quantities of good X, its utility diminishes. Consequently at diminishing price, the amount demanded of the good X increases. At X1, quantity the utility of good is MU1, which is adequate P1. Within the same way the quantity demanded of the good X increases, at X2 the quantity of utility of good is MU2, which is adequate to P2. Within the same way the quantity demanded of the good X increases at X3, the quantity of utility of good is MU3, which is equal to P3 as shown within the figure.

Note: The negative section of the utility curve is not the a part of demand curve, because negative quantities do not make sense in economics.

From the above explanation we may say that as the purchase of the units of commodity increases, its utility diminishes. The demand curve slope downwards when price falls, the quantity demanded of commodity increases, in this case the consumer purchase more and more units of commodity. On the opposite hand the quantity demanded for commodity decreases when the price increases.

2: Derivation Of the demand curve in the case of two or more than two commodities

The law of diminishing utility also can be applied just in case of two or over two goods. When a consumer has spend a specific amount of cash on variety of goods to get maximum satisfaction, when the costs of commodities are constant as shown within the following figure stated below.

Explanation

In the figure given the cash income, the price of commodity A is P1 and therefore the price of commodity B is P2 and also the utility of money is Z which is constant. The demand curve derived is illustrated CC for commodity A and DD for commodity B. The consumer allocates his money income between A and B commodities to urge O, Q1 units of commodity A and O, Q2 units of commodity B because the combination corresponds to MU/P1=MU/P2=Z at maximum level.

Let us assume that cash income and also the price of B commodity remain constant but the price of A commodity decreases. As a results of this money expenditure on commodity A raises resulting the curve DD slope downward from left to right, as the price decrease from P2 to P1 the quantity of demand increases from O, Q1 to O,Q2. Thus when the price falls from P2 to P1 the consumer will take more quantity of commodity A from O, Q1 level to O, Q2. 

Assumptions

The utility analysis of demand is predicated on the subsequent assumptions.

1) Utility is cardinally measurable.

2) Commodities are independent in utilities.

3) The utility of money remains constant.

4) Utility gained from the successive units goes on diminishing.