Derivation of Demand Curve under Cardinal Approach Derivation of Demand Curve under Cardinal Approach

# Derivation of Demand Curve under Cardinal Approach

## Derivation of Demand Curve (Cardinal Approach)

### 1. Derivation of Demand Curve under One Commodity Model

In the Cardinal utility approach, the consumer reaches equilibrium when the marginal utility of a commodity is equaled to marginal utility money or price of the commodity [MUx /Px = (MUm)]. On the basis of this equilibrium condition, we can derive the consumer's demand curve which can be  explained with the help of the following figure:

In the upper portion of the above figure, the initial equilibrium is point E1 where the price of commodity 'X' is P3; and MUx = P3 = (MUm). At this point of equilibrium, the consumer consumes OQ1 units of the commodity X. If the price of the commodity decreases from P3 to P2, then the consumer will be in equilibrium at point E2, where MUx = P2 = (MUm). Here, the consumer consumes more units of commodity X, ie. OQ2. Similarly, the consumer will be in equilibrium at point E3 when the price falls from P2 to P1. At this price, he consumes OQ3 units of the commodity-X.

The lower portion of the figure explains the relationship between price and quantity demanded. When Price is P3 consumer consumes the OQ1 quantity of the commodity X which gives the combination J. Similarly, when the price falls to P2 and P1, the quantity demanded increases to Q2 and Q3 respectively which gives the combination K and L. If we join all these combinations, we get downward sloping demand curve Dx.

### 2. Derivation of Demand Curve under Two Commodity Model

To derive the demand curve for the two-commodity model, the law of equi marginal utility is applicable. According to this law, the consumer is in equilibrium when the ratios of marginal utility and price of each commodity are equal to the marginal utility of money.

The equilibrium situation can be expressed as MUx/Px = MUy/Py = MUm. Now, suppose the price of goods 'X’ falls where the price of Y and income of the consumer is constant (MUx/Px > MUy/Py =  MUm). To achieve the equilibrium, the marginal utility of goods ‘X’ must be reduced which is possible by consuming morÃ© units of the commodity. So it is clear that when the price of the commodity falls to attain the equilibrium condition, the consumer must consume more units of that particular commodity and vice versa. So the demand curve is downward sloping. It is presented in the figure above.

In the figure, we can observe that the marginal utility of money is MUm. The initial equilibrium point is E1 which gives the combination J to consume OQ1 quantity at OP3 price. If the price of commodity X falls, consumers' demand for the commodity increases, and the new equilibrium point is E2 which gives the combination K where consumers consume OQ2 quantity at OP2 price. Similarly, at price OP1, the consumer consumes OQ3 quantity, which gives the combination L. When we join combinations J, K, and L, we get a downward sloping demand curve Dx.

### Criticisms (Limitations) of Cardinal Utility Approach

The cardinal utility approach has been criticized on the following major ground.

1. Cardinal measurement of utility is not practical: Cardinal utility analysis believes that utility can be measured in terms of cardinal numbers which is impossible because the utility is subjective and cannot be measured objectively. As a subjective phenomenon, utility is expressed in ordinal numbers rather than a cardinal number. Cardinal measurement of utility is practically meaningless.

2 Marginal utility of money may not be constant:
cardinal measurement is possible by using money as a measuring scale. But marginal utility of money differs from one income group to another and one consumer to another. The marginal utility of money is higher for lower-income earners and vice-versa. If it changes from one income group to another, we cannot use money as a standard measuring scale.

3. Diminishing marginal utility is not valid for all type of goods: There are some exceptional goods which do not obey the law of diminishing marginal utility. The hobby of collecting stamps, coins, scarce goods, etc. may have increasing marginal utility. Likewise, listening to music, earning money, drinking wine, etc. may also have increasing marginal utility.

4. Utilities are dependent: One of the strong assumptions of this theory is utilities remain independent. But in practical life utilities remain dependent on each other. If various goods are consumed at the same time, consumption of one good can affect the level of satisfaction obtained by the consumption of another good.

5. No classification of goods: This cardinal utility analysis is not able to classify the various type of goods like Giffen, normal, inferior, superior, etc. but in ordinal utility analysis we can classify all type of goods

6. No analysis of price effect: In this approach, there is no analysis of price effect. But in ordinal utility analysis price change can be decomposed into two effects: income effect and substitution effect.

7. Less work and more assumptions: This theory assumes more and explains less. Most of the assumptions are unrealistic which are criticized strongly on various grounds.