Why Derivation of Demand Curve is known as Consumers Planning Curve?

The demand curve indicates what the consumer plans or intends to purchase and consume at alternative prices of a good. It is a consumer’s planning curve. At each price, it records consumer’s utility maximising choice. The demand curve is derived from the utility schedule by using an optimisation (maximisation) process.

As a consumer takes more and more units of a commodity, he gets lesser and lesser utility from the consumption of each successive unit of the commodity. Since marginal utility of the commodity diminishes, the price which the consumer would be willing to pay for an additional unit will also be less. The consumer would be prepared to pay more for only those units of the commodity, which give him greater utility.

Now, we consider a simple example for the derivation of demand curve, where a consumer consumes only oranges. Table 4.2 records marginal utility of oranges in the form of utility schedule. In the market, price of a commodity is quoted, received and paid in units of money and not in terms of utility.

Therefore, it is necessary to express utility a person gets in terms of money, he is prepared to spend. We assume that each rupee has the same marginal utility (constancy of marginal utility of money, irrespective of stock of money with the buyer), say, 10 units. On this basis, the marginal utilities of oranges expressed in money terms are shown in last column of this table.

An important fact of market is that a consumer purchases all the units of the commodity at the same price (though when converted into utility, the price paid may differ from buyer to buyer). A rational consumer does not purchase the commodity, if the utility lost by him by way of its price is more than the marginal utility.

He does purchase it if the price paid is less than marginal utility. He will be in equilibrium, if the price and marginal utility are equal. This is known as the point of satiety. In other words, the price which the consumer is ready to pay never exceeds the marginal utility of the commodity.

From the Table 4.2, it is clear that the consumer gets utility worth one rupee from the first orange. So, if the market price is Rs. 1, the consumer will purchase only one orange. At Rs. 0.80, he will demand 2 oranges.

The third orange will be demanded at Rs. 0.60 and so on. In this manner, through equality of market price and marginal utility, the quantity demanded by a consumer is determined by the marginal utility, which he derives from the different units of the commodity. Now, the marginal utility schedule can be used to derive a demand schedule, which is presented in Table 4.3.

Thus, we observe that as marginal utility of a good diminishes, the price a consumer is willing to pay for an additional unit will be less. Alternatively, if the price of a commodity falls, situations would emerge in which marginal utility of the commodity will exceed its price and the consumer would purchase more of it to make marginal utility equal to new lower price.

Demand curve based on Table 4.3 (showing demand schedule) is illustrated in Fig. 4.6. The demand (DD) curve shown in Fig. 4.6 expresses inverse price-demand relationship, i.e., the law of demand. If this curve is compared with the marginal utility (MU) curve shown in Fig. 4.7, we notice that the two curves are similar.

Therefore, no demand curve can actually be derived from the marginal utility curve. In fact, if the marginal utility of a commodity is expressed in terms of money, which a consumer is willing to pay, the marginal utility curve itself becomes the demand curve. Further, marginal utility does not determine the price, it only shows, where the price is determined.

Example: Derive a demand curve from the utility function U = log x + log y and comment open its nature.

Solution: Assuming prices of the two goods as p_x, p and income ‘M’ as given, the

condition for utility maximisation is MU_x/P_x = MU_y/P_y

This demand function has the property that the amount of money spent on commodity ‘x’ is constant. The demand curve is, thus, an rectangular hyperbola.