We know that demand refers to the various quantities of a given commodity of services, which consumers would buy in one market in a given period of time at various prices, incomes, time, place, and prices of related goods.

Specific Demand Function is also known as individual demand function. Individual's demand for a commodity depends on the own price of a commodities (which may be either substitutes or complements), his tastes and preferences, and advertising expenses made by the producers. Specific demand for a commodity can be expressed mathematically in the following general function form:

Qdx = f (Px, Y, T, Py, E, A)………………(i)

Where, Px = Price of commodity x Y = Level of income

T = Taste and preferences Py = Price of commodity y

E = Expectation of price & A = Advertising expenditure

Keeping other determining factors such as income price of other goods, etc constant, following relation can be established between demand and price.

Qd = f (Px)……………………….(ii)

This equation means that demand is a function of price i.e. demand of a commodity depends on its price. It means if price increases demand decreases and if price decreases demand increases. This relationship can be shown with the help of table and a curve:

Here, quantity demanded of a commodity at Rs. 5 is 10 kg, at Rs. 4 is 20 kg, and at Rs.3 is 30 kg and so on. It shows that quantity demanded increases with every fall in price.

{FIGURE HERE}

Here, OX and OY axes represents Quantity demanded and Price respectively. DD is the individual demand curve, which slopes downward to the right. Here, when the price is OP individual demands OQ quantity and if the price decreases from P-P1 the he demands more i.e. quantity demanded increases from Q-Q1.

The individual's demand function in equation (ii) does not show how much quantity demanded of a consumer will change following a unit change in price (Px). For the purpose of actually estimating demand for a commodity we need a specific form of demand function. The specific demand function of linear form is written as:

Qd = a-bPx………………………..(iii)

Where, a = constant intercept term on X - axis

b = coefficient showing the slope of the demand curve

If on estimating the Demand Function equation (iii) from the information about monthly quantities demanded of sugar at various prices by an individual consumer, we find the constant 'a' to be equal to 12 and the constant 'b' to be equal to 2, we can write individual's demand function as,

Qd = 12 - 2 px

This is interpreted as One Rupee fall in price of sugar will cause its quantity demanded to increase by 2 units of sugar.

GENERAL DEMAND FUNCTION

A market consists of several individuals. General demand function is obtained by summing up the demand function of the individuals constituting the market.

Example

A market for a commodity consists of three individuals A, B & C, whose demand functions for the commodities are given as given below. Find out the market demand function.

QA = 40-2p

QB = 25.5 - 0.75p

QC = 36.5 - 1.25p

When individual demand functions are expressed as 'quantity as a function of price' as in the case in our problem stated above, market demand function can be obtained by summing up the individual demand functions. Thus, general demand function is,

QA + QB + QC

= (40 - 2p) + (25.5 - 0.75) + (36.5 + 1.25p)

= (40 + 25.5 + 36.5) - (2 + 0.75 + 1.25) p

= 102 - 4p.

This can be explained with the help of a table and a curve:

In the above schedule, in the 1st column price pre kg in Rs. Is shown. In the 2nd, 3rd, and 4th column quantity demanded by a consumer A, B and C are shown and in the last column market demand is shown. When the price of the commodity is Rs. 1, consumer A demands 8 units, consumer B demands 10 units, consumer C demands 7 units. If it is summed, we get general demand 25. when the price of a commodity decreases general demand increases and when its price increases general demand decreases which is clearly shown in the table, like when price increases to Rs.2, demand of A, B, and C also declined to 6 units, 7 units and 6 units respectively. This in turn decreased general demand to 19 units. So, with every rise in the price, general demand falls.

{FIGURE HERE}

In the above diagrams, in fig, A, DD is the demand curve of a consumer A, in fig. B, DD is the demand curve of consumer B and in fig. C, DD is the demand curve of consumer C and by the horizontal summation of all these curves, we get a curve called General Demand Curve, which is shown in fig. M as MD. This curve slopes downward to the right showing negative relationship between price and quantity demanded.

Thus, specific demand function is affected only by price, whereas, the general demand function is affected also by the other determinants of demand.

Determinants Of Demand

Simply, demand refers to desire backed up by willingness and ability to pay. Besides, demand also signifies price and period of time in which demand is to be fulfilled. It is clear that a persons demand for anything varies with the price at which it is offered. He buys more of it at lower price and less of it at higher price; similarly, his demand varies with the period of time, income level and prices of related goods and services. So, demand has many determinants, which are as follows:

1.Price of the Commodity:

This is related to the law of demand, i.e. if other things remaining the same, there is inverse relation between price & demand.

Here, when the price of a product is Rs.5, quantity demanded is 100 Kgs and when the price of the product decreases to Rs.4, the quantity demanded increases to 200 Kgs. Similarly, when the price falls to Rs.3, Rs.2, then, quantity demanded increases to 300, 400 Kgs. respectively.

{FIGURE HERE}

Here, when price is, OP quantity demanded is OQ But when the price increases to OP1, quantity demanded decreases to OQ1.

2.Price of Related Commodities:

Mainly there are two types of goods, viz.: substitute goods and complementary goods. In case of substitute goods, the increase in the price of one commodity leads to an increase in demand of other commodity. But in case of the complementary goods when price of one commodity increases the demand for another commodity decreases.

{FIGURE HERE}

In figure A, when price of tea is OP, quantity demanded of coffee is OQ and when the price of tea increase to OP1, quantity demanded also increases to OQ1.

In figure B, when price of tea is OP, quantity is OQ and when the price of tea increases to OP1, quantity demanded of sugar decreases to OQ1.

3.Consumer's Income:

The change in money leads to the change in quantity demanded of a commodity, which is applicable to almost all goods and individuals. Besides, demand also depends upon the consumer's income. If the income of the consumer increases, then the demand for inferior goods will decline and the demand for necessary goods will increase. It can be shown through following diagrams:

{FIGURE HERE}

In figure A, when income is OI, demand is OQ and when income increases to OI, the quantity demanded increases to OI1. In figure B, when income is OI, demand is OQ and when income increases to OI1, quantity demanded decreases to OQ1. Because as income increases consumers shift towards superior goods and reduce consumption of inferior goods.

4. Taste and Preferences:

If the taste for a commodity is strong, the quantity demanded would be high and if there is a loose taste for a commodity, the quantity demanded will be low. For example, if people develop taste for coffee instead of tea, the demand curve of coffee will shift upward towards right.

5. Distribution of National Income:

If the distribution of the national income is unequal, i.e. more poor people than rich, then the demand for both luxurious goods as well as inferior goods will be high. Similarly, if the distribution of national income is equal, then the demand for normal goods will be high and luxurious goods will be low.

6. Populations and Its Composition:

If the size of population increases demand for goods and services also increases. Likewise the change in composition of population brings change in the demand for goods. For example, the increase in child population leads to increase in demand for toys.

7. Consumers' Expectation:

When the consumers expect the price to fall continue, they do not buy more even if the price is low. Likewise, when the consumers expect further rise in price, they buy more even if the price is high. Besides, if the people feel that the commodity is going to be scarce in near future, they buy more of it even if the price is high.

8. Advertisement Expenditure:

Goods that are widely advertised become popular and are more demanded.

{FIGURE HERE}

Here, when the advertisement expense is OP, quantity demanded is OQ and when the advertisement expenses increases to OP1 quantity demanded by people also increases to OQ1.

Assumptions:

• Demand should not reach the saturation level.
• The consumers should be sensitive to advertisement.
• The rivals should not respond.
• The price increase due to advertisement cost should not discourage the consumers.
• The other determinants of demand like income, taste should not go to the opposite direction.

CONCLUSION
Thus we can conclude that demand is the function of price and it is also affected by many other factors, such as, Advertisement Expenditure, Consumers' Expectation, Consumers' income and all the others mentioned above.