In this article we will discuss about the relationship between demand function and demand curve for a good.
Demand curve is a relation between the price and the quantity demanded of a good. The main point of this relation is that, “other things” remaining the same, if the price of a good increases or decreases, then its quantity demanded decreases or increases, respectively. This relation is known as the law of demand.
The main thing about the demand function, on the other hand, is that demand for a good, apart from depending on its own price, depends on “other things” as well, e.g., income of the buyers, prices of substitute and complementary goods, the tastes and habits of the buyers, number of buyers, etc. The influence of these “other things” on the demand for a good is also very important.
If one (or more) of these things changes, then, at any particular price, the quantity demanded of the good would also change, i.e., the demand curve for the good would shift to the right or to the left. For example, in Fig. 1.6, initially, the demand curve for a good is D1D1.
This curve tells us that at prices p1 and p2, quantities demanded of the good are p1F1 and p2F2, respectively. Suppose, now there is an increase in the income of the buyers of the good. As a consequence of this, the quantity demanded of the good that was obtained initially at any particular price, would now increase (provided the good is a normal good).
For example, after the increase in income, at the prices p1 and p2, the quantity demanded of the good has been p1H1 (> p1F1) and p2H2 (> p2F2), respectively. That is, now, the demand curve for the good would shift to the right from D1D1 to D2D2. Similarly, if the income of the buyers diminishes, the demand curve would shift to the left from D1D1 to, say, D3D3.
The relation between the demand curve and the demand function for a good can be clearly understood in the above discussion. Demand curve is a relation between the price and the quantity demanded of the good. This curve tells us what the qd would be at any particular price.
The demand function, on the other hand, represents a more general relation between not only the (own) price and demand for the good (along a particular demand curve), but also between the other demand determinants and the demand for the good.
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It gives how the demand curve itself would change its position, i.e., how it would shift, if any of the “other” demand determinants, e.g., income, changes. While a demand curve is a particular curve, the demand function gives rise to a number of demand curves to which the initial demand curve may shift as a consequence of a change in any of the demand determinants other than the own price of the good.
Thus, the scope of the demand function is much more wide than that of the demand curve. A simple example may further clarify the matter.
Suppose that the demand function for a good is given to be:
q = − 2p + 5y = q (p, y) (1.3)
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where p = price of the good;
y = income of the buyers (or index of their income);
q = quantity demanded of the good from demand function (1.3),
It is obtained:
(i) Demand for the good is a function of p and y.
(ii) As p decreases (or increases) by 1 unit of money, q increases (or decreases) by 2 units.
(iii) Position of the demand curves depends upon y. If y increases by 1, q increases by 5 units at any particular price. That is, the demand curve would shift horizontally to the right by 5 units. Conversely, if y decreases by 1, q decreases by 5 units at any particular price. That is, in this case, the demand curve would shift horizontally to the left by 5 units.
It is illustrated with the help of Fig. 1.7. In this figure, at y = 10, the demand curve is D1D1, and its equation is:
q = − 2p + 50 .…(1.4)
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Also, at y = 11 or y = 9, the demand curve for the good would be, respectively,
q = − 2p + 55 and ….(1.5)
q = − 2p + 45 . …(1.6)
Therefore, here, the demand curve for the good may be any one of D1D1, D2D2, D3D3, and so on, but exactly what would be the demand curve for the good, would depend upon the value of y. The demand function, on the other hand, comprises all these demand curves, viz., D1D1, D2D2 and D3D3.
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If the income of the buyers remains fixed at y = 10, then from the demand curve D1D1 [eq. (1.4)], it is obtained:
at p = Rs 20, q = 10 units and
at p = Rs 10, q = 30 units.
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Again, when y = 11, the value of q at any p from the demand curve D2D2 [eq. (1.5)]. For example, at p = Rs 20, q = 15 units. Similarly, when y = 9, the value of q at any p from the demand curve D3D3 [eq. (1.6)].
From the above analysis it is obtained that the demand curve for a good would be obtained from its demand function. For example, the demand curves like (1.4)-(1.6) is obtained from the demand function (1.3). It is also clear from the above analysis that the demand function is made up of all the demand curves D1D1, D2D2, etc. in Fig. 1.7.
It is also noted that it obtains the value of q at the given values of y and p from Fig. 1.7 just as it is obtained from the demand function (1.3). For example, at y = 11 and p = 10, the demand function (1.3) gives q = 35. In this particular case, Fig. 1.7 gives: at y = 11, the demand curve is D1D1 [eq. (1.5)] and along this demand curve, obtains q = 35 at p = Rs 10.
From the demand function, the demand curve for the given values of the demand determinants other than the (own) price of the good can be obtained.
But a demand curve of the system cannot be obtained from the demand function. For example, the demand function (1.3), can be obtained from the demand curve at any value of y like the curve D1D1 [eq. (2.4)] at y = 10. But the demand function (1.3) cannot be obtained from the demand curve (1.4).