Supply and demand/Tutorials

For practical purposes, and in the teaching of economics at the basic level, the law of supply and demand is normally taken as given - almost a statement of the obvious. Closer examination, reveals some features that are so far from obvious as to have been a matter of prolonged academic controversy.

Although not necessary for the understanding of the concepts, the graphical depiction of the law of supply and demand and the mathematical expressions of elasticities are presented in this tutorial because of their familiarity to students of economics.

The supply and demand functions

The demand function

The converse of the premise stated in the article is that the less of a thing that a person possesses, the more he is prepared to pay to acquire a little more of it. That means that, as price is increased, a progressively larger increase is needed to produce a given reduction in demand. Thus the slope of the price/demand curve increases as price is increased and falls as price is reduced - leading to a curve that is concave when viewed from above. However, it can be treated as a straight line without any loss of meaning when it is used in depicting the operation of the law of supply and demand.

The supply function

The assumption that the price of a product rises with the amount supplied can be justified by reference to the law of diminishing returns, but there has been a lengthy debate about how generally that law can be assumed to apply. Marshall's pupil Arthur Pigou argued that to get a true picture, it was necessary to "step outside" the supplying industry, and consider the effect of its supply upon other industries. Jacob Viner developed the argument, using Wieser's law to demonstrate that in calling upon inputs that would otherwise be used elsewhere, the supplying industry would drive up their prices , but Lionel Robbins used Walras' law, and the concept of general equilibrium to challenge that interpretation . Most economics text books accept Viner's thesis, but a recent review of the controversy that followed has concluded that the question remains unresolved.

Graphical representations

The basic diagram

PD Image

This is the stylised representation of the law of supply and demand that is often used for teaching purposes.

As it stands it adds nothing to Marshall's simple statement, but it is used as an introduction to the use of such diagrams to illustrate the concepts of consumer's and supplier's surplus, and to demonstrate the impact upon them of taxes and subsidies, as in the following diagram.

Consumers surplus and the effect of tax

PD Image

The algebra of elasticity

Price elasticity

The change in the quantity q of a product that is demanded, in response to change in its price, p is expressed in elasticity terms as:

$e_{p}={\frac {\delta q/q}{\delta p/p}}$

Income elasticity

Similarly, the demand response to a change in consumer's income, I is expressed as :

$e_{I}={\frac {\delta q/q}{\delta I/I}}$

Cross elasticity

The change in the quantity q_a of product a that is demanded, in response to change in the price, p_b of substitute product b is expressed in elasticity terms as:

$e_{c}={\frac {\delta q_{a}/q_{a}}{\delta p_{b}/p_{b}}}$

References

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