Thus, this imaginary budget line reflects the new fallen price. When combination ‘E’ is bought at the lower price of combination ‘G’, there is a reduction in cost, which is the ‘cost difference’.

The old combination ‘E’, now on imaginary budget line CD is still affordable to the consumer. All combinations to the left of point ‘E’ on the segment CE were available to him in the initial situation (as these all fall within triangle OAB) and were rejected in favour of combination ‘E’ The assumption of consistency requires that the consumer will either choose combination ‘E’ or what is more likely, he will choose a combination on segment ED.

If the consumer chooses combination ‘F, the movement from point ‘E’ to point ‘F’ indicates the substitution effect. The consumer always substitutes relatively cheaper commodity ‘X’ for the expensive one (commodity ‘Y’).

It can never be negative. So, point ‘F’ cannot lie to the left of point ‘E’. When points ‘E’ and ‘F’ happen to coincide, the substitution effect will be equal to zero. In such situation, the whole of the price effect will be equal to income effect.

When the income equal to cost difference variation is restored back to the consumer, he buys more of commodity ‘X’ (given a positive income elasticity of demand, which means with an increase in income, quantity demanded will increase). Now, the new equilibrium point ‘G’ lies vertically to the right of point ‘F’.

The movement from point ‘F’ to point ‘G’ represents income effect. The income effect, given the positive income elasticity of demand will reinforce the substitution effect. In quantity terms, price effect, substitution effect and income effect are shown as increase in the demand for commodity ‘X’ from OX1 to OX3, from OX1 to OX2 and from OX2 to OX3 respectively.

Therefore,

Price Effect = Substitution Effect + Income Effect

Or, X1 X3 = X1 X2 + X2 X3

The mathematical sign of all the three effects is negative. Thus, when the price of a commodity falls, the quantity demanded rises. This makes the demand curve for a commodity downward sloping.

Hence, the law of demand is established. A negative income effect or a positive income elasticity of demand for a commodity is a necessary condition for the validity of the law of demand and a negative substitution effect is sufficient to make demand curve of a commodity downward sloping.