The splitting of the price effect under Slutsky’s approach is illustrated in Fig. 5.49. The initial equilibrium of the consumer is at point ‘E’ at the point of contact of the indifference curve IC and the initial budget line AB. Now, suppose the price of commodity ‘X’ falls, the new equilibrium of the consumer occurs at point ‘F’ on the new budget line AB1. The price effect given by the movement from point ‘E’ to point ‘F’ is equal to X1X2 in quantity terms.
To isolate the substitution effect from the price effect, the money income of the consumer is by such an amount that he is in a position to purchase the original combination of the commodities. For this purpose, an imaginary line CD is drawn parallel to new budget line AB1, and passing through original equilibrium point ‘E’.
In this manner, an income equal to CA in terms of commodity ‘Y’ or DB, in terms of commodity ‘X’ has been taken away from the consumer. Now, the consumer will not choose to buy the combination of the two commodities represented by point ‘E’, but will opt for and settle at point ‘G’, where the imaginary budget line CD touches a indifference curve IC. This is on account of the fact that commodity ‘X’ becomes relatively cheaper and the consumer substitutes this commodity for commodity ‘Y’.
The consumer cannot move along the same indifference curve in this Slutsky substitution case, since the imaginary price line CD, on which the consumer has to remain is nowhere tangent to the indifference curve IC. Under Slutsky approach, what remains constant is only the apparent real income and not the real income of the consumer, as the consumer is able to move on to a higher indifference curve.
In Fig. 5.49, the movement from point ‘E’ to point ‘G’ is called Slutsky substitution effect, which is equal to X1,X3 in quantity terms like Hicksian substitution effect. Slutsky substitution effect of a price change is also always negative, since change in quantity demanded due to a substitution effect is opposite to the change in price of the commodity. The Slutsky substitution effect is due to the change in relative prices along, as the effect due to rise in real income has been eliminated by reducing money income equal to cost difference.
If now, the money income taken from the consumer is given back to him, he will move from point ‘G’ to point ‘F’ on the difference curve IC1. The journey from point ‘G’ to point ‘F’ is income effect, which is equal to X3X2 in quantity terms.
Now, we can say that
Price Effect (X1X2) = Substitution Effect (X1X3) + Income Effect (X3X2)
The decomposition of price effect into substitution effect and income effect for the rise in the price of commodity ‘X’ under this approach can be similarly explained.