The substitution effect is the effect on the demand of a commodity due to a change in the relative price of the commodity, the real income of the consumer remaining constant. It can be further explained with the help of the following figure:
In the above figure, initially, the consumer is equilibrium at point E1 where the budget line AB just tangent to the indifference curve IC1 at point E1 where the consumer consumes OX1 units of X and OY1 units of Y. When there is a decrease in the price of X, the budget line rotates toward rightward to AB’. The real income of the consumer also increases. As per the Hicksian approach, we need to reduce the consumer’s money income to bring her or him to the initial real income level. This adjustment in money income shifts the budget constraint backward and it is a parallel shift as shown by the price line AB”. The budget line AB” is just tangent to the indifference curve IC1 at point E2 where the consumer consumes OX2 units of X and OY2 units of Y. Also, the consumer substitutes X1X2 units of X for Y1Y2 units of Y.