Substitution effect

Substitution effect relates to the change in the quantity demanded resulting from a change in the price of good-Y due to the substitution of relatively cheaper good for a dearer one,  while keeping the price of the other good and real income and tastes of the consumer constant.
                                   
                       HICK'S SUBSTITUTION EFFECT

Prof.  Hicks has explained the substitution effect independent of the income effect through compensating variation in income. The substitution effect is the increase in the quantity bought as the price of the commodity falls, after adjusting income so as to keep the real purchasing power of the consumer the same as before. This adjustment in income is called COMPENSATING VARIATION and is shown graphically by a parallel shift of the new budget line until it becomes tangent to the initial IC.  Thus,  on the basis of the methods of compensating variation, the substitution effect measures the effect of change in the relative price of a good with real income constant. The increase in the real income of the consumer as a result of fall in the price of,  say Good-X,  is so withdrawn that he is neither better off nor worse-off than before.

DIAGRAMMATIC EXPLANATION

****DRAW DIAGRAM
The substitution effect is explained in the above figure where the original budget line is PQ with equilibrium at point R on the IC curve I1.at R,  the consumer is buying OB of X and BR of Y. Suppose the price of good-X falls so that his new budget line is PQ1. With the fall in the price of Good-X,  the real income of the consumer increases. To make the compensating variation in income or to keep the consumer's real income constant, take away the increase in his income equal to PM of Good-Y or Q1N of Good-X so that his budget line PQ1 shifts to the left as MN and is oparallel to it.  At the same time, MN is tangent to the original IC I1 but at point H where the consumer buys OD of X and DH of Y. Thus PM of Y or Q1N of X represents the compensating variation in income, as shown by the line MN being tangent to the curve I1 at point H. Now the consumer substitutes X for Y and moves from point R to H or the horizontal distance from B to D. This movement is called the SUBSTITUTION EFFECT.  The S. E.  Is always NEGATIVE because when the PRICE of a good FALLS ( OR RISES), MORE (OR LESS)  of it would be purchased,  the real income of the consumer and price of the other good remaining constant.

In other words,  THE RELATION BETWEEN PRICE AND QUANTITY DEMANDED BEING INVERSE,  SUBSTITUTION EFFECT IS ALWAYS NEGATIVE. 

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