Income effect + substitution effect

Prove that price effect= Income effect + substitution effect i.e. P.E= I.E+ S.E.


Off the two goods if price of one good change and price of other good remain constant we see two things.

i) Change in income due to change in price.
ii) Consumption of one good increase instead of other good.

Preliminary budget line is AB, indifference curve is I2 and equilibrium is at point C.

Now if price of good x decrease (remaining price of good Y unchanged) we get new budget line AB1 and it touches indifference curve I2 at point y. So, new equilibrium is g. change in equilibrium from e to g due to change in price of x (y constant) is price effect shown by M1M3 in the figure.

Now due to reduction of price of good x money income of consumer increase. To reduce to money income by compensation variation we have to drew new price line CD parallel to AB1 that can reduce the income and touch primary indifference curve i.e. he get indifferent utility as was before. CD line, touches I1 at point f, so new equilibrium is f it means that when price of good x decreases [y constant] consumer would purchase more of x instead of y and it is substitution effect shown by M1M2 in the diagram.

Again, if we return back the income that we cut in compensation variation, the consumer reaches to equilibrium point g from f and it is the income effect as shown by M2M3 in the figure.

Hence, M1M3= M1M2 + M2M3
Price effect= Substitution effect + income effect

P.E= I.E + S.E (Proved)