Rationing is another field in which the difference curve technique can be applied. Suppose in non price rationing an equal quantity of the rationed commodity is allotted to each individual. Take two  P and Q is allotted  the same quantity is allotted to Q. P will be curve , and Q difference curve. But the absence of rationing P will move from R to  S and Q from R to N. which are both on higher indifference curves. This shows that the absence of rationing(leaving people too buy according to ‘heir tastes and means) is more advantageous than rationing. The  get  answer to the question whether the individual will prefer income tax or excise duty.

Income lax (Direct) "S excise duty (Indirect

Income lax (Direct) “S excise duty (Indirect

XI YI is the initial price line. The individual is in equilibrium at P on indifference curve CI . When an
excise duty is imposed, the price of X commodity shown along OX rises and the new price line is Y I X 2
and now the individual is ill equilibrium at Q 011 indifference curve . It is dear that he is now buying a smaller quantity of X. To buy this quantity he has to pay SQ amount of money. If he bought no X at all. he would have. pent SN amount is the amount of tax.

In case he paid income-tax equal to 1 Q (= Y I Y 2 ), he is left with Y20 income after paying income-tax. Draw a new price . Indifferent. once curve C I touches this new price line at R. Indifference curve C I is at a higher level than C , which shows that the tax-payer is hurt duty than by income-tax Excise duty put.In a lower indifference curve.