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# Introduction to the compensating variation

DOI link for Introduction to the compensating variation

Introduction to the compensating variation book

# Introduction to the compensating variation

DOI link for Introduction to the compensating variation

Introduction to the compensating variation book

## ABSTRACT

To be more precise, it is so for what is sometimes called a normal good – one of which more is bought when the individual’s real income, or more generally his welfare, is increased. The so-called inferior good, of which less is bought when his welfare is increased, is exceptional (a favourite example ismargarine, at least when it is regarded as a poor man’s substitute for butter) and, unless otherwise stated, we may consider only normal goods, which will, of course, include collective goods. Why this must be so can be understood if we bear in mind that the CV12 is

the maximum a person would pay for a good that would increase his welfare, say, from his original indifference curve I1 to a higher indifference curve I2. This maximum sum he would pay will therefore be such as to return him to his original indifference curve I1. Conversely, his CV21 is the minimum sum he must receive, this being the (larger) sum that will maintain him on his I2 indifference curve. Now, if the welfare effect is normal (as posited), then whatever the price of

the good x, the individual buys more of it the higher his real income, which – on a diagram with real income y on the vertical axis and good x on the horizontal axis – would show that, for a given slope of the indifference curves, the amount of x taken on the higher indifference curve is larger. Therefore for the same amount of good x taken, the slope on the I2 curve is steeper than that on the I1 curve. It follows that if, with respect to each of these two indifference curves in turn,

we were to plot the increments of y, or real income, that have to be given up for successive and equal increments of x, the resulting ‘marginal indifference curve’ or what we may call the marginal valuation curve MV2, that is derived from the I2 indifference curve will at all points be above the MV1 curve derived, that is, from the I1 indifference curve. The area below the MV2 curve in Figure 7.1 is, of course, the measure of the

minimum sum a person would accept for having to part with the x2 amount of

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x, the corresponding smaller area below the MV1 curve being the measure of the largest sum he would pay for the x1 amount of x. This figure can also be used to trace the locus of amounts of x a personwould buy

as the price of x, from being so high that no x at all is bought, is gradually lowered to zero. This price-quantity locus is clearly that of the individual’s demand curve and, for all normal goods, it will lie diagonally between two marginal valuation curves, as shown: the higher MV2 curve being appropriate to the level of welfare reached when a person has, at the zero price, taken all the x that he wants; the lower MV1 curve being appropriate to his welfare before he buys any x at all.