at a pricey + at +
It should also be noticed that for any demand curve the arc elasticity for a given arc is different according to which end of the arc is taken as the base, from which elasticity is measured. If the number of units demanded changes from x to (x +h), when the price changes from y to (y + k), the arc elasticity, measured from the base (x, y) is - t• while measured from the base (x + h, y + k) it is - h (y + kL_ But the difference between
§4. The distinction between point elasticity and arc elasticity is of no practical importance in qualitative statements, e.g., that a certain result is the more likely, the greater some elasticity of demand. But it is of practical importance in quantitative statements, e.g., that a certain result will folJow, if some elasticity of demand is greater than a certain definite amount. An illustration
is provided by Professor Pigou's formula, noted in the previous chapter, to the effect that an increase in the supply of a factor of production, its demand curve remaining unchanged, will increase its absolute share of the product, provided that its elasticity of demand is greater than one. Elasticity here is point elasticity, and the formula is strictly correct only when the proportionate increase in supply is so small as to be negligible. But this is obviously a case of no practical interest. When, as will be the case in reality, the increase of supply is of moderate amount, the relevant elasticity will be arc elasticity, and, as argued in the preceding chapter and in §3 of this Note, the formula should be amended, so as to read that the absolute share of the factor, whose supply increases, will be increased, provided that its elasticity of demand is greater than one plus the proportionate intreas~ in supply. Similarly, wh.en the supply of a factor decreases, its absolute share increases, provided that its elasticity of demand is less than one minus the proportionate decrease in supply.