CH. 8 COMPARISONS OF PURCHASING POWER 115

and rice are 50 per cent cheaper in the first than inthe second ; then

price of a unit of beef and a unit of whisky in 1st positionprice of ditto in 2nd position

_ price of a unit of rice and a unit of coffee in 1st positionprice of ditto in 2nd position

(our units being chosen so that expenditure is equallydivided between beef and whisky in the first positionand between rice and coffee in the second position).The assumption that coffee and rice are not consumedat all in the first position, nor beef and whisky in thesecond, is not essential to the argument and is onlyintroduced for simplicity of statement. Substantiallythe same equation would hold if we were to giverelatively small weights to coffee and rice in the firstposition, and to beef and whisky in the second position.Now, if we were to neglect the conditions required forthe Method of Limits or were to suppose that the ideasunderlying Professor Fisher’s ideal formula were uni-versally valid, we could conclude from the above withcomplete precision that the purchasing power of moneyin the position where people mainly consume Beef andWhisky is exactly the same as in the position wherethey mainly consume Rice and Coffee. Yet this con-clusion might be quite wrong. Suppose, for example,that in the second position rice is consumed in prefer-ence to beef, in spite of rice being relatively dearerthan in the first position, because the climate requiresit, so that consumers prefer rice ; whereas coffee isconsumed in the second position in preference to whiskymerely because it is cheaper, so that whisky would beconsumed if it was as cheap compared with coffee as itwas in the first position. If we knew the money-incomes of “ similar ” persons in the two positions,we might find that the purchasing power of money wasmuch lower in the second position than in the first.