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Question 1121299: In order to obtain an increase in the price of its product higher than the inflation of the period, a factory that sold chocolate biscuits in packs of 200 g replaced these packages with others of 180 g, and started to sell the product with reduction of 4% of the original price. Assuming that the inflation rate of the period was constant and equal to 0.5% per month, at the end of the first month of the beginning of this practice, the real increase in the price of the kilogram of this product was:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! a 200 gram packet sold for x dollars before the increase in price.
after the increase in price, a 180 gram packet sold for .96 * x.
the price per gram went from x/200 to .96x/180.
the new price per gram divided by the old price per gram is .96x/180 divided by x/200.
that's the same as .96x/180 * 200/x.
the x in the numerator and denominator cancels out and the ratio of the new price to the old price becomes .96/180 * 200 which is equal to 1.066666667.
the inflation rate is equal to .5% per month.
this means that what cost y dollars today will cost 1.005 * y dollars next month.
this means your purchasing power next month in today's dollars is divided by 1.005.
therefore the increase in the price per gram is offset by the decrease in purchasing power.
you get 1.066666667 / 1.005 = a real increase in price that gives you a new price to old price ratio of 1.061359867 rather than 1.066666667.
let's assume 200 grams of chocolate cost 18.00 today.
that's a cost per gram of .09 = 9 cents.
.96 * 18.00 = 17.8 for 180 grams.
that's a cost per gram of .096 = 9.6 cents.
the increase in price is 9.6 / 9 = 1.0666666667.
if it was all profit and there was no inflation, you could buy 9.6 cents worth of goods next month for every gram of chocolate you sold when you previously were only able to buy 9 cents of goods.
your purchasing power increase by a ratio of 9.6/9 = 1.06666666667
because of inflation, however, what would have cost 9.6 cents now costs 9.6 * 1.005 = 9.648 cents.
whereas before, your 9.6 cents bought 100% of that something that cost 9.6 cents today, can only buy 9.6 / 9.648 = .9950248756 of that same something next month.
in other words, your purchasing power is now only .9950248756 times what it was without inflation.
therefore your increase of purchasing power from 9 to 9.6 cents is now only an increase in purchasing power of 9 to 9.6 * .9950248756 = 9.552238806 cents.
9.552238806 / 9 = an increase in purchasing power of 1.061359867 times what it was today in today's dollars.
1.066666666667 / 1.005 = 1.061359867.
so, if i did this right, your solution is:
the real increase in the price per kilogram of this product was .061359867 or 6.1359867% with inflation, rather than .0666666667 = 6.666666667% without inflation.
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