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Answer to Question #60038 in Other Economics for AG

Question #60038
The average consumer divides his expenditure between food, clothing, accommodation and transport in the ratio 2 : 1 : 4 : 3. During the course of a year, the price of food falls by 2 %, the price of clothing increases by 4 %, the price of accommodation increases by 10 % and the price of transport remains constant. Assuming that the weights of a price index reflect the expenditure of the average consumer, what is the increase in the index over the year?
A 2.5 % B 4 % C 10 % D 12 %

At the start of 2009, a worker earned $100 a week. In 2009, the Retail Price Index (RPI) rose 4 % and his average wage rose 7 %. In 2010, the RPI fell 3 % and his wage fell 2 %. What happened to his real wage between the start of 2009 and the end of 2010?
It fell by less than 5 %.
It fell by more than 5 %.
It rose by less than 5 %.
It rose by more than 5 %.
Expert's answer
The average consumer divides his expenditure between food, clothing, accommodation and transport in the ratio 2 : 1 : 4 : 3. During the course of a year, the price of food falls by 2 %, the price of clothing increases by 4 %, the price of accommodation increases by 10 % and the price of transport remains constant. The increase in the index over the year is -2%*2/10 + 4%*1/10 + 10%*4/10 + 0%*3/10 = -0.4% + 0.4% + 4% + 0% = 4%.
So, the right answer is B 4 %.

At the start of 2009, a worker earned $100 a week. In 2009, the Retail Price Index (RPI) rose 4% and his average wage rose 7%. In 2010, the RPI fell 3% and his wage fell 2%. The real wage in 2009 increased by 7% - 4% = 3%. In 2010 the real wage decreased by 2% - 3% = -1%, so it really increased by 1%. So, the total increase in the real wage is 3% + 1% = 4%. So, the right answer is C. It rose by less than 5 %.

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