Suppose that in a simple economy people consume only three goods, as shown below
ID: 1132792 • Letter: S
Question
Suppose that in a simple economy people consume only three goods, as shown below with their prices in each year, and the economy-wide consumption in each year.
a) What is the percentage change in the price of marbles? Of sunglasses? And of fidget spinners?
b) From 2017 to 2018, did sunglasses become more or less expensive, relative to fidget spinners?
Use the 2017 quantities as the fixed basket of goods and services for the CPI calculations to follow.
c) Calculate CPI in 2017, using 2017 as the base year.
d) Calculate CPI in 2018, using 2017 as the base year.
e) Calculate the CPI rate of inflation between 2017 and 2018.
Suppose that between 2017 and 2018 all wages rose by exactly the inflation rate calculated above.
f) In 2018, would people be better off or worse off than in 2017? Or something else? Explain.
Year Marbles Sunglasses Fidget Spinners 2017 price $10 $125 $4.50 2017 quantity 100 10 200 2018 price $12 $140 $5 2018 quantity 110 12 180Explanation / Answer
a) % Change in price of marbles = (2/10)*100 = 20%
% Change in price of sunglasses = (15/125)*100 = 12%
% Change in price of fidget spinners = (0.5/4.5)*100 = 11.1%
b) From 2017 to 2018, the price of sunglasses became more expensive relative to fidget spinners. To elaborate, $1,000 could have been used to purchase 8 units of sunglasses in 2017 and this declined to 7.1 units in 2018. This represents a 10.7% decline in units purchased relative to 2017.
Similarly, $1,000 could have been used to purchase 222.2 units of fidget spinners in 2017 and using the same amount of $1,000, one could purchase 200 units of fidget spinners. This represents a 10% decline in units purchased relative to 2017.
Therefore, relative to fidget spinners, sunglasses because more expensive.
c) 2017 CPI using 2017 as Base Year = (10*100) + (125*10) + (4.5*200) = 3,150
d) 2018 CPI using 2017 as Base Year = (12*100) + (140*10) + (5*200) = 3,600
e) CPI rate of inflation = ((3,600-3,150)/3,150)*100 = 14.3%
f) With a same consumption basket, an increase in wages would be completely offset by an increase in price of goods. Therefore, the purchasing power for individuals would remain the same.
However, the weightage of goods consumed is likely to make a difference. Just as an example, if an individual purchases more marbles, which saw an increase in price by 20%, the personal inflation can be potentially higher than the broad inflation of 14.3%. This would imply a decline in purchasing power.
In the same way, if a person purchases more of fidget spinners, which saw price increase of 11.1%, his personal inflation is likely to be lower than the brroad CPI inflation of 14.3%. This might result in an increase in purchasing power for that individual.
Bottomline: The answer to (f) depends on an individuals product basket and the inflation in the product that has higher weightage in his/her consumption basket.
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