As an example of a price index, consider the A.C.D.P.I. (a fictitious price index). The associated basket of goods is:


Good Price
Coffee $8/lb.
Bread $1/loaf
Tea $15/lb.
Aspirin $2/bottle
Cola $6/case

A. If the price of coffee doubles, what is the resulting percentage change in the price level? (2 points)
16/8*100=200%
B. If the price of bread doubles, what is the resulting percentage change in the price level? (2 points)
2/1*100=200%
C. Why is the effect of a 100% increase in the price of coffee so much greater than the effect of a similar change in the price of bread? (4 points)

The problem I'm having is with part C. I don't see a difference in price when coffee doubles or when bread doubles. I see that there is a 200% increase for both

What you just did was calculate what the percent change for both prices was. What you need to do is divide the summation of all prices*quantities for new prices and divide that by old prices (and then multiply that number by 100) to get the percentage change in price level

In part C, the question is asking why the effect of a 100% increase in the price of coffee is so much greater than the effect of a similar change in the price of bread.

While it may seem that both scenarios result in a 200% increase, there is actually a fundamental difference in their impact on the price level. This difference is related to the weight or significance of each good in the basket of goods.

In the given scenario, the basket of goods consists of coffee, bread, tea, aspirin, and cola. The associated prices of these goods determine the overall price level.

When the price of coffee doubles, it has a significant impact on the overall price level because coffee is an important component of the basket. The weight assigned to coffee in the calculation of the price index is likely relatively high, meaning that it has a larger influence on the overall index.

On the other hand, bread, although also experiencing a 100% increase in price, might have a lower weight or significance in the basket of goods. Therefore, the impact of a similar price increase in bread is relatively smaller compared to coffee.

In essence, the effect of a 100% increase in the price of coffee is greater because coffee has a higher weight or significance in the price index compared to bread.

In the given scenario, the problem might seem confusing at first because both coffee and bread have doubled in price resulting in a 200% increase. However, the question asks why the effect of a 100% increase in the price of coffee is much greater than a similar change in the price of bread.

To understand this, let's focus on the calculation of the price index. A price index measures the average percentage change in the prices of a basket of goods over time. In this case, we are considering the initial prices of the goods in the basket:

Coffee: $8/lb
Bread: $1/loaf
Tea: $15/lb
Aspirin: $2/bottle
Cola: $6/case

Now, let's calculate the initial price level using the given prices:

Price level = (8 + 1 + 15 + 2 + 6) / 5 = 32 / 5 = 6.4

After coffee doubles in price, the new price becomes $16/lb. To calculate the new price level, we need to add up the new prices of all goods in the basket:

New price level = (16 + 1 + 15 + 2 + 6) / 5 = 40 / 5 = 8

Now, let's calculate the percentage change in the price level:

Percentage change = ((New price level - Initial price level) / Initial price level) * 100
= ((8 - 6.4) / 6.4) * 100
= (1.6 / 6.4) * 100
= 0.25 * 100
= 25%

So, when the price of coffee doubles, the resulting percentage change in the price level is 25%.

Now, let's consider the case when bread doubles in price. The new price of bread becomes $2/loaf.
To calculate the new price level:

New price level = (8 + 2 + 15 + 2 + 6) / 5 = 33 / 5 = 6.6

Percentage change = ((New price level - Initial price level) / Initial price level) * 100
= ((6.6 - 6.4) / 6.4) * 100
= (0.2 / 6.4) * 100
≈ 3.13%

So, when the price of bread doubles, the resulting percentage change in the price level is approximately 3.13%.

Comparing the two results, we can see that even though the percentage increase in price is the same for coffee and bread (both doubling), the impact on the overall price level is different. This difference is due to the starting weights of coffee and bread in the price index.

In the given scenario, coffee initially has a higher price compared to bread, which means it carries more weight in the overall price level. So, when the price of coffee doubles, it has a larger impact on the price level as compared to the doubling of the price of bread. This explains why the effect of a 100% increase in the price of coffee is much greater than a similar change in the price of bread.

I hope this explanation clarifies the difference in the effect of price changes for coffee and bread in terms of the overall price level!