1. 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 Quantity Price
Coffee 3 lb $8/lb
Bread 3 loaves $1/loaf
Tea 1 lb $15/lb
Aspirin 1 200-tablet bottle $2/bottle
Cola 1 case $6/case
A. If the price of coffee doubles, what is the resulting percentage change in the
price level? (2 points)
B. If the price of bread doubles, what is the resulting percentage change in the
price level? (2 points)
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)
D. Assume that the mix of goods in a basket is kept constant for long periods. If
the price of one good rises very rapidly over several years, what will happen to
the relative importance of the other goods in the basket? Is this a problem? (6
points)
E. If the price of coffee increases, we get a positive rate of inflation, even if no
other price rises. Is this really inflation? Explain. (6 points)
Understand that tutors won't do your work for you.
You need to indicate exactly what you have done to solve each problem and where you're running into trouble.
A. To calculate the resulting percentage change in the price level when the price of coffee doubles, we need to compare the original price level to the new price level.
First, we need to calculate the original price level (OP) by multiplying the quantity of each good by its price and adding them up:
OP = (3 lb x $8/lb) + (3 loaves x $1/loaf) + (1 lb x $15/lb) + (1 bottle x $2/bottle) + (1 case x $6/case)
OP = $24 + $3 + $15 + $2 + $6
OP = $50
Next, we need to calculate the new price level (NP) when the price of coffee doubles. Since coffee represents 3 lb of the basket, the new price for coffee would be $16/lb:
NP = (3 lb x $16/lb) + (3 loaves x $1/loaf) + (1 lb x $15/lb) + (1 bottle x $2/bottle) + (1 case x $6/case)
NP = $48 + $3 + $15 + $2 + $6
NP = $74
To calculate the percentage change, we can use the formula:
Percentage Change = ((NP - OP) / OP) x 100
Percentage Change = (($74 - $50) / $50) x 100
Percentage Change = ($24 / $50) x 100
Percentage Change = 48%
Therefore, the resulting percentage change in the price level when the price of coffee doubles is 48%.
B. To calculate the resulting percentage change in the price level when the price of bread doubles, we use a similar process.
The original price level (OP) remains the same as in part A:
OP = $50
The new price level (NP) is calculated by doubling the price of bread to $2/loaf:
NP = (3 lb x $8/lb) + (3 loaves x $2/loaf) + (1 lb x $15/lb) + (1 bottle x $2/bottle) + (1 case x $6/case)
NP = $24 + $6 + $15 + $2 + $6
NP = $53
Percentage Change = ((NP - OP) / OP) x 100
Percentage Change = (($53 - $50) / $50) x 100
Percentage Change = ($3 / $50) x 100
Percentage Change = 6%
Therefore, the resulting percentage change in the price level when the price of bread doubles is 6%.
C. The effect of a 100% increase in the price of coffee is greater than a similar change in the price of bread because coffee has a higher weight or quantity in the basket. In this particular example, the basket contains 3 lb of coffee and 3 loaves of bread. When the price of coffee doubles, it affects a larger portion of the basket, leading to a larger impact on the overall price level. On the other hand, bread represents a smaller portion of the basket, so a similar change in its price has a lesser impact on the overall price level.
D. If the price of one good in the basket rises very rapidly over several years while the mix of goods remains constant, its relative importance within the basket will increase. This means that the weight or quantity of that good in the basket will become larger, while the weight of other goods may become relatively smaller.
This could potentially be a problem for the price index because it may not accurately reflect the changing consumption patterns and preferences of individuals. If a good becomes significantly more expensive but its weight in the index does not change, it might not fully capture the true impact on the cost of living. To address this, it is important to regularly update the basket of goods and their weights to reflect current consumption patterns.
E. Inflation refers to a sustained increase in the general price level of goods and services in an economy over time. If the price of coffee increases, it contributes to the overall price level, but it does not necessarily represent inflation on its own unless it is accompanied by a broad-based increase in prices across multiple goods and services.
To determine whether there is true inflation, we need to consider the changes in the prices of various goods and services, not just a single item. Inflation is typically measured using a price index, like the consumer price index (CPI), which tracks the average change in prices of a basket of goods and services. If the overall price level, as represented by the price index, consistently increases over time, then it is considered inflation.
In the given example, if the price of coffee increases and no other prices rise, it can contribute to a positive rate of inflation in the A.C.D.P.I index but may not necessarily represent broader inflation in the economy.