Suppose that the 2022 price of corn were to rise to $8.60
per bushel, but that the price of a digital device were to fall to $275
.
The quantities of the two commodities remain the same, however. How would these changes affect the value of the 2022 price index?
Part 2
Holding the quantities of the two commodities the same, a rise in the 2022 price of corn to $8.60
and a fall in the price of a digital device to $275
would cause the value of the 2022 price index to
increase. This is because the price of corn has increased, indicating inflation, while the price of the digital device has decreased, indicating deflation. The price index takes into account the prices of a basket of goods and services, and a change in the prices of either commodity can have an impact on the overall index value. With the increase in corn prices and decrease in digital device prices, the price index would reflect an increase in the overall cost of living, as consumers would need to pay more for basic food items like corn, and less for electronics.
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Question content area right
Part 1
Corn
Digital Devices
Totals
Market Basket Quantity
100 bushels
2
2012 Price per Unit: corn=$4, device=$450
Cost of Market Basket in 2012: corn=$400, device=$900= total=$1,300
2022 Price per Unit: corn=$8 device=$350
Cost of Market Basket in 2022: corn=$800, device=$700=total=$1,500
the value of the 2022 price index to rise to?
.
To calculate the value of the 2022 price index, we need to use the following formula:
2022 Price Index = (Cost of Market Basket in 2022 / Cost of Market Basket in 2012) x 100
Substituting the given values, we get:
2022 Price Index = ($1,500 / $1,300) x 100 = 115.38
Therefore, the value of the 2022 price index would rise to 115.38.
To determine how these changes would affect the value of the 2022 price index, we need to use the formula for a price index. The price index is calculated by dividing the price of a basket of goods in a specific year by the price of the same basket of goods in a base year, then multiplying by 100.
Let's assume the base year is 2021 and the basket of goods contains one bushel of corn and one digital device.
Part 1:
If the price of corn rises to $8.60 per bushel and the price of a digital device falls to $275, but the quantities remain the same, the value of the 2022 price index would be:
[(Price of corn in 2022 / Price of corn in base year) + (Price of digital device in 2022 / Price of digital device in base year)] * 100
= [(8.60 / Price of corn in base year) + (275 / Price of digital device in base year)] * 100
Since we don't have information about the prices in the base year, we cannot calculate the exact value of the price index.
Part 2:
Holding the quantities of the two commodities the same, if the price of corn rises to $8.60 and the price of a digital device falls to $275, the value of the 2022 price index would be calculated in the same way as above. However, without information about the prices in the base year, we cannot calculate the exact value of the price index.
To determine how these changes would affect the value of the 2022 price index, we first need to understand what a price index is and how it is calculated.
A price index is a measure of the average price level of a basket of goods and services over time. It is often used to track inflation or changes in the cost of living. The most commonly used price index is the Consumer Price Index (CPI), which measures the price changes for a predetermined basket of goods and services that are representative of the average consumer's purchases.
The formula for calculating the price index is as follows:
Price Index = (Current Year Cost / Base Year Cost) * 100
Now let's analyze the impact of the changes in corn and digital device prices on the 2022 price index:
1. If the price of corn rises to $8.60 per bushel: Assuming the quantity of corn remains the same, the cost of corn in the current year (2022) will increase compared to the base year. This increase will contribute to a higher overall price level in the index.
2. If the price of a digital device falls to $275: Assuming the quantity of digital devices remains the same, the cost of digital devices in the current year (2022) will decrease compared to the base year. This decrease will contribute to a lower overall price level in the index.
To determine the overall impact on the 2022 price index, we need to consider the relative weights or importance of corn and digital devices in the basket of goods and services used for calculating the index. The weights are typically based on consumer spending patterns.
If the relative importance of corn in the index is higher than that of digital devices, the rise in corn prices will have a larger effect on the index, resulting in a higher value. Conversely, if the relative importance of digital devices is higher, the fall in their prices will have a larger effect, resulting in a lower value.
Without information on the specific weights of corn and digital devices in the price index, we cannot determine the exact impact on the 2022 price index. However, based on the information given, we can infer that the rise in corn prices will likely have a greater influence on the index than the fall in digital device prices, assuming all other factors remain constant.
In conclusion, the changes in the prices of corn and digital devices would affect the value of the 2022 price index depending on the relative weights of these commodities in the index.