Assuming that the following table describes a typical consumer’s complete budget, compute the item weights for each product.
Item: Quantity: Unit price:
Coffee 20 pounds $5
Tuition 1 year $4,000
Pizza 100 pizzas $8
DVD rental 75 days $5
Vacation 2 weeks $450
Q6 Suppose the prices listed in the table for Problem 5 changed from one year to the next, as shown below. Use the rest of the table to complete the average inflation rate.
Unit Price
____________________________
Item Last Year This Year % Change in Price X Item Weight = Inflation Impact
Coffee $5 $6_____ ______ _______
Tuition $4,000 $7,000 _____ ____ ____
Pizza $8 $10 _____ _____ _____
DVDrent $5 $10 ____ _____ ____
Vacation$450 $500 ____ ___ ____
Coffee 25 item weight
Tuition 4,000
Pizza 1,500
DVD rental 150
Vacation 250
To compute the item weights for each product, we need to calculate the percentage of the total budget that each item represents.
First, let's calculate the total budget:
20 pounds of Coffee * $5 per pound = $100
1 year of Tuition * $4,000 per year = $4,000
100 pizzas * $8 per pizza = $800
75 days of DVD rental * $5 per day = $375
2 weeks of Vacation * $450 per week = $900
Total budget = $100 + $4,000 + $800 + $375 + $900 = $6,175
Now, let's calculate the item weights for each product:
Coffee: $100 / $6,175 = 0.0162 (rounded to four decimal places)
Tuition: $4,000 / $6,175 = 0.6477 (rounded to four decimal places)
Pizza: $800 / $6,175 = 0.1296 (rounded to four decimal places)
DVD rental: $375 / $6,175 = 0.0607 (rounded to four decimal places)
Vacation: $900 / $6,175 = 0.1458 (rounded to four decimal places)
Now, we can use these item weights to calculate the inflation impact for each item:
Coffee:
% Change in Price = ($6 - $5) / $5 = 0.2 (or 20%)
Inflation Impact = 0.0162 * 0.2 = 0.0032 (rounded to four decimal places)
Tuition:
% Change in Price = ($7,000 - $4,000) / $4,000 = 0.75 (or 75%)
Inflation Impact = 0.6477 * 0.75 = 0.4858 (rounded to four decimal places)
Pizza:
% Change in Price = ($10 - $8) / $8 = 0.25 (or 25%)
Inflation Impact = 0.1296 * 0.25 = 0.0324 (rounded to four decimal places)
DVD rental:
% Change in Price = ($10 - $5) / $5 = 1 (or 100%)
Inflation Impact = 0.0607 * 1 = 0.0607 (rounded to four decimal places)
Vacation:
% Change in Price = ($500 - $450) / $450 = 0.1111 (or 11.11%)
Inflation Impact = 0.1458 * 0.1111 = 0.0162 (rounded to four decimal places)
Therefore, the item weights and inflation impacts are as follows:
Item: Item Weight % Change in Price Inflation Impact
Coffee: 0.0162 20% 0.0032
Tuition: 0.6477 75% 0.4858
Pizza: 0.1296 25% 0.0324
DVD rental: 0.0607 100% 0.0607
Vacation: 0.1458 11.11% 0.0162
To calculate the item weights for each product, we need to divide the total spending on each item by the total budget.
The total spending on each item can be calculated by multiplying the quantity of each item by its unit price.
Let's calculate the total spending on each item:
1. Coffee: 20 pounds * $5 = $100
2. Tuition: 1 year * $4,000 = $4,000
3. Pizza: 100 pizzas * $8 = $800
4. DVD rental: 75 days * $5 = $375
5. Vacation: 2 weeks * $450 = $900
The total budget is the sum of the total spending on all items:
Total budget = $100 + $4,000 + $800 + $375 + $900 = $6,175
Now, let's calculate the item weights for each product by dividing the total spending on each item by the total budget:
1. Coffee: $100 / $6,175 ≈ 0.0162 (rounded to four decimal places)
2. Tuition: $4,000 / $6,175 ≈ 0.6485
3. Pizza: $800 / $6,175 ≈ 0.1296
4. DVD rental: $375 / $6,175 ≈ 0.0607
5. Vacation: $900 / $6,175 ≈ 0.1459
Therefore, the item weights for each product are approximately as follows:
1. Coffee: 0.0162
2. Tuition: 0.6485
3. Pizza: 0.1296
4. DVD rental: 0.0607
5. Vacation: 0.1459