Question

table 2-4.1
prices of three goods compared with base-year price

	quantity bought in base year	unit price in base year	spending in base year	unit price in year 1	spending in year 1	unit price in year 2	spending in year 2
flash drive	40	$6.00		$5.00		$4.00
six - pack of soda	60	$1.50		$2.00		$2.50
total	-	-		-		-

fill in the blanks in table 2 - 4.1.

1. how much would $100 of goods and services purchased in the base year cost in year 1?

1. what was the percentage increase in prices in this case? show your calculations.

the rate of change in this index is determined by looking at the percentage change from one year to the next. if, for example, the cpi were 150 in one year and 165 the next, then the year - to - year percentage change is 10 percent. you can compute the change using this formula:

price change = \\(\frac{\text{change in cpi}}{\text{beginning cpi}}\times100\\).

1. what is the percentage increase in prices from the base year to year 2?

Answer:

Sub - question 1: Fill in the blanks in Table 2 - 4.1

To fill in the table, we calculate the spending for each good in each year (Base year, Year 1, Year 2) and then the total.

Step 1: Calculate Spending in Base Year

• Whole pizza: Quantity = 30, Unit price in base year = $5.00. Spending = \(30\times5 = 150\)
• Flash drive: Quantity = 40, Unit price in base year = $6.00. Spending = \(40\times6=240\)
• Six - pack of soda: Quantity = 60, Unit price in base year = $1.50. Spending = \(60\times1.5 = 90\)
• Total (Base year): \(150 + 240+90=480\)

Step 2: Calculate Spending in Year 1

• Whole pizza: Quantity = 30, Unit price in Year 1 = $7.00. Spending = \(30\times7 = 210\)
• Flash drive: Quantity = 40, Unit price in Year 1 = $5.00. Spending = \(40\times5 = 200\)
• Six - pack of soda: Quantity = 60, Unit price in Year 1 = $2.00. Spending = \(60\times2=120\)
• Total (Year 1): \(210 + 200+120 = 530\)

Step 3: Calculate Spending in Year 2

• Whole pizza: Quantity = 30, Unit price in Year 2 = $9.00. Spending = \(30\times9=270\)
• Flash drive: Quantity = 40, Unit price in Year 2 = $4.00. Spending = \(40\times4 = 160\)
• Six - pack of soda: Quantity = 60, Unit price in Year 2 = $2.50. Spending = \(60\times2.5=150\)
• Total (Year 2): \(270+160 + 150=580\)

Sub - question 2: How much would $100 of goods and services purchased in the base year cost in Year 1?

Step 1: Find the CPI - like index for base year and Year 1

Let the base - year total spending be \(C_0 = 480\) and Year 1 total spending be \(C_1=530\). The index for base year \(I_0 = 100\) (by definition, since it's the base year). The index for Year 1 \(I_1\) is calculated as \(I_1=\frac{C_1}{C_0}\times100=\frac{530}{480}\times100\approx110.42\)

Step 2: Calculate the cost in Year 1 for $100 of base - year goods

If $100 of base - year goods cost $100 in base year, in Year 1 it would cost \(100\times\frac{I_1}{I_0}=100\times\frac{530}{480}\approx110.42\)

Sub - question 3: What was the percentage increase in prices in this case?

Step 1: Identify the formula for percentage change

The formula for percentage change in CPI (or price level) is \(\text{Percentage change}=\frac{I_1 - I_0}{I_0}\times100\), where \(I_0\) is the initial index (base year, \(I_0 = 100\)) and \(I_1\) is the new index (Year 1, \(I_1=\frac{530}{480}\times100\approx110.42\))

Step 2: Calculate the percentage change

\(\text{Percentage change}=\frac{110.42-100}{100}\times100=\frac{10.42}{100}\times100 = 10.42\%\) (using the values from sub - question 2, where \(I_0 = 100\) and \(I_1\approx110.42\))

Sub - question 4: What is the percentage increase in prices from the base year to Year 2?

Step 1: Calculate the index for Year 2

The index for Year 2 \(I_2=\frac{C_2}{C_0}\times100=\frac{580}{480}\times100\approx120.83\)

Step 2: Calculate the percentage change

Using the formula \(\text{Percentage change}=\frac{I_2 - I_0}{I_0}\times100\), with \(I_0 = 100\) and \(I_2\approx120.83\)

\(\text{Percentage change}=\frac{120.83 - 100}{100}\times100=\frac{20.83}{100}\times100=20.83\%\)

Final Answers (for each sub - question):

1. Filled table (spending columns):

• Base year: Whole pizza = 150, Flash drive = 240, Six - pack of soda = 90, Total = 480
• Year 1: Whole pizza = 210, Flash drive = 200, Six - pack of soda = 120, Total = 530
• Year 2: Whole pizza = 270, Flash drive = 160, Six - pack of soda = 150, Total = 580

1. Cost in Year 1 for $100 of base - year goods: \(\approx\$110.42\)
2. Percentage increase (Year 1 from base year): \(\approx10.42\%\)
3. Percentage increase (Year 2 from base year): \(\approx20.83\%\)