Explanation:
a. To compute the percentage change in the overall price level using a method similar to the consumer price index (CPI), we first need to calculate the expenditure in each year for the fixed basket of goods (1 karaoke machine and 3 CDs).
For 2014:
Expenditure = (Quantity of Karaoke machines * Price of Karaoke machine) + (Quantity of CDs * Price of CD)
Expenditure = (10 * $40) + (30 * $10) = $400 + $300 = $700
For 2015:
Expenditure = (Quantity of Karaoke machines * Price of Karaoke machine) + (Quantity of CDs * Price of CD)
Expenditure = (12 * $60) + (50 * $12) = $720 + $600 = $1320
Now, we calculate the percentage change in the overall price level using the formula:
\[ \text{Percentage change} = \left( \frac{\text{Expenditure in 2015} - \text{Expenditure in 2014}}{\text{Expenditure in 2014}} \right) \times 100 \]
\[ \text{Percentage change} = \left( \frac{1320 - 700}{700} \right) \times 100 \]
\[ \text{Percentage change} = \left( \frac{620}{700} \right) \times 100 \]
\[ \text{Percentage change} ≈ 88.57\% \]
b. To compute the percentage change in the overall price level using a method similar to the GDP deflator, we use the formula:
\[ \text{Percentage change} = \left( \frac{\text{Nominal GDP in 2015} - \text{Nominal GDP in 2014}}{\text{Real GDP in 2014}} \right) \times 100 \]
For both the numerator and the denominator, we calculate the nominal GDP, which is the sum of the current year's expenditures:
For 2014:
Nominal GDP = Expenditure = $700
For 2015:
Nominal GDP = Expenditure = $1320
\[ \text{Percentage change} = \left( \frac{1320 - 700}{700} \right) \times 100 \]
\[ \text{Percentage change} = \left( \frac{620}{700} \right) \times 100 \]
\[ \text{Percentage change} ≈ 88.57\% \]
c. The inflation rate in 2015 is the same using both methods. This is because both methods essentially compare the change in the cost of the fixed basket of goods (1 karaoke machine and 3 CDs) from one year to the next relative to the cost in the base year (2014). Therefore, regardless of the specific method used, the result should be the same.
