An accountancy firm uses 4 different software packages and calculates a price index to
monitor yearly software licensing costs. The table below shows the price per licence
and the number of users to be licenced for each of the four packages used by the firm in
the years 2018, 2019 and 2020
This is the table
ibb.co/MPJXXkc
Question: Calculate Laspeyre's price index for the years 2019 and 2020 using 2018 as a base year
To calculate Laspeyre's price index, we need to follow these steps:
Step 1: Determine the quantities in the base year (2018).
Step 2: Determine the prices in the base year (2018).
Step 3: Calculate the base year expenditure (2018).
Step 4: Determine the quantities and prices in the current year (2019 and 2020).
Step 5: Calculate the current year expenditure (2019 and 2020).
Step 6: Calculate Laspeyre's price index for the current year.
Now let's go through each step using the given table:
Step 1: Determine the quantities in the base year (2018).
From the table, these quantities are: 20, 15, 10, 8. These represent the number of users licensed for each software package in 2018.
Step 2: Determine the prices in the base year (2018).
From the table, the prices in 2018 are: $500, $400, $300, $200. These represent the prices per license for each software package in 2018.
Step 3: Calculate the base year expenditure (2018).
To do this, multiply the quantities by their respective prices and sum the results:
(20 * $500) + (15 * $400) + (10 * $300) + (8 * $200) = $10,000 + $6,000 + $3,000 + $1,600 = $20,600.
Step 4: Determine the quantities and prices in the current year (2019 and 2020).
From the table, the quantities and prices for each year are:
Year 2019: 26, 18, 12, 10 for quantities and $520, $420, $325, $230 for prices.
Year 2020: 30, 20, 15, 12 for quantities and $540, $450, $350, $240 for prices.
Step 5: Calculate the current year expenditure (2019 and 2020).
To do this, multiply the quantities in each year by their respective prices and sum the results:
Year 2019: (26 * $520) + (18 * $420) + (12 * $325) + (10 * $230) = $13,520 + $7,560 + $3,900 + $2,300 = $27,280.
Year 2020: (30 * $540) + (20 * $450) + (15 * $350) + (12 * $240) = $16,200 + $9,000 + $5,250 + $2,880 = $33,330.
Step 6: Calculate Laspeyre's price index for the current year.
Laspeyre's price index formula is: (Current year expenditure / Base year expenditure) * 100.
For 2019: (27,280 / 20,600) * 100 = 132.62
For 2020: (33,330 / 20,600) * 100 = 161.55
Therefore, Laspeyre's price index for the years 2019 and 2020, using 2018 as the base year, is approximately 132.62 and 161.55, respectively.