Question

Construct a Laspeyres Price Index (show working) for 2018, 2019 and 2020 from the following sales data, using 2018 as the base year. YEAR Commodity 2018 2019 2020 Quantity Price Quantity Price Quantity Price Cassava 15 20 16 40 45 Maize 20 80 22 82 24 90 Cocoa 10 60 20 75 30 70

Answer 1

Solution:

The Laspeyres Price Index is a consumer price index that measures the change in the prices of a basket of goods and services in relation to a predetermined base period weighting.

 

The Laspeyres Price Index Formula = $\frac{Sum\; of\;(Price \;at \;observation\; period\; \times \; Base \;quantity)}{Sum\; of\;(Price\; at\; Base\; period \;\times\; Base\; quantity)} \times 100$

Year 2018 The Laspeyres Price Index = $\frac{(20\times 15) + (80\times 20) + 60\times 10)}{(20\times 15) + (80\times 20) + 60\times 10)} \times100 = \frac{300 + 1600 + 600}{300 + 1600 + 600} = \frac{2500}{2500} \times100 = 100$

The Year 2018 The Laspeyres Price Index = 100

 

Year 2019 The Laspeyres Price Index $\frac{(40\times 15) + (82\times 20) + (75\times 10)}{(20\times 15) + (80\times 20) + 60\times 10)} \times100 = \frac{600 + 1640 + 750}{300 + 1600 + 600} = \frac{2990}{2500} \times100 = 119.6$

The Year 2019 The Laspeyres Price Index = 119.6

 

Year 2020 The Laspeyres Price Index = $\frac{(45\times 15) + (90\times 20) + (70\times 10)}{(20\times 15) + (80\times 20) + 60\times 10)} \times100 = \frac{675 + 1800 + 700}{300 + 1600 + 600} = \frac{3175}{2500} \times100 = 127$

The Year 2020 The Laspeyres Price Index = 127