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Example 1

The prices of 3 food items for 2012 and 2020 and the quantities consumed by a certain commodity in 2012 are shown below:
Construct the Laspeyres price index using 2012 as the base year.
Interpret your results.

Item	2012 price	2012 quantity	2020 price
Item	p₀	q₀	p_n
Milk	0.64	100	0.61
Bread	0.65	1000	0.59
Sugar	0.5	1	1

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soln

Item	2012 price	2012 quantity	2020 price
Item	p₀	q₀	p_n	p₀q₀	p_nq₀
Milk	0.64	100	0.61	64	61
Bread	0.65	1000	0.59	650	590
Sugar	0.5	1	1	0.5	1

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Example 2

The table below shows the production (in tons) and unit prices (in cedis) of some selected commodities in Northern region of Ghana for 2015 – 2019.
Using 2015 as the base year, calculate:
(a) The Laspeyres quantity index
(b) The value index
(c) Interpret your results in (a) and (b) for the year 2018.

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	2015		2016		2017		2018		2019
items	Price	Quantity	Price	Quantity	Price	Quantity	Price	Quantity	Price	Quantity
Maize	4	200	4.4	240	4.84	288	5.32	346	6.12	415
Tomato	9	500	10.8	700	12.96	980	15.6	1372	18.7	1921
Rice	15	700	15.8	910	16.54	1183	17.4	1538	21.7	1999
Ginger	20	1000	28	1200	39.2	1440	54.9	1728	82.3	2074
Meat	6	700	6.3	721	6.62	743	7.61	765	10.3	788
Fish	3	1500	3.9	2250	5.07	3375	6.59	5063	8.57	7594
Yam	5	2000	5.25	2220	6.04	2464	6.34	2735	9.51	3036
Groundnut	7	150	10.5	210	15.75	294	23.6	412	35.4	576
Milo	10	600	11.1	726	12.32	878	13.7	1063	15.2	1286

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Soln

items	2015	2016	2017	2018	2019
Maize	800	960	1152	1384	1660
Tomato	4500	6300	8820	12348	17289
Rice	10500	13650	17745	23070	29985
Ginger	20000	24000	28800	34560	41480
Meat	4200	4326	4458	4590	4728
Fish	4500	6750	10125	15189	22782
Yam	10000	11100	12320	13675	15180
Groundnut	1050	1470	2058	2884	4032
Milo	6000	7260	8780	10630	12860
	61550	75816	94258	118330	149996
Iq (L)	100	123.178	153.14	192.25	243.7

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Value index, Iv (L)

items	2015	2016	2017	2018	2019
Maize	800	1056	1393.9	1840.72	2539.8
Tomato	4500	7560	12701	21403.2	35923
Rice	10500	14378	19567	26761.2	43378
Ginger	20000	33600	56448	94867.2	170690
Meat	4200	4542.3	4918.7	5821.65	8116.4
Fish	4500	8775	17111	33365.2	65081
Yam	10000	11655	14883	17339.9	28872
Groundnut	1050	2205	4630.5	9723.2	20390
Milo	6000	8058.6	10817	14563.1	19547
	61550	91829.9	142469	225685	394538
Iv (L)	100	149.196	231.47	366.67	641

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Paasche Price Index

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soln

Item	2012 price	2012 quantity	2020 price	2020 quantity
Item	p₀	q₀	p_n	q_n	p₀q_n	p_nq_n
Milk	0.64	100	0.61	200	128	122
Bread	0.65	1000	0.59	900	585	531
Sugar	0.5	1	1	2	1	2
					714	655

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Example 2

The table below shows the production (in tons) and unit prices (in cedis) of some selected commodities in Ghana for 2015 – 2019.
Using 2015 as the base year, calculate:
(a) The Paasche quantity index and interpret your results in 2019
(b) The Paasche value index and interpret your result in 2018
(c)The Paasche price index and interpret your result in 2019.

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	2015		2016		2017		2018		2019
items	Price	Quantity	Price	Quantity	Price	Quantity	Price	Quantity	Price	Quantity
Maize	25	11200	27.5	11424	27.78	11652	30.55	12002	35.15	13442
Tomato	30	11300	36	11752	36.72	12222	44.06	12711	52.88	14363
Rice	15	11100	15.75	11433	16.54	11776	17.36	12129	21.71	12493
Ginger	11	14000	15.4	14280	16.02	14566	22.42	14857	33.63	15154
Meat	9	12700	9.45	13081	9.92	13473	11.41	13878	15.4	14294
Fish	8	12300	10.4	12915	13.52	13561	17.58	14103	22.85	14808

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soln

	p_nq_n					p_nq₀
items	2015	2016	2017	2018	2019	2015	2016	2017	2018	2019
Maize	280000	314160	323692.6	366661.1	472486.3	280000	308000	311136	342160	393680
Tomato	339000	423072	448791.8	560046.7	759515.4	339000	406800	414936	497878	597544
Rice	166500	180069.8	194775	210559.4	271223	166500	174825	183594	192696	240981
Ginger	154000	219912	233347.3	333093.9	509629	154000	215600	224280	313880	470820
Meat	114300	123615.5	133652.2	158348	220127.6	114300	120015	125984	144907	195580
Fish	98400	134316	183344.7	247930.7	338362.8	98400	127920	166296	216234	281055
Sum	1152200	1395145	1517604	1876640	2571344	1152200	1353160	1426226	1707755	2179660
	Iq (P)
	2015	2016	2017	2018	2019
	100	103.1028	106.407	109.8893	117.97

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�Comparison of Laspeyres and Paasche Price Index�

The Laspeyres price index (LPI) measures change in a fixed market basket of goods and services (same quantities used in each period) whiles the Paasche index continually updates the quantities to the levels of current consumption.
LPI is generally expected to overestimate or have an upward bias. The LPI is upward bias because all things been equal, when prices increase there is usually a reduction in the consumption of those items for which the increase has been the most pronounced and, hence, by using base year quantities we will be giving too much weight to the prices of the items whose prices have increased.

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Paasche price index (PPI) tends to underestimate or shows a downward bias. People tend to spend less on goods when their prices are rising.
Hence the use of current quantities as weights produces an index which tends to underestimate the rise in prices.

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Relationship between value, quantity and price indices�

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Commodity	2021		2023
	Price	Quantity	Price	Quantity
A	2	8	4	6
B	5	10	6	5
C	4	14	5	10
D	2	19	2	13

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