Question

[10:15 am, 27/01/2022] Siyad: a) The average prices and quantities of six hypothetical items offered by a government agency running a social protection program for a marginalized community are shown in the following table:

2020

2021

Items

Price (Kshs/Kg)

Quantity (Kg,000)

Price (Kshs/Kg)

Quantity (Kg,000)

Maize Flour (A)

10

4

12

5

Vegetables (B)

15

6

18

10

Peas (C)

10

6

10

10

Beans (D)

20

10

22

20

Wheat (E)

30

12

40

18

Millet (F)

40

10

50

12

Tessy, the programs manager has hired you as a consultant to advice if she needs to ask the government for additional budgetary support. Using 2020 as base year, compute Kelly’s and Fisher’s Price index numbers for 2021 and in each case comment on the result

Answer 1

$Fisher price index= ( Laspeyeres Price Index\times Paasche Price Index)^{0.5}$

LPI$= \frac{\Sigma(P_i, t)\ times (Q_i, o)}{\Sigma(P_i,o)\times(Q_i,o)}$

$= \frac{(12\times5)+ (18\times10)+ (10\times10)+ (22\times20)+ (40\times18)+( 50\times12)}{(40\times4)+ (15\times6)+ (10\times6)+( 20\times10)+ (30\times12)+(40\times10)}$

$= \frac{2100}{1150}= 182.61$

$Paasche Price Index= \frac{\Sigma(P_i,t)\times Q_i,t)}{(\Sigma P_0,t)\ times ( Q_i,t)}$

$=\frac{(12\times 5)+ (18\times10)+ ( 10\times10)+ ( 22\times 20)+ (40\times18)+ ( 50\times 12)}{( 10\times5)+ (15\times10)+ (10\times10)+ 20\times 20)+ (30\times18)+(40\times12)}$

=$\frac{2100}{1820}= 115.38$

$Fishers Price Index= (115.38\times182.61)^{0.5} FishersPriceIndex=(115.38×182.61) 0.5= 145.15$

This shows inflation has gone up by 45.15% and therefore means prices are not affordable with the same amount as in the previous year.

Kelly's Price Index$= \frac{\Sigma P_iq}{\Sigma P_0q}$

$q= \frac{(Q_0+Q_1)}{2}$

Maize, q= $\frac{(4+5)}{2}= 4.5$

$Vegetables, q= \frac{(6+10)}{2}= 8 ​$

$Peas, q= \frac{(6+10)}{2}= 8$

$Beans, q= \frac{(10+20)}{2}= 15$

$Wheat, q= \frac{(12+18)}{2}= 15$

$Millet, q= \frac{(10+12)}{2}= 11$

Kelly's Price Index= $\frac{(12\times 4.5)+ (18\times8)+ (10\times8)+ (22\times15)+ (40\times4.5)+ (50\times11)}{( 10\times4.5)+ (15\times8)+ ( 10\times8)+ ( 20\times15)+ ( 30\times15)+ (40\times11)}\times 100$

$= \frac{1858}{1535}\times 100= 121.04$ %

This shows that there is an inflation of 21.04%.

There is therefore the need to request for more funds from the government to cater for the increased prices and be able to meet the budget.