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#### Question 1:

From the data given below, construct the index number for the year 2016 on the base of 2011 by simple aggregative method:

 Commodities Unit Price (In â‚¹) 2011 2016 Wheat quintal 200 250 Rice quintal 300 400 Pulses quintal 400 500 Milk litre 2 3 Clothing meter 4 5

 Commodity Price in 2011 (P0) Price in 2016 (P1) Wheat Rice Pulses Milk Clothing 200 300 400 2 4 250 400 500 3 5 ΣP0 = 906 ΣP1 = 1158

#### Question 2:

Construct index numbers by (aggregative method) based on the price of 2011 from the following figures:

 Items A B C D E F Prices (2011) 200 60 350 100 60 80 Prices (2016) 240 90 600 110 62 90

 Items Price in 2011 (P0) Price in 2016 (P1) A B C D E F 200 60 350 100 60 80 240 90 600 110 62 90 ΣP0 = 850 ΣP1 = 1192

#### Question 3:

Following are the prices of commodities in the year 2011 and 2016. Calculate the price index using price relatives method.

 Commodity Prices in year 2011 Prices in 2016 A 45 55 B 60 70 C 20 30 D 50 75 E 85 90 F 120 130

 Commodity Price in 2011 (P0) Price in 2016 (P1) Price Relative=$\frac{{\mathbit{P}}_{\mathbf{1}}}{{\mathbit{P}}_{\mathbf{0}}}\mathbf{×}\mathbf{100}$ A 45 55 $\frac{55}{45}×100=122.22$ B 60 70 $\frac{70}{60}×100=116.67$ C 20 30 $\frac{30}{20}×100=150$ D 50 75 $\frac{75}{50}×100=150$ E 85 90 $\frac{90}{85}×100=105.88$ F 120 130 $\frac{130}{120}×100=108.33$

#### Question 4:

4. Calculate the index numbers from the following data using:
(i) Laspeyre's method,
(ii) Paasche's method,
(iii) Fisher's ideal method:

 Commodity Base year Current year Price (in â‚¹) p 0 Quantity q0 Price (in â‚¹) p1 Quantity q1 A 8 100 10 120 B 4 60 5 80 C 10 20 12 25 D 12 25 15 30 E 3 5 4 6

 Base Year Current Year Commodity Pricep0 Quantityq0 Pricep1 Quantity    q1 p0q0 p0q1 p1q0 p1q1 A 8 100 10 120 800 960 1000 1200 B 4 60 5 80 240 320 300 400 C 10 20 12 25 200 250 240 300 D 12 25 15 30 300 360 375 450 E 3 5 4 6 15 18 20 24 Σp0q0 = 1555 Σp0q1 = 1908 Σp1q0 = 1935 Σp1q1 = 2374

(i) Laspeyre's Method

${p}_{01}=\frac{\mathrm{\Sigma }{p}_{1}{q}_{0}}{\mathrm{\Sigma }{p}_{0}{q}_{0}}×100=\frac{1935}{1555}×100=124.44$

(ii) Paasche's Method

${p}_{01}=\frac{\mathrm{\Sigma }{p}_{1}{q}_{1}}{\mathrm{\Sigma }{p}_{0}{q}_{1}}×100=\frac{2374}{1908}×100=124.42$

(iii) Fisher's Method

#### Question 5:

Calculate Laspeyre's; Paasche's and Fisher's index numbers from the following data:

 Commodity Base year Current year Price (in â‚¹) p0 Quantity q0 Price (in â‚¹) Quantity q1 A 10 30 12 50 B 8 15 10 25 C 6 20 6 30 D 4 10 6 20

 Base Year Current Year Commodity Pricep0 Quantityq0 Pricep1 Quantityq1 p0q0 p0q1 p1q0 p1q1 A 10 30 12 50 300 500 360 600 B 8 15 10 25 120 200 150 250 C 6 20 6 30 120 180 120 180 D 4 10 6 20 40 80 60 120 Σp0q0 = 580 Σp0q1 = 960 Σp1q0 = 690 Σp1q1 = 1150

(i) Laspeyre's Method

${p}_{01}=\frac{\mathrm{\Sigma }{p}_{1}{q}_{0}}{\mathrm{\Sigma }{p}_{0}{q}_{0}}×100=\frac{690}{580}×100=\frac{69000}{580}=118.965$

(ii) Paasche's Method

${p}_{01}=\frac{\mathrm{\Sigma }{p}_{1}{q}_{1}}{\mathrm{\Sigma }{p}_{0}{q}_{1}}×100=\frac{1150}{960}×100=\frac{115000}{960}=119.79$

(iii) Fisher's Method

#### Question 6:

The following table contains information from the eaw material purchase records of a small factory to the year 2011-12 and 2016-17:

 Commodity 2011-12 2016-17 Price (â‚¹/Unit) p0 Total Valule q0 Price (â‚¹/Unit) Total Value q1 A 5 50 6 72 B 7 84 10 80 C 10 80 12 96 D 4 20 5 30 E 8 56 8 64
Calculate Fisher's Ideal Index Number.

 Base Year        (2011-12) Current Year(2016-17) Commodity Pricep0 Quantityq0 Pricep1 Quantityq1 p0q0 p0q1 p1q0 p1q1 A 5 50 6 72 250 360 300 432 B 7 84 10 80 588 560 840 800 C 10 80 12 96 800 960 960 1152 D 4 20 5 30 80 120 100 150 E 8 56 8 64 448 512 448 512 Σp0q0 = 2166 Σp0q1 = 2512 Σp1q0 = 2648 Σp1q1 = 3046

Fisher's Method

#### Question 7:

Calculate weighted average of price relative index number of prices for 2016 on the basis of 2011 from the following data:

 Comity Quantity in 2011 Price (in â‚¹)2011 Price (in â‚¹) 2016 A 20 20 35 B 12 15 18 C 8 10 11 D 4 5 5 E 6 4 5

 Commodity Quantity in 2011 (q0)Weights Price in 2011 (p0) Price in 2016 (p1) p0q0(W) R=$\frac{{\mathbf{p}}_{\mathbf{1}}}{{\mathbf{p}}_{\mathbf{0}}}\mathbf{×}\mathbf{100}$ RW A 20 20 35 400 175 70000 B 12 15 18 180 120 21600 C 8 10 11 80 110 8800 D 4 5 5 20 100 2000 E 6 4 5 24 125 3000 ΣW = 704 ΣRW = 105400

Weighted Average of Price Relatives

${p}_{01}=\frac{\mathrm{\Sigma RW}}{\mathrm{\Sigma W}}=\frac{105400}{704}\phantom{\rule{0ex}{0ex}}⇒{p}_{01}=149.715$

#### Question 8:

Construct cost of index number for 2016 on the basis of 2011 from the following data using Aggregate Expenditure Method and Family Budget Method.

 Article Quantity (kg.) Prices in â‚¹ 2011 2016 A 10 20 30 B 7 21 28 C 5 20 25 D 2 10 12 E 2 6 8
Calculate Fisher's Ideal Index Number.

 Article Price in 2011(p0) Price in 2016(p1) Quantity (q0) p0q0 p1q0 A 20 30 10 200 300 B 21 28 7 147 196 C 20 25 5 100 125 D 10 12 2 20 24 E 6 8 2 12 16 Σp0q0 = 479 Σp1q0 = 661

Consumer price index for the year 2016
$=\frac{\mathrm{\Sigma }{p}_{1}{q}_{0}}{\mathrm{\Sigma }{p}_{0}{q}_{0}}×100=\frac{661}{479}×100=137.99=138$

 Article Price in 2011(p0) Price in 2016(p1) Price Relative (R)$R=\frac{{p}_{1}}{{p}_{0}}×100$ Quantity (q0) p0q0(W) RW A 20 30 150 10 200 30000 B 21 28 133.33 7 147 19599.51 C 20 25 125 5 100 12500 D 10 12 120 2 20 2400 E 6 8 133.33 2 12 1599.96 ΣW = 479 ΣRW = 66099.47

Consumer price index for the year 2016

$=\frac{\mathrm{\Sigma R}W}{\Sigma W}=\frac{66099.47}{479}=137.99=138$

#### Question 9:

Calculate consumer price index number for the following data by aggregate expenditure and family budget Method.

 Expenses Weights Price (in â‚¹) Base Year Price (in â‚¹) Current year Food 45 300 350 Rent 20 200 225 Fuel 8 100 110 Clothing 10 150 175 Misc. 17 250 300

 Expenses Price in Base Year (p0) Price in Current Year (p1) Quantity (q0) p0q0 p1q0 Food 300 350 45 13500 15750 Rent 200 225 20 4000 4500 Fuel 100 110 8 800 880 Clothing 150 175 10 1500 1750 Misc. 250 300 17 4250 5100 Σp0q0 = 24050 Σp1q0 = 27980

Consumer price index for the current year

$=\frac{\mathrm{\Sigma }{p}_{1}{q}_{0}}{\mathrm{\Sigma }{p}_{0}{q}_{0}}×100=\frac{27980}{24050}×100=116.34$

 Expenses Price in Base Year (p0) Price in Current Year (p1) $R=\frac{{p}_{1}}{{p}_{0}}×100$ Quantity (q0) p0q0(W) RW Food 300 350 116.67 45 13500 1575045 Rent 200 225 112.5 20 4000 450000 Fuel 100 110 110 8 800 88000 Clothing 150 175 116.67 10 1500 175005 Misc. 250 300 120 17 4250 510000 ΣW= 24050 ΣRW = 2798050

Consumer price index for the current year

$=\frac{\Sigma RW}{\Sigma W}=\frac{2798050}{24050}=116.34$

#### Question 10:

Construct the index of industrial production from the following data:

 Commodity Output (in tonnes) Weights 2011-12 2016-17 Mining 120 180 25 Electrical Products 200 290 45 Manufactured Goods 150 220 30

 Industry Output in 2011-12 (q0) Output in 2016-17 (q1) Weights (W) $\left(\frac{{q}_{1}}{{q}_{0}}×100\right)$ $\left(\frac{{q}_{1}}{{q}_{0}}×100\right)W$ Mining 120 180 25 150 3750 Electrical Products 200 290 45 145 6525 Manufactured Goods 150 220 30 146.67 4400.1 ΣW=100 14675.1

Index Number of Industrial Production

#### Question 11:

Calculate the cost of living index number for 2016 taking 2012 as base year from the following data by family budget Method.

 Times Quantity (in kg.) Price 2012 (in â‚¹/kg) Price 2016 (in â‚¹/kg) A 15 10.00 12.00 B 20 16.50 20.00 C 8 6.00 7.50 D 12 15.00 16.00 E 10 8.00 11.50

 Items Price Price Relative(R) Quantity 2012 (p0) 2016 (p1) $R=\frac{{p}_{1}}{{p}_{0}}×100$ 2012 (q0) p0q0(W) RW A 10.00 12.00 120.00 15 150 18000.0 B 16.50 20.00 121.21 20 330 39999.3 C 6.00 7.50 125.00 8 48 6000.0 D 15.00 16.00 106.67 12 180 19200.6 E 8.00 11.50 143.75 10 80 11500.0 ΣW = 788 ΣRW = 94699.9

#### Question 12:

The following data relate to the prices and quantities of 4 commodities in the years 2011-12 and 2016-17. Construct the index numbers of price for the year 2016-17 by using 2011-12 the base year by: (i) Laspeyre's method, (ii) Paasche's method, (iii) Fisher's ideal method:

 Commodity 2011-12 2016-17 Price (in â‚¹) p0 Quantity q0 Price (in â‚¹) Quantity q1 A 5 100 6 150 B 4 80 5 100 C 2.5 60 5 72 D 12 30 9 33

 Commodity p0 q0 p1 q1 p0q0 p0q1 p1q0 p1q1 A 5 100 6 150 500 750 600 900 B 4 80 5 100 320 400 400 500 C 2.5 60 5 72 150 180 300 360 D 12 30 9 33 360 396 270 297 Total 1330 1726 1570 2057

(i) Laspeyre's Method

${P}_{01}=\frac{\mathrm{\Sigma }{p}_{1}{q}_{0}}{\mathrm{\Sigma }{p}_{0}{q}_{0}}×100=\frac{1570}{1330}×100=118.05$

(ii) Paasche's Method

${P}_{01}=\frac{\mathrm{\Sigma }{p}_{1}{q}_{1}}{\mathrm{\Sigma }{p}_{0}{q}_{1}}×100=\frac{2057}{1726}×100=119.18$

(iii) Fisher's Method

#### Question 13:

Calculate the index number for 2016 with 2012 as base using the weighted average of price relative method for the following data:

 Commodity Quantity (in units) 2012 Price (in â‚¹)2012 Price (in â‚¹)2016 A 2 12 24 B 8 8 12 C 4 15 27 D 5 6 18 E 1 10 12

 Commodity 2012q0 2012p0 2016p1 p0q0 (W) Price Relative (R)=$\frac{{\mathbf{p}}_{\mathbf{1}}}{{\mathbf{p}}_{\mathbf{0}}}\mathbf{×}\mathbf{100}$ RW A 2 12 24 24 200 4800 B 8 8 12 64 150 9600 C 4 15 27 60 180 10800 D 5 6 18 30 300 9000 E 1 10 12 10 120 1200 ΣW = 188 ΣRW = 35400

Weighted Average of Price Relatives

${P}_{01}=\frac{\Sigma RW}{\Sigma W}=\frac{35400}{188}=188.297$

#### Question 14:

Construct an index for the year 2016 taking 2011 as base by simple average of price relatives method

 Items P Q R S Price (in â‚¹) 30 50 70 90 Price (in â‚¹) 40 60 80 100

 Items Price in 2011 (P0) Price in 2016 (P1) Price Relative=$\frac{{p}_{1}}{{p}_{0}}×100$ P 30 40 133.33 Q 50 60 120 R 70 80 114.29 S 90 100 111.11

Simple Average of Price Relatives

#### Question 15:

Using Paasche's formula, compute the quantity index for the year 2016 with 2011 as base year.

 Commodity Quantify (in Units) Value (in â‚¹) 2011 2016 2011 2016 A 5 100 6 150 B 100 150 500 900 C 80 100 320 500 D 60 72 150 360 E 30 33 360 297