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Chapter 4

MARKET AND DEMAND ANALYSIS

1. We have to estimate the parameters a and b in the linear relationship
Yt = a + bT
Using the least squares method.
According to the least squares method the parameters are:

∑ T Y – n T Y
b =
∑ T 2 – n T 2

a = Y – bT
The parameters are calculated below:
Calculation in the Least Squares Method
T
YTYT 2
12,0002,0001
22,2004,4004
32,1006,3009
42,3009,20016
52,50012,50025
63,20019,20036
73,60025,20049
84,00032,00064
93,90035,10081
104,00040,000100
114,20046,200121
124,30051,600144
134,90063,700169
14
5,30074,200196
∑ T = 105∑ Y = 48,500∑ TY = 421,600∑ T 2 = 1,015 T = 7.5
Y = 3,464

∑ T Y – n T Y421,600 – 14 x 7.5 x 3,464
b = =
∑ T 2 – n T 2 1,015 – 14 x 7.5 x 7.5

57,880
= = 254
227.5
a = Y – bT
= 3,464 – 254 (7.5)
= 1,559
Thus linear regression is
Y = 1,559 + 254 T
2. In general, in exponential smoothing the forecast for t + 1 is
Ft + 1 = Ft + α et

Where Ft + 1 = forecast for year )α = smoothing parameter
et = error in the forecast for year t = St = Ft
F1 is given to be 2100 and α is given to be 0.3
The forecasts for periods 2 to 14 are calculated below:
Period tData (St)Forecast (Ft)Error
(et St =Ft)
Forecast for t + 1
(Ft + 1 = Ft + α et)

12,0002100.0-100F2 = 2100 + 0.3 (-100) = 2070
22,2002070130F3 = 2070 + 0.3(130) = 2109
32,1002109.0-9F4 = 2109 + 0.3 (-9) = 2111.7
42,3002111.7188.3F5 = 2111.7 + 0.3(188.3) = 2168.19
52,5002168.19331.81F6 = 2168.19 + 0.3(331.81) = 2267.7
63,2002267.7932.3F7 = 2267.7 + 0.3(9332.3) = 2547.4
73,6002547.41052.6F8 = 2547.4 + 0.3(1052.6) = 2863.2
84,0002863.21136.8F9 = 2863.2 + 0.3(1136.8) = 3204.24
93,9003204.24695.76F10 = 33204.24 + 0.3(695.76) = 3413.0 104,0003413587.0F11 = 3413.0 + 0.3(587) = 3589.1
114,2003589.1610.9F12 = 3589.1 + 0.3(610.9) = 3773.4
124,3003772.4527.6F13 = 3772.4 + 0.3(527.6) = 3930.7
134,9003930.7969.3F14 = 3930.7 + 0.3(969.3) = 4221.5

3. According to the moving average method
St + S t – 1 +…+ S t – n +1
Ft + 1 =
n
where Ft + 1 = forecast for the next period
St = sales for the current period
n = period over which averaging is done

Given n = 3, the forecasts for the period 4 to 14 are given below:

Period tData (St)Forecast (Ft)Forecast for t + 1
Ft + 1 = (St+ S t – 1 + S t – 2)/ 3

12,000
22,200
32,100F4 = (2000 + 2200 + 2100)/3 = 2100
42,3002100F5 =(2200 + 2100 + 2300)/3= 2200
52,5002200F6 = (2100 + 2300 + 2500)/3 = 2300
63,2002300F7 = (2300 + 2500 + 3200)/3= 2667
73,6002667F8 = (2500 + 3200 + 3600)/3 = 3100
84,0003100F9 = (3200 + 3600 + 4000)/3 = 3600
93,9003600F10 = (3600 + 4000 + 3900)/3 = 3833
104,0003833F11 = (4000 + 3900 + 4000)/3 =3967
114,2003967F12 =(3900 + 4000 + 4200)/3 = 4033
124,3004033F13 = (4000 + 4200 + 4300)/3 = 4167
134,9004167F14 = (4200 + 4300 + 4900) = 4467
145,3004467

4.
Q1 = 60
Q2 = 70
I1 = 1000
I2 = 1200
Q1 – Q2 I1 + I2
Income Elasticity of Demand E1 = x
I2 - I1 Q2 – Q1
E1 = Income Elasticity of Demand
Q1 = Quantity demanded in the base year
Q2 = Quantity demanded in the following year
I1 = Income level in base year
I2 = Income level in the following year

70 – 60 1000 + 1200
E1 = x
1200 – 1000 70 + 60

22000
E1 = = 0.846
26000

5.
P1 = Rs.40
P2 = Rs.50
Q1 = 1,00,000
Q2 = 95,000
Q2 – Q1 P1 + P2
Price Elasticity of Demand = Ep = x
P2 –P1 Q2 + Q1

P1 , Q1 = Price per unit and quantity demanded in the base year P2, Q2 = Price per unit and quantity demanded in the...
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