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...